Foundations of Biochemical Engineering. Kinetics and Thermodynamics in Biological Systems 9780841207523, 9780841210110, 0-8412-0752-6

Table of contents :
Title Page......Page 1
Half Title Page......Page 3
Copyright......Page 4
ACS Symposium Series......Page 5
FOREWORD......Page 6
PREFACE......Page 7
ACKNOWLEDGMENTS......Page 9
PdftkEmptyString......Page 0
1 Models of Gene Function General Methods of Kinetic Analysis and Specific Ecological Correlates......Page 10
Power-law Formalism......Page 11
Demand Theory of Gene Regulation......Page 14
Experimental Implications......Page 24
Discussion......Page 30
Literature cited......Page 31
1. Soluble substrates......Page 33
2. Particulate substrates......Page 38
Immobilized Enzymes......Page 44
Summary......Page 54
Literature Cited......Page 57
3 Optimization of Fermentation Processes Through the Control of In Vivo Inactivation of Microbial Biosynthetic Enzymes......Page 59
Results and Discussion......Page 63
Conclusions......Page 70
Literature Cited......Page 72
4 Microbial Regulatory Mechanisms: Obstacles and Tools for the Biochemical Engineer......Page 74
Literature Cited......Page 93
Why Single-Cell Models?......Page 96
Examples of Single-Cell Models......Page 100
The Cornell Single-Cell Model......Page 103
Population Models From Single-Cell Models......Page 126
Acknowledgment......Page 132
Literature Cited......Page 134
6 Single-Cell Metabolic Model Determination by Analysis of Microbial Populations......Page 137
A Mathematical Model for Growth of E. coli Populations......Page 140
Cell Cycle Operation and Single-Cell Protein Synthesis Kinetics for S. pombe......Page 144
Growth and Nuclear Cycle Operation in Single Cells of S. cerevisiae......Page 152
Discussion......Page 157
LITERATURE CITED......Page 158
7 A Cybernetic Perspective of Microbial Growth......Page 160
THE CYBERNETIC FRAMEWORK. SOME ISSUES......Page 164
Growth in Multiple Substrate Systems......Page 165
Nomenclature......Page 175
Literature Cited......Page 176
8 Strategies for Optimizing Microbial Growth and Product Formation......Page 178
Production of Cell Mass......Page 179
Enzyme Production......Page 186
Maltase Production......Page 188
Heparinase Production......Page 190
Metabolite Production......Page 192
Literature Cited......Page 196
9 Interactions of Microbial Populations in Mixed Culture Situations......Page 198
Classification of population interactions......Page 199
Discussion of the interactions......Page 202
Summary and discussion......Page 220
Acknowledgement......Page 221
Literature Cited......Page 222
10 The Role of Specialists and Generalists in Microbial Population Interactions......Page 225
Literature Cited......Page 247
11 Microbial Predation Dynamics......Page 248
Methods......Page 251
Results......Page 252
Discussion......Page 257
Literature Cited......Page 259
12 Effects of Cell Motility Properties on Cell Populations in Ecosystems......Page 260
Experimental Observations......Page 265
Theoretical Analyses......Page 268
Literature Cited......Page 284
13 Macroscopic Thermodynamics and the Description of Growth and Product Formation in Microorganisms......Page 288
Macroscopic thermodynamics and processes in open systems. (5, 6)......Page 289
The thermodynamic efficiency.......Page 293
Applications of the theory......Page 297
The constant efficiency hypothesis......Page 309
List of symbols......Page 313
Literature Cited......Page 314
14 Ion Pumps as Energy Transducers......Page 316
Literature Cited......Page 323
15 Kinetics and Transport Phenomena in Biological Reactor Design......Page 325
RATE-CONTROLLING STEPS......Page 326
EFFECT OF INTERFACIAL PHENOMENA......Page 328
Moving Particles with Rigid Surfaces......Page 329
Non-Newtonian Floy Effects......Page 331
General Concepts......Page 332
Immobilized Enzyme Kinetics......Page 333
Bubble-Columns......Page 335
Systems with Stationary Internals......Page 336
Non-Viscous Systems......Page 337
Viscous Systems......Page 340
NOMENCLATURE......Page 341
Abbreviations for Dimensionless Groups......Page 342
Literature Cited......Page 343
16 Reactor Design Fundamentals Hydrodynamics, Mass Transfer, Heat Exchange, Control, and Scale-up......Page 345
Hydrodynamics......Page 348
Mass Transfer......Page 349
Heat Exchange......Page 355
Reactor Control......Page 359
Reactor Scale-Up......Page 360
Literature Cited......Page 364
17 Immobilized Cells Catalyst Preparation and Reaction Performance......Page 367
Ionotropic Gelation of Polyelectrolytes......Page 368
Polycondensation of Epoxy Resins......Page 370
Effectiveness of Immobilized Cell Catalysts......Page 373
Acknowledgements......Page 380
Literature cited......Page 382
Materials and Methods......Page 383
Results and Discussion......Page 384
Literature Cited......Page 389
19 Stochastic Growth Patterns Generated by Phycomyces Sporangiophores......Page 390
Materials and Methods......Page 392
Discussion......Page 402
Appendix: A Brief Description of Time Series Analysis......Page 405
Literature Cited......Page 406
20 Growth Characteristics of Microorganisms in Solid State Fermentation for Upgrading of Protein Values of Lignocelluloses and Cellulase Production......Page 408
Origin of Solid State Fermentation......Page 409
Nature of the Substrate......Page 410
Pretreatment of Lignocelluloses......Page 411
Mechanism of Fungal Growth During Solid State Fermentation......Page 413
Postulated Mechanism of Fungal Growth in Solid State......Page 419
Physiological Aspects......Page 424
Literature Cited......Page 426
21 Molecular Size Distribution of Starch During Enzymatic Hydrolysis......Page 430
Experimental......Page 432
Results and Discussion......Page 435
Conclusion......Page 444
Literature Cited......Page 448
22 Thermochemical Optimization of Microbial Biomass-Production and Metabolite-Excretion Rates......Page 449
Reaction Mechanism......Page 450
Rate Laws......Page 452
Thermal Sensitivity of the Macro-Coefficients......Page 456
Thermal Sensitivity of Process Rates......Page 463
Summary and Conclusions......Page 470
Legend of Symbols......Page 471
Literature Cited......Page 473
23 Kinetics of Yeast Growth and Metabolism in Beer Fermentation......Page 475
THE KINETIC MODEL......Page 476
RESULTS AND DISCUSSION......Page 480
CONCLUSIONS......Page 481
LITERATURE CITED......Page 486
24 Growth Inhibition Kinetics for the Acetone—Butanol Fermentation......Page 487
Materials and Methods......Page 488
Results and Discussion......Page 489
Literature Cited......Page 497
C......Page 499
Ε......Page 500
H......Page 501
M......Page 502
Ρ......Page 504
S......Page 505
Y......Page 506

Citation preview

of Biochemical Engineering

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Foundations of Biochemical Engineering Kinetics and Thermodynamics in Biological Systems Harve W Blanch EDITOR University of California, Berkeley

E. Terry Papoutsakis, EDITOR Rice University

Gregory Stephanopoulos, EDITOR California Institute of Technology

Based on the 1982 Winter Symposium of the ACS Division of Industrial and Engineering Chemistry jointly sponsored by the Division of Microbial and Biochemical Technology, Boulder, Colorado, January 17-20, 1982 ACS SYMPOSIUM SERIES 207 AMERICAN

CHEMICAL

W A S H I N G T O N , D.C.

SOCIETY 1983

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Library of Congress Cataloging in Publication Data American Chemical Society. Division of Industrial and Engineering Chemistry. Winter Symposium (1982: Boulder, Colo.) Foundations of biochemical engineering. (ACS symposium series, ISSN 0097-6156; 207) Includes bibliographies and index. 1. Biochemical engineering—Congresses I. Blanch, Harvey W., 1947 E. Terry, 1951. III. American Chemical Society. Division of Industrial and Engineering Chemistry. V. American Chemical Society. Division of Microbial and Biochemical Technology. VI. Title. VII. Series. TP248.3.A48 1982 ISBN 0-8412-0752-6

Copyright ©

660'.63

82-20694

1983

American Chemical Society All Rights Reserved. The appearance of the code at the bottom of the first page of each article in this volume indicates the copyright owner's consent that reprographic copies of the article may be made for personal or internal use or for the personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating new collective work, for resale, or for information storage and retrieval systems. The copying fee for each chapter is indicated in the code at the bottom of the first page of the chapter. The citation of trade names and/or names of manufacturers in this publication is not to be construed as an endorsement or as approval by ACS of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission, to the holder, reader, or any other person or corporation, to manufacture, reproduce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. PRINTED IN THE UNITED STATES OF AMERICA

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

ACS Symposium Series M. Joa

Advisory Board

David L. Allara

Robert Ory

Robert Baker

Geoffrey D. Parfitt

Donald D. Dollberg

Theodore Provder

Brian M . Harney

Charles N. Satterfield

W. Jeffrey Howe

Dennis Schuetzle

Herbert D. Kaesz

Davis L. Temple, Jr.

Marvin Margoshes

Charles S. Tuesday

Donald E. Moreland

C. Grant Willson

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

FOREWORD The ACS SYMPOSIUM SERIES was founded in 1974 to provide

a medium for publishing symposia quickly in book form. The format of the Series parallels that of the continuing ADVANCES IN CHEMISTRY SERIES except that in order to save time the papers are not typeset but are reproduced as they are submitted by the authors in camera-ready form. Papers are reviewed under the supervision of the Editors with the assistance of the Series Advisory Board and are selected to maintain the integrity of the symposia; however, verbatim reproductions of previously published papers are not accepted. Both reviews and reports of research are acceptable since symposia may embrace both types of presentation.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

PREFACE THIS V O L U M E IS BASED on the 1982 Winter Symposium. Following recent tradition, this Winter Symposium was organized to provide a forum for expression of new ideas and new research approaches. This volume discusses the fundamentals of biotechnology; that is, kinetics and thermodynamics in biological systems. State-of-the-art keynote chapters by established researchers are employed to provide the proper perspective and direction approaches. In the last few years biotechnology has grown tremendously in scope and significance, both as an active research area and as an industrial activity. There has also been a clear trend toward the exploration of the most sophisticated aspects of biological growth: tissue cultures, active biomolecules, antitumor compounds, chemical feedstocks from biomass, and gene cloning, to mention only a few. This trend has been accompanied by the increased use of computers in the design and control of the biological reactor. The explosive growth of the field and the use of computers have magnified, however, a fact that had been realized for quite some time by a few. That is, that the kinetics and thermodynamics of biochemical reactions and biological growth are understood only primitively. We should remind ourselves that biological systems are immensely more complicated than the nonbiological systems upon which most of chemical technology is based. We should not forget that until quite recently there were relatively few active investigators in biotechnology throughout the world, and that most of these were microbiologists by training. This has changed dramatically, however, as biotechnology has become a common word among biochemists, cell geneticists, molecular biologists, gene doners, engineers, protein chemists, and others. In preparing this book, we strived to stress two things: • the interdisciplinary nature of biotechnology. We thus made every effort to bring together prominent researchers from both the life sciences and biochemical engineering. • the need to examine the fundamentals of biotechnology more systematically and vigorously. We believe that no structure can grow well and last long without good foundations. ix

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

The topics in this volume represent both keynote chapters and chapters on new research. They have been arranged in six sections, such that each section builds on the preceding one. The volume begins with an examina­ tion of fundamental biochemical events in the cells. It proceeds with the examination of the interaction of the biochemical events that constitute the growth of an individual cell; then it examines homogeneous and hetero­ geneous cell populations. The book continues with thermodynamic aspects of biological growth, and ends with the application of all of the above to bioreactor design. Obviously, completeness has been sacrificed to diversity. We felt that the examination of the interactions among these fundamental aspects was more important than looking in depth at only a few of these aspects. Most of you would agree that ongoing research is a vital and exciting process, consisting of active and ofte heated interaction f data ideas d minds We hope that the reader in this process. In putting together the symposium on which this book is based, we relied on the judgement, help, and advice of many colleagues, to whom we express our sincere thanks. We also thank the organizing committee of the Winter Symposia of the Division of Industrial and Engineering Chemistry and, in particular, the former chairman of the committee, Nicholas A . Peppas. Thanks are also due to R. W. Eltz, chairman of the Division of Microbial and Biochemical Technology of the American Chemical Society, joint sponsor of the symposium. We are sincerely indebted to Steve Drew of Merck, Sharp & Dohme Research Labora­ tories for bringing us the private sector's views on the symposium's theme. HARVEY W. BLANCH

University of California Berkeley, CA E. TERRY PAPOUTSAKIS

Rice University Houston, TX GREGORY STEPHANOPOULOS

California Institute of Technology Pasadena, CA June 1, 1982

χ

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

ACKNOWLEDGMENTS Financial assistance for the 1982 Winter symposium was received from National Science Foundation and Abbott Laboratories Beckman Instruments Inc Becton Dickinso Carnation Company Chevron Research Company E.I. du Pont de Nemours & Company, Inc. Eastman Kodak Company Exxon Research and Engineering Company General Mills, Inc. Gist-Brocades N V Research & Development Glaxo Operations U K Limited W. R. Grace & Company Gulf Research and Development Company Hoffmann-La Roche, Inc. Kraft, Inc. Merck Sharp and Dohme Research Laboratories Monsanto Company PPG Industries, Inc. Pfizer, Inc. Phillips Petroleum Company The Procter and Gamble Company Stauffer Chemical Company Syntex Corporation Weyerhaeuser Company

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1

Models of Gene Function General Methods of Kinetic Analysis and Specific Ecological Correlates

MICHAEL A. SAVAGEAU University of Michigan, Department of Microbiology and Immunology, Ann Arbor, MI 48109 Alternative molecular designs for gene control involving positiv related to the that harbors them: positive elements are associated with high demand for expression of the regulated structural genes; while negative elements are associated with low demand for their expression. This is called the demand theory of gene regulation. These results are based on a mathematical analysis of the alternative models. The formalism used is a general one involving power-law functions that has been developed previously for the mathematical analysis of complex biological systems. This formalism, which is of interest in its own right, is briefly reviewed, although details of the analysis are not presented. The principal steps in the development of the demand theory are presented and the molecular, physiological and ecological implications are made e x p l i c i t . This theory i s supported by experimental evidence from more than 40 different systems and is used to make testable experimental predictions for more than 14 additional systems. The primary purpose o f t h i s symposium i s t o have b i o l o g i s t s and e n g i n e e r s examine the i n t e r d i s c i p l i n a r y area o f biotechnology from the fundamental p e r s p e c t i v e o f k i n e t i c s and thermodynamics* As w i t h any i n t e r d i s c i p l i n a r y area, p a r t i c u l a r l y one undergoing r a p i d change and i n t e l l e c t u a l ferment, biotechnology means d i f f e r e n t things t o d i f f e r e n t people* I t i s therefore appropriate to give a thumb-nail sketch o f t h i s area as I see i t * B i o t e c h n o l o g y i s as o l d as r e c o r d e d h i s t o r y . The e a r l y domestication o f microorganisms f o r wine making, b r e w i n g , b a k i n g and f o o d p r e s e r v a t i o n i s a prime example g r a p h i c a l l y depicted on

0097-6156/83/0207-0003$06.75/0 © 1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4

BIOCHEMICAL

ENGINEERING

Egyptian tombs (1)· Of course, t h i s was a very e m p i r i c a l a r t t h a t advanced o n l y s l o w l y . Even i n more r e c e n t times, d u r i n g the p o s t war expansion o f modern i n d u s t r i a l t e c h n o l o g y , t h e r e has been important biotechnology, e.g., as a sector of modern pharmaceutical and chemical i n d u s t r i e s . Throughout t h i s p a s t , the b i o l o g i c a l component has o f t e n been t h e weakest l i n k i n t h e o v e r a l l bio-technology c h a i n . To be sure, there was mass balance and the Monod growth law, which helped t o p r e d i c t the b e h a v i o r o f t h e b i o l o g i c a l component, but t h a t was about a l l . One g e n e r a l l y had t o l i v e w i t h t h e u n c e r t a i n t i e s i n h e r e n t i n t h e b i o l o g i c a l component o f the o v e r a l l system. Recent developments i n b i o l o g y have ushered i n a " r e v o l u t i o n " i n o u r knowledge o f the c e l l , p a r t i c u l a r l y the m i c r o b i a l c e l l . For the f a m i l i a r b a c i l l u s E s c h e r i c h i a c o l l 3/5 t o 4/5 of a l l i t s molecular elements are known and new p r o t e i n s e p a r a t i o n techniques are speeding t h i s i d e n t i f i c a t i o we s h a l l soon have t h However, we s t i l l know r e l a t i v e l y l i t t l e about t h e i n t e g r a t e d b e h a v i o r o f t h e c e l l , how i t w i l l behave when i t s m o l e c u l a r elements are changed or when i t f i n d s i t s e l f i n a novel environment· The f u l l p o t e n t i a l of biotechnology w i l l be r e a l i z e d , i n my view, o n l y when (a) the b i o l o g i c a l component i s brought w i t h i n the realm o f engineering design and (b) e n g i n e e r i n g methods of systems a n a l y s i s and p r e d i c t i o n are brought w i t h i n the realm o f c e l l and m o l e c u l a r b i o l o g y . O n l y t h e n w i l l t h e r e be a s t r o n g u n i t a r y b i o t e c h n o l o g y . In the l a s t few years developments i n recombinant DNA methodology have shown t h a t the f i r s t of t h e s e o b j e c t i v e s i s now f e a s i b l e . T h e r e a l s o has been p r o g r e s s toward the second o b j e c t i v e , but t h e r e i s s t i l l much t o be done here. In t h i s paper I s h a l l f i r s t r e v i e w b r i e f l y some o f our own a t t e m p t s t o d e v e l o p general methods o f k i n e t i c a n a l y s i s t h a t are a p p r o p r i a t e f o r complex b i o l o g i c a l systems. Next I s h a l l d i s c u s s t h e a p p l i c a t i o n o f t h e s e methods t o a l t e r n a t i v e models o f gene r e g u l a t i o n . The r e s u l t o f such an a n a l y s i s i s t h e demand t h e o r y of g e n e r e g u l a t i o n i n which t h e m o l e c u l a r n a t u r e o f g e n e t i c r e g u l a t o r y s y s t e m s i s d i r e c t l y r e l a t e d t o t h e demand f o r gene expression, as determined by the organism's e c o l o g i c a l n i c h e . Power-law Formalism E a r l y e f f o r t s t o a n a l y z e b i o l o g i c a l systems were b l i n d e d by the success t h a t engineers have had in analyzing complex t e c h n o l o g i c a l ( o f t e n e l e c t r i c a l and mechanical) systems and by the power and elegance o f the mathematical methods a t t h e i r d i s p o s a l . Over a p e r i o d o f years the e f f o r t t o make b i o l o g i c a l phenomena f i t i n t o the same mold became i n c r e a s i n g l y f r u s t r a t e d . Biological phenomena a r e h i g h l y n o n l i n e a r and cannot be made t o wear the l i n e a r s t r a i g h t j a c k e t t h a t t e c h n o l o g i c a l systems o f t e n s u b m i t t o willingly. F u r t h e r m o r e , t h e t y p e s o f n o n l i n e a r i t i e s t h a t are

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1.

SAVAGEAU

Models

of

Gene

Function

found i n t e c h n o l o g i c a l systems are very d i f f e r e n t from those found i n b i o l o g i c a l systems. On the other hand, d i s e n c h a n t m e n t set i n w i t h t h e t h e n f a s h i o n a b l e approach o f p i e c i n g together i n an ad hoc manner complex computer models t h a t could be " a d j u s t e d " u n t i l t h e y came t o mimic some aspect o f the b i o l o g i c a l phenomenon under study. In f o r m u l a t i n g our approach t o these problems, we d e c i d e d t o go back and s t a r t from s c r a t c h . T h i s r e q u i r e d going back t o fundamental k i n e t i c s , i d e n t i f y i n g the e s s e n t i a l character of b i o l o g i c a l n o n l i n e a r i t i e s , and a t t e m p t i n g the development o f a mathematical formalism rooted i n b a s i c b i o l o g y and s p e c i f i c a l l y designed t o d e a l with these types of systems. The fundamental kinetic d e s c r i p t i o n o f the u n d e r l y i n g mechanisms i n b i o l o g i c a l systems i n v o l v e s rational-function n o n l i n e a r i t i e s ( 2 - 4 ) . Although i n p r i n c i p l e these f u n c t i o n s can a c c u r a t e l y represent any mechanism of interest they are mathematically much b i o l o g i c a l systems compose some form o f s i m p l i f y i n g a p p r o x i m a t i o n i s r e q u i r e d f o r t h e s e systems; such methods must capture the e s s e n t i a l n o n l i n e a r a t t r i b u t e s o f b i o l o g i c a l phenomena and yet be s u f f i c i e n t l y simple so t h a t complex b i o l o g i c a l systems can be handled m a t h e m a t i c a l l y . These methods a l s o s h o u l d y i e l d a standard or c a n o n i c a l form to f a c i l i t a t e comparisons o f a l t e r n a t i v e models and t o a l l o w a n a l y s i s of a p r i o r i as w e l l as ad hoc models. Although t h e s e a r e i d e a l s and no c u r r e n t l y a v a i l a b l e method o f k i n e t i c a n a l y s i s f u l l y s a t i s f i e s a l l of these requirements, a method based on power-law f u n c t i o n s i s p a r t i c u l a r l y promising. D e r i v a t i o n o f t h e B a s i c Equations. The b a s i c equations are obtained by forming the T a y l o r s e r i e s e x p a n s i o n o f the r a t i o n a l f u n c t i o n i n a l o g a r i t h m i c space and t h e n r e t a i n i n g o n l y t h e constant and l i n e a r terms (2,5,6,3)· T h i s procedure y i e l d s a product o f power f u n c t i o n s i n the corresponding C a r t e s i a n space. The f u n c t i o n a l e q u a t i o n s d e s c r i b i n g a g e n e r a l system of η elements d i f f e r e n t i n k i n d and/or l o c a t i o n a r e composed o f sums and d i f f e r e n c e s o f r a t i o n a l f u n c t i o n s , but s i n c e the sum o f two r a t i o n a l f u n c t i o n s i s a l s o a r a t i o n a l f u n c t i o n , the system of e q u a t i o n s can be r e w r i t t e n as a s i m p l e d i f f e r e n c e between two composite r a t i o n a l f u n c t i o n s that are each p o s i t i v e . When these composite r a t i o n a l f u n c t i o n s a r e a p p r o x i m a t e d by power-law f u n c t i o n s , the d e s c r i p t i o n o f the e n t i r e system can be w r i t t e n (5,7,3,4):

(1)

i

= 1, 2 ,

···

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

6

BIOCHEMICAL

ENGINEERING

The behavior of complex b i o l o g i c a l systems i s d e t e r m i n e d by the nature o f the u n d e r l y i n g mechanisms and their abundant i n t e r r e l a t i o n s h i p s , as expressed mathematically i n Eqn. ( 1 ) . Exact Representation. Although the power-law f o r m a l i s m was o r i g i n a l l y d e r i v e d as an a p p r o x i m a t i o n , one can o f t e n o b t a i n an exact representation of rational-function nonlinearities by i n t r o d u c i n g a d d i t i o n a l v a r i a b l e s ( 8 ) . T h i s o b v i o u s l y extends the g e n e r a l i t y and utility of the power-law formalism. Any disadvantage caused by the i n c r e a s e i n number of v a r i a b l e s i s more t h a n o f f s e t by t h e decrease i n complexity o f the n o n l i n e a r i t i e s . The number of parameter values plus i n i t i a l c o n d i t i o n s n e c e s s a r y to characterize a system remains the same in either representation. T h i s procedure allows a set o f d i f f e r e n t i a l equations involving rational functions form, t o be transformed functions, which do have a standard form. This greatly f a c i l i t a t e s modeling and a n a l y s i s . One can e a s i l y a l t e r the model or change c o n d i t i o n s without r e w r i t i n g e q u a t i o n s , f u n c t i o n s , o r subroutines. One s i m p l y i n s e r t s an a l t e r n a t i v e s e t or subset o f parameter values i n t o the standard format. T h i s has allowed us t o develop a standardized s e t o f e f f i c i e n t computer a l g o r i t h m s f o r g r a p h i c a l i n t e r a c t i v e modeling and a n a l y s i s of b i o l o g i c a l systems. Justification. The power-law formalism i s j u s t i f i e d by f o u r types of evidence. F i r s t , i t s v a l i d i t y r e s t s on t h e o r e t i c a l grounds. Because t h e a p p r o x i m a t i o n i s d e r i v e d u s i n g T a y l o r ' s theorem, i t i s g u a r a n t e e d t o be an a c c u r a t e r e p r e s e n t a t i o n a t l e a s t o v e r a c e r t a i n range of values f o r the c o n c e n t r a t i o n v a r i a b l e s . Because the approximation i s n o n l i n e a r , t h e r a n g e o f v a l i d i t y i s c o n s i d e r a b l y g r e a t e r than t h a t f o r the corresponding l i n e a r approximation. Second, the power-law f o r m a l i s m has been j u s t i f i e d by d i r e c t experimental o b s e r v a t i o n o f r e a c t i o n s i n s i t u . Kohen etal. (9) have examined the k i n e t i c s o f individual biochemical r e a c t i o n s w i t h i n l i v i n g c e l l s and found t h a t these are best described by power-law f u n c t i o n s of the reactant concentrations. T h i r d , t h i s formalism p r e d i c t s t h a t i n a s e r i e s of steady s t a t e s the c o n c e n t r a t i o n v a r i a b l e s should be r e l a t e d t o one a n o t h e r by a s t r a i g h t l i n e i n a l o g - l o g p l o t . The range o f concentration v a l u e s f o r which a s t r a i g h t - l i n e r e l a t i o n h o l d s c o r r e s p o n d s t o t h e range o f v a l i d i t y f o r the approximation. A number o f d i f f e r e n t systems have been examined p r e v i o u s l y i n t h i s regard and the approximation was found t o be v a l i d f o r more than a 1 0 0 - f o l d change i n c o n c e n t r a t i o n v a r i a b l e s ( 3 ) . F i n a l l y , one can d e r i v e a general growth law i n t h i s f o r m a l i s m and a s k t o what e x t e n t r e a l systems adhere t o the law. As i t turns out, a l l of the w e l l - e s t a b l i s h e d growth laws t h a t one finds i n the b i o l o g i c a l l i t e r a t u r e are s p e c i a l cases o f t h i s general growth law (**,10K There a r e a number o f other i m p l i c a t i o n s that have been

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1.

SAVAGEAU

Models

of Gene

Function

7

deduced with t h i s formalism and t e s t e d a g a i n s t experimental evidence, and agreement has been found (e.g., see Ref. Thus, t h e agreement between t h e o r e t i c a l p r e d i c t i o n s and a l a r g e number of independent e x p e r i m e n t a l o b s e r v a t i o n s p r o v i d e s a w e a l t h o f evidence j u s t i f y i n g use o f the power-law formalism. P r i n c i p a l Advantages. T h e r e a r e a number o f d i f f i c u l t i e s a s s o c i a t e d with the m o d e l i n g and a n a l y s i s o f complex n o n l i n e a r systems, ( a ) The f u n c t i o n a l form o f the n o n l i n e a r i t i e s i s o f t e n unknown, as are the numbers o f i n t e r a c t i o n s and p a r a m e t e r s t h a t must be s p e c i f i e d , ( b ) Once one h a s assumed a f u n c t i o n a l form there i s s t i l l d i f f i c u l t y i n e x t r a c t i n g s t a t i s t i c a l e s t i m a t e s o f the p a r a m e t e r v a l u e s from experimental data, (c) The amount o f experimental data i t s e l f t h a t i s r e q u i r e d t o c h a r a c t e r i z e many n o n l i n e a r mechanisms i n c r e a s e s e x p o n e n t i a l l y with the dimensions of the problem, (d) Genera system o f n o n l i n e a r equation Linear analysis largely overcomes these difficulties. However, there i s a c o n s i d e r a b l e c o s t . I t i s v a l i d f o r only small v a r i a t i o n s i n t h e c o n c e n t r a t i o n v a r i a b l e s and t h i s i s u s u a l l y u n r e a l i s t i c f o r most b i o l o g i c a l systems o f i n t e r e s t . The power-law formalism provides a j u d i c i o u s compromise that has many o f the advantages o f l i n e a r a n a l y s i s w i t h o u t i t s s e v e r e limitations. ( a ) The f u n c t i o n a l form i s known and the i n t e r a c t i o n s and p a r a m e t e r s a r e r e a d i l y s p e c i f i e d , ( b ) From experimental data one can e x t r a c t parameter values f o r the i n d i v i d u a l r a t e laws by l i n e a r r e g r e s s i o n i n a l o g a r i t h m i c s p a c e , (c) The d a t a n e c e s s a r y f o r such an a n a l y s i s has a p o l y n o m i a l ( r a t h e r than e x p o n e n t i a l ) i n c r e a s e w i t h t h e d i m e n s i o n s o f t h e problem, (d) General methods f o r o b t a i n i n g s t e a d y - s t a t e s o l u t i o n s a r e a v a i l a b l e by t r a n s f o r m i n g t h e p r o b l e m i n t o l i n e a r t e r m s . General purpose computer algorithms have been developed f o r dynamic s o l u t i o n s , and parameter e s t i m a t i o n from i n t e g r a t e d system behavior i s also possible. (For more d e t a i l e d d i s c u s s i o n o f the advantages and disadvantages o f t h i s and o t h e r a p p r o a c h e s t o t h e modeling and a n a l y s i s o f n o n l i n e a r systems, see Ref. 3·) T h i s concludes my b r i e f review o f the k i n e t i c methods t h a t we have developed f o r d e a l i n g w i t h complex b i o l o g i c a l systems. These methods a l r e a d y have been a p p l i e d t o a v a r i e t y o f biochemical and g e n e t i c systems (e.g., see Réf. 3)· However, f o r the remainder o f t h i s paper I s h a l l t r e a t one p a r t i c u l a r a p p l i c a t i o n i n some detail· Demand Theory o f Gene Regulation The c e n t r a l theme t h a t I would l i k e t o emphasize i n t h i s a p p l i c a t i o n i s summarized g r a p h i c a l l y as f o l l o w s :

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

8

BIOCHEMICAL

ENGINEERING

Environment + Physiology

Demand f o r Gene E x p r e s s i o n

Molecular Design o f Gene C o n t r o l

By the c o n c l u s i o n o f t h i s paper you w i l l come t o a p p r e c i a t e t h e l o g i c and i m p l i c a t i o n s of t h i s diagram, and, as you w i l l see, the message i s a simple but general one. A l t e r n a t i v e M o l e c u l a r Designs. Let us begin w i t h the i n f l u e n t i a l model of Jacob and Monod (J2) shown i n F i g u r e 1 Note t h a t c o n t r o l i s exercise i n i t i a t i o n of t r a n s c r i p t i o n paradigm of b i o l o g i s t s c o n c e r n e d w i t h t h e n o r m a l p r o c e s s e s o f homeostasis, growth and d i f f e r e n t i a t i o n , as w e l l as their pathological manifestations—infectious diseases, inborn g e n e t i c e r r o r s and c a n c e r . By almost any c r i t e r i o n t h i s has been one o f the most f r u i t f u l ideas i n modern b i o l o g y . What i s the evidence f o r i t s v a l i d i t y ? B a c t e r i a l systems were t h e f i r s t t o be understood i n s u f f i c i e n t molecular d e t a i l t o t e s t these i d e a s . There i s now good evidence s u p p o r t i n g t h i s mode o f r e g u l a t i o n i n many p r o k a r y o t i c s y s t e m s (V3) · However, i n r e c e n t y e a r s e v i d e n c e f o r a l t e r n a t i v e molecular designs a l s o has been accumulated. In some systems the r e g u l a t o r y p r o t e i n i s not a r e p r e s s o r but an activator that i s necessary for the initiation of transcription. The example most o f t e n c i t e d i s t h e arabinose c a t a b o l i c operon o f E. c o l i (14). A schematic model i s shown i n F i g u r e 2. The N-gene product of bacteriophage lambda i s another example o f a p o s i t i v e - a c t i n g r e g u l a t o r p r o t e i n , but i n t h i s c a s e i t a c t s as an a n t i t e r m i n a t o r m o d u l a t i n g the t e r m i n a t i o n o f RNA transcripts before they can be extended i n t o the r e g u l a t e d s t r u c t u r a l genes (15-19) · A schematic model of t h i s mechanism i s given i n F i g u r e 3· We can p r e d i c t a t h i r d a l t e r n a t i v e i n w h i c h the regulatory protein i s a n e g a t i v e - a c t i n g proterminator a f f e c t i n g t h e t e r m i n a t i o n o f RNA t r a n s c r i p t s a t a s i t e t h a t precedes the r e g u l a t e d s t r u c t u r a l genes (see F i g u r e 4 ) . D e t a i l s o f t h e s e a l t e r n a t i v e s , and t h e terminology t h a t I s h a l l adopt i n d i s c u s s i n g them, a r e g i v e n i n t h e c a p t i o n s o f F i g u r e s 1-4 and summarized i n T a b l e I . T h e r e a r e a number of e s t a b l i s h e d v a r i a t i o n s on these themes. Although we are c u r r e n t l y a t a l o s s t o r a t i o n a l i z e the e n t i r e v a r i e t y o f molecular d e s i g n s , some s u c c e s s i n u n d e r s t a n d i n g t h e r o l e o f p o s i t i v e vs negative elements has been achieved with the demand theory o f gene r e g u l a t i o n (20).

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Ï1

IPIOJ

I

S62

• OPERON-

SG|

2

\T\j

{

|R J

inducers.

jf

REPRESSOR

|Q|

SG 2

SG

2

RNA transcript ^

SGi

RNA transcript ^

SGi

In an inducible system, the repressor protein normally binds to a modulator site called the operator, O, and consequently blocks transcription of the adjacent structural genes. However, when the specific inducer for the system is present in an appropriate environment, inducer binds to the repressor and alters its conformation so that the repressor is released from the operator site. The promoter site is thereby freed, and the transcription machinery can initiate synthesis of mRNA. The mRNA, in turn, is translated to yield the protein products of the operon. In a repressible system, the operon is normally expressed because the repressor protein normally has a conformation that prevents its binding to the operator site. However, when the specific corepressor for the system is present, corepressor binds to the {apo)remessor protein and alters its conformation so that repressor now binds the operator and blocks the initiation of transcription at the promoter site.

Figure 1. Repressor control of transcription initiation. A regulatory gene, R, codes for a repressor protein. Structural genes, SG, are preceded by a control region in the DNA consisting of a promoter site, P, and a modulator site, O.

corepressor^.

SG

• OPERON-

SG|

REPRESSIBLE SYSTEMS

REPRESSOR

INDUCIBLE SYSTEMS

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

OPERON-

SGi

SG

• OPERON•

SGi

2

2

SG

1

I I

inducer

Π » Π (

ACTIVATOR

1

SG 2

I

SG

2

1τ|$ RNA transcript^

SGi

RNA tronscript~*>

SGi

In an inducible system, the activator protein normally has a conformation that prevents it from interacting with a modulator site called the initiator, I. Without this specific interaction, transcription is not initiated and there is no expression of the operon. However, when inducer is present in an appropriate environment, activator is con­ verted to a conformation that can bind the initiator site and facilitate the initiation of transcription at the promoter. In a repressible system, the activator protein normally interacts with the initiator site to facilitate initiation of transcription. However, when the specific corepressor (antagonist) is present, activator is no longer able to facilitate the initiation of transcription at the promoter site and expression of the operon is turned off. See also Figure I.

Figure 2. Activator control of transcription initiation. A regulatory gene, R, codes for an activator protein. Structural genes, SG, are preceded by a control region in the DNA consisting of a promoter site, P, and a modulator site, I.

compressor^.

REPRESSIBLE SYSTEMS

3C

ACTIVATOR

INDUCIBLE SYSTEMS

§

w w δ

w

ο >

Ο

Ο m

ο

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

corepressor

SGi

SG,

SG2

inducer

ANTITERMINATOR

RNA tronscript

SG.

SG

2

In an inducible system, the antiterminator protein normally is not able to interact with a modulator site (called the liberator, L) and transcripts initiated at Ρ terminate at T. However, under inducing conditions when the anti­ terminator protein interacts with the liberator site, the transcription machinery is freed from the influence of the terminator T, and the transcripts initiated at Ρ continue on through the adjacent structural genes. In a repressible system, the antiterminator protein normally interacts with the liberator site and there is expression of the adjacent structural genes. However, under repressing conditions when the antiterminator protein no longer interacts with the liberator, transcripts initiated at the promoter, P, terminate at the terminator, T.

Figure 3. Antiterminator control of transcription termination. A regulatory gene, R, codes for an antiterminator protein. The control region of DNA preceding the structural genes, SG, which in Figures 1 and 2 consisted of modulator and promoter sites, has been expanded and redefined as the "leader region," which begins with a promoter, P, and ends with a terminator, T. (For sim­ plicity, initiation of transcription is assumed to occur constitutively at the promoter.)

«—LEADER

REPRESSOR SYSTEMS

• LEADERLT

ANT I TERMINATOR

INDUCIBLE SYSTEMS

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1-

te =>

SGi

SG, i m

{

inducer

PROTERMINATOR

In an inducible system, the proterminator protein normally interacts with a modulator site called the arrestor, A , to facilitate termination of transcription at T. However, under inducing conditions the proterminator is unable to interact with the arrestor site and transcripts initiated at the promoter, P, can be extended beyond the terminator, T, through the adjacent structural genes. In a repressive system, the proterminator protein normally is unable to interact with the arrestor site, and there is transcription through the structural genes resulting in expression of the operon. However, under repressing conditions, when the proterminator protein interacts with the arrestor site to facilitate termination of transcripts at T, expression of the operon is turned off. See also Figure 3.

Figure 4. Proterminator control of transcription termination. A regulatory gene, R, codes for a proterminator protein. The leader region preceding the structural genes, SG, extends from the promoter, P, to the terminator, T, with its associated modulator site, A.

REPRESSOR SYSTEMS corepressor »...

PROTERMINATOR

INDUCIBLE SYSTEMS

1.

SAVAGEAU

Models

of Gene

Function

13

Why are there p o s i t i v e and negative mechanisms o f r e g u l a t i n g gene expression? Are these d i f f e r e n c e s simply historical a c c i d e n t s r e p r e s e n t i n g e q u i v a l e n t e v o l u t i o n a r y s o l u t i o n s t o the same r e g u l a t o r y problem, a s some have c l a i m e d ? Alternatively, have t h e y been s e l e c t e d f o r t h e i r a b i l i t y t o p e r f o r m s p e c i f i c f u n c t i o n s and, i f so, can we d i s c o v e r what these may be? These are important b i o l o g i c a l questions t h a t a r e d i f f i c u l t t o answer by u s i n g o n l y t h e d i r e c t e x p e r i m e n t a l approach. For example, one can not s i m p l y compare r e p r e s e n t a t i v e examples o f s y s t e m s r e g u l a t e d by p o s i t i v e ( e . g . , t h e m a l t o s e o p e r o n ) and negative (e.g., the l a c t o s e operon) elements. T h i s i s not a w e l l c o n t r o l l e d experiment. In other cases, an a l t e r n a t i v e may not be a v a i l a b l e f o r s u c h a comparative t e s t because i t may e x i s t i n an undiscovered s t a t e . I d e a l l y one would l i k e a w e l l - c o n t r o l l e d comparison. F o r some systems t h i s may soon be p o s s i b l e through the imaginative use o f a r e a l a r g e number o g e n e r a l l y a r e , t h i s approach becomes i m p r a c t i c a l . At the p r e s e n t t i m e , i t i s much more p r a c t i c a l t o simulate such experiments by a p p r o p r i a t e mathematical a n a l y s i s and, u l t i m a t e l y , t h i s may be the o n l y acceptable approach f o r d e a l i n g with more general q u e s t i o n s . I have used s u c h an a p p r o a c h i n an a t t e m p t t o answer t h e q u e s t i o n , why p o s i t i v e and negative mechanisms of gene r e g u l a t i o n ? I n what f o l l o w s I s h a l l not be c o n c e r n e d with the mathematical methods p e r s e . I n s t e a d , my a p p r o a c h w i l l be t o o u t l i n e t h e principal steps i n the development o f the theory and then emphasize the most important r e s u l t s . Development o f the T h e o r y . What I have c a l l e d t h e demand t h e o r y o f gene r e g u l a t i o n may be summarized as f o l l o w s . The regulatory element will be positive (e.g., activator a n t i t e r m i n a t o r ) when i n t h e n a t u r a l environment t h e r e i s a high demand f o r expression o f the r e g u l a t e d s t r u c t u r a l genes; i t w i l l be n e g a t i v e ( e . g . , r e p r e s s o r , proterminator) when t h e r e i s a low demand (20-22). The development o f t h i s t h e o r y b e g i n s w i t h an a s s e s s m e n t o f the f u n c t i o n a l d i f f e r e n c e s between p o s i t i v e and n e g a t i v e mechanisms o f r e g u l a t i o n . D e t a i l e d a n a l y s i s o f t h e a l t e r n a t i v e mechanisms has shown t h a t i n most r e s p e c t s they behave identically. The i n h e r e n t d i f f e r e n c e s a p p e a r i n r e s p o n s e t o common r e g u l a t o r y mutations (3) · To d i s c e r n t h e i m p l i c a t i o n s o f these functional d i f f e r e n c e s one asks how f r e q u e n t l y these mutations a r i s e and how the mutant organisms f a r e i n t h e i r n a t u r a l environment when competing with the wild-type parent organism. An a n a l y s i s of the r e l e v a n t p o p u l a t i o n dynamics y i e l d s t h e r e s u l t s shown i n T a b l e I I . Thus, a c o r r e l a t i o n i s p r e d i c t e d between the ( p o s i t i v e or n e g a t i v e ) n a t u r e o f the r e g u l a t o r and t h e n o r m a l demand f o r expression o f the r e g u l a t e d s t r u c t u r a l genes: p o s i t i v e with high demand; negative w i t h low demand.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

14

Table I .

ENGINEERING

Terminology

Nature o f control

Regulator molecule

Modulator site

Transcript delimitor

Negative

Repressor

Operator

Promoter

Positive

Activato

Negative

Proterminator

Arrestor

Terminator

Positive

Antiterminator

Liberator

Terminator

Table II· P r e d i c t e d c o r r e l a t i o n between r e g u l a t o r y mechanism and demand

Regulatory mechanism Demand Positive

Negative

High

Functional regulatory mechanism s e l e c t e d

Regulation l o s t through g e n e t i c d r i f t

Low

Regulation l o s t through g e n e t i c d r i f t

Functional regulatory mechanism s e l e c t e d

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1.

SAVAGE AU

Models of Gene

Function

15

Physiology and Demand. In o r d e r t o make t h i s c o r r e l a t i o n u s e f u l , we need t o know what high/low demand means i n d i f f e r e n t p h y s i o l o g i c a l contexts. Table I I I l i s t s s e v e r a l d i f f e r e n t t y p e s of physiological functions that have been i d e n t i f i e d in microorganisms and t h e i r phages, and the a s s o c i a t e d e n v i r o n m e n t a l c o n d i t i o n c o r r e s p o n d i n g t o h i g h demand. F o r example, when an amino a c i d i s absent from an organism's environment, the o r g a n i s m must s y n t h e s i z e t h a t amino a c i d endogenously. Thus, expression o f t h e c o r r e s p o n d i n g amino a c i d b i o s y n t h e t i c o p e r o n i s i n h i g h demand. When a given carbon source i s absent from an o r g a n i s m ' s e n v i r o n m e n t and, t h e r e f o r e , cannot be u t i l i z e d , expression o f the corresponding c a t a b o l i c operon i s i n low demand. I f gene exchange between organisms o c c u r s i n f r e q u e n t l y , t h e n e x p r e s s i o n o f the genes c o d i n g f o r t h e exchange m a c h i n e r y i t s e l f w i l l be i n low demand· Ecology and Demand t o the n a t u r a l environment of the organism. S i n c e most w e l l s t u d i e d systems are found i n e n t e r i c b a c t e r i a and t h e i r phages, I s h a l l f o c u s on t h e i r e n v i r o n m e n t . T h i s has t h e a d v a n t a g e o f p r o v i d i n g a l a r g e number o f e x p e r i m e n t a l r e s u l t s w i t h w h i c h t o t e s t the theory. The l o w e r i n t e s t i n a l t r a c t o f warm-blooded animals i s the p r i n c i p a l h a b i t a t of these microbes. I t i s a r a t h e r complex ecosystem t h a t i s p o o r l y understood. The l o c a l environment to which the microbes are exposed depends upon t h e d i e t , p h y s i o l o g y and immunological s t a t e o f the host, the microorganisms t h a t share t h e same g e n e r a l h a b i t a t , as w e l l as complex p h y s i c a l and geometrical f a c t o r s . Nevertheless, one can estimate the l e v e l s of c e r t a i n c o n s t i t u e n t s of t h i s microenvironment. I s h a l l describe two types of estimates: those made i n d i r e c t l y from measurements of a b s o r p t i o n by t h e h o s t and those made d i r e c t l y from measurements of i n t e s t i n a l contents. The host enzymes that cleave v a r i o u s d i e t a r y s u b s t a n c e s t o a l l o w a b s o r p t i o n by the host are not uniformly d i s t r i b u t e d along the i n t e s t i n a l t r a c t . Some are l o c a t e d i n the proximal p o r t i o n o f the s m a l l i n t e s t i n e ( e . g . , t h e l a c t a s e enzymes); o t h e r s a r e l o c a t e d i n t h e d i s t a l p o r t i o n o f the small i n t e s t i n e and i n the colon i t s e l f (e.g., the maltase enzymes). T h i s l o c a l i z a t i o n alone a l l o w s one t o make c e r t a i n i n f e r e n c e s about t h e p r e s e n c e or a b s e n c e o f t h e s u b s t r a t e s f o r t h e s e c l e a v a g e and a b s o r p t i o n enzymes. Furthermore, the d i f f e r e n t absorption systems w i t h i n the same general r e g i o n o f t e n e x h i b i t very d i f f e r e n t a c t i v i t i e s . For example, the host's t r a n s p o r t system f o r the a b s o r p t i o n o f g a l a c t o s e i s very a c t i v e and n e a r l y impossible t o s a t u r a t e under p h y s i o l o g i c a l c o n d i t i o n s ; whereas t h a t f o r t h e a b s o r p t i o n o f arabinose i s r e l a t i v e l y i n e f f e c t i v e . Thus, from indirect information concerning the relative abundance o f v a r i o u s substances i n the d i e t , the l o c a l i z a t i o n o f h o s t enzyme s y s t e m s that permit absorption o f these, and the r a t e s at which a b s o r p t i o n

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16

BIOCHEMICAL ENGINEERING

Table I I I .

Physiology and demand

Type o f system

Repress!ble pathway

scavenging

C o n d i t i o n corresponding t o high demand f o r expression

Substrate seldom present i high concentration

R e p r e s s i b l e drug sensitivity

g f r e q u e n t l y presen i n high concentrations

Repressible biosynthetic pathway

End product seldom present i n high concentrations

Inducible biosynthetic enzymes

End product seldom present i n high concentrations

Inducible pathways

catabolic

Substrate f r e q u e n t l y present i n high concentrations

Inducible pathway

detoxification

Substrate f r e q u e n t l y present i n high c o n c e n t r a t i o n

Inducible exchange

genetic

Genetic exchange f r e q u e n t l y occurs

Inducible repair response

Repair response f r e q u e n t l y required

Inducible toxin production

Toxin f r e q u e n t l y produced

Inducible biosynthesis of s u r f a c e antigens

A n t i g e n i c determinants frequently required

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1. SAVAGEAU

Models

of Gene

17

Function

by the host occurs, one can estimate the r e l a t i v e c o n c e n t r a t i o n s o f s u b s t a n c e s t o which the e n t e r i c microorganisms are exposed i n the c o l o n (2^,3)· For example, the a f f i n i t i e s o f v a r i o u s s u g a r s f o r t r a n s p o r t s y s t e m s i n the i n t e s t i n e can be ranked as f o l l o w s : (High) D-glucose > D - g a l a c t o s e > g l y c e r o l ; (Low) D - x y l o s e > L g l u c o s e > L-mannose > L - f u c o s e > L-rhamnose > L-arabinose. I t should be emphasized t h a t t h i s r a n k i n g i s o n l y s u f f i c i e n t ( a t l e a s t i n the extreme cases) t o determine whether a given sugar has a "high" o r "low" r e l a t i v e c o n c e n t r a t i o n i n t h e c o l o n . Amino a c i d l e v e l s i n t h e c o l o n have been measured more directly. Samples were removed from v a r i o u s l o c a t i o n s a l o n g t h e i n t e s t i n a l t r a c t with a c a t h e t e r and t h e i r amino a c i d content was analyzed (23). The p a t t e r n o f r e l a t i v e c o n c e n t r a t i o n s , w h i c h i s i n d e p e n d e n t o f d i e t , can be summarized as f o l l o w s : (High) l y s i n e > glutamate > a r g i n i n e > t y r o s i n e > t r y p t o p h a n ; (Low) g l y c i n e > l e u c i n e > phenylalanin aspartate > proline > methionine. A g a i n , t h e r a n k i n g i s o n l y s u f f i c i e n t t o determine whether a g i v e n amino a c i d h a s a " h i g h " o r l o w relative c o n c e n t r a t i o n i n the c o l o n . w

Experimental

n

Implications

The p r e d i c t i o n s o f demand t h e o r y ( T a b l e I I ) can be t e s t e d with systems f o r which t h e p o s i t i v e o r n e g a t i v e n a t u r e o f t h e r e g u l a t o r y element i s known a t the molecular l e v e l and f o r which the p h y s i o l o g i c a l f u n c t i o n and e c o l o g i c a l context a l s o a r e known. The r e s u l t s f o r 40 such systems r e p r e s e n t i n g 11 d i f f e r e n t types o f physiological f u n c t i o n s a r e summarized i n Table IV. Five p r e d i c t i o n s r e g a r d i n g the molecular n a t u r e o f t h e r e g u l a t o r and nine p r e d i c t i o n s regarding the demand f o r gene expression a l s o are given i n Table IV f o r cases i n which p a r t i a l experimental evidence is available. E v i d e n c e f o r some o f t h e s e examples has been presented elsewhere (24). Since a complete review o f the m a t e r i a l (25) i s beyond the scope o f t h i s a r t i c l e , o n l y a few cases w i l l be t r e a t e d here as examples. R e p r e s s i b l e B i o s y n t h e t i c Systems. In e n t e r i c b a c t e r i a the r e p r e s s i b l e s y s t e m s f o r h i s t i d i n e and t r y p t o p h a n b i o s y n t h e s i s provide examples o f systems c o n t r o l l e d by p o s i t i v e and n e g a t i v e elements, r e s p e c t i v e l y (see Table I V ) . Since the l e v e l o f h i s t i d i n e i n the colon i s among t h e l o w e s t o f a l l amino a c i d s , e x p r e s s i o n o f t h e h i s t i d i n e b i o s y n t h e t i c operon i n the bacterium w i l l be i n high demand (Table I I I ) . Thus, demand theory p r e d i c t s that the h i s t i d i n e b i o s y n t h e t i c operon w i l l be p o s i t i v e l y r e g u l a t e d (Table I I ) . I n f a c t , t h e r e i s good e v i d e n c e t o show t h a t t h i s o p e r o n i s c o n t r o l l e d p r i m a r i l y by an a n t i t e r m i n a t o r mechanism (26.27). On the other hand, the l e v e l o f t r y p t o p h a n i n t h e c o l o n i s among the h i g h e s t o f the amino a c i d s and, t h e r e f o r e , expression o f the tryptophan b i o s y n t h e t i c operon i n the b a c t e r i u m

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

18

Table IV. Nature o f r e g u l a t o r c o r r e l a t e s with demand f o r e x p r e s s i o n

1

System" "

Nature o f regulator

Demand f o r expression

R e p r e s s i b l e b i o s y n t h e t i c systems:

Arginine

Negative

Low

Cysteine

Positive

High

Isoleucine-valine

Positive

High

Leucine

Positive

High

Lysine

Negative

Low

Phenylalanine

Positive

High

Threonine

Positive

High

Tryptophan

Negative

Low

Biotin

Negative

Low

Arabinose

Positive

High

Deoxyribonucleotides

Negative

Low

Galactose

Negative

Low

Glycerol

Negative

Low

Histidine

Negative

Low

Lactose

Negative

Low

Maltose

Positive

High

Positive

High

Negative

Low

Histidine

Inducible catabolic

Nitrogen f i x a t i o n

systems:

(K. pneumoniae)

Octopine (A. tumefaciens)

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1.

SAVAGEAU

Models

of Gene Function

19

Table IV. Continued.

1

System" "

Nature o f regulator

Demand f o r expression

Rhamnose

Positive

High

Xylose

Positive

High

•

Tryptophanase

High

Positive I n d u c i b l e g e n e t i c movement: Prophage i n d u c t i o n λ

Negative

Low

P1

Negative

Low

P2

Negative

Low

P22

Negative

Low

Tn3

Negative

Low

Tn5

Negative

Low

Tn10

Negative

Low

Negative

Low

F

Negative

Low

R100

Negative

Low

Positive

High

Positive

High

Negative

Low

Transposition

Conjugation Ti

(A. tumefaciens)

Inducible resistance/ d e t o x i f i c a t i o n systems: Alcohol

(yeast)

Mercury Penicillinase

(S. aureus)

Continued on next page.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

20

BIOCHEMICAL

ENGINEERING

Table IV. Continued. Nature o f regulator

1

System" "

Chloramphenicol

Low

Negative

Tetracycline (S. aureus)

Demand f o r expression

»

Low

«

Low

Negative Erythromycin (S. aureus) Negative Positive

High*

(lexA-recA)

Negative

Low

Adaptive response t o a l k y l a t i n g agents

Negative

D-serine Toluene

(P. p u t i d a )

Inducible r e p a i r SOS

systems:

*

Inducible biosynthetic

Low

systems:

Isoleucine-valine

Positive

Tryptophan

Negative

(P. p u t i d a )

High

• Low

R e p r e s s i b l e scavenging Alkaline

systems:

phosphatase

General aromatic AA

transport

Tyrosine-specific transport

Positive

High

Negative

Low

Negative

Low

«

Iron

High

Positive Positive

High*

C o l i c i n e E1

Negative

Low

Cholera (V. cholerae)

Negative

Low

D i p t h e r i a (C. d i p h t h e r i a e )

Negative

Sulfate Inducible toxin production:

« Low

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1.

SAVAGE AU

Models of Gene

21

Function

Table IV. Continued.

1

System" "

Inducible surface

Nature o f

Demand f o r

regulator

expression

antigens:

Outer c e l l w a l l p r o t e i n 1b

Positive

High*

K88 (K)

Positive

High*

+

Enteric bacteria

unless i n d i c a t e d otherwise

ft Predicted

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

22

BIOCHEMICAL

ENGINEERING

w i l l be i n low demand* Here demand t h e o r y p r e d i c t s n e g a t i v e c o n t r o l , which i s i n agreement with the wealth o f evidence showing t h a t r e g u l a t i o n o f t h i s operon i s accomplished p r i m a r i l y through the c l a s s i c a l r e p r e s s o r mechanism ( 1 8 ) . I n d u c i b l e C a t a b o l i c Systems* Among the i n d u c i b l e c a t a b o l i c s y s t e m s i n e n t e r i c b a c t e r i a , the g a l a c t o s e and arabinose opérons a r e examples o f systems c o n t r o l l e d by n e g a t i v e and p o s i t i v e e l e m e n t s , r e s p e c t i v e l y ( s e e T a b l e IV)· G a l a c t o s e i s absorbed e a r l y i n the s m a l l i n t e s t i n e a t a very r a p i d r a t e and i s u n l i k e l y t o s u r v i v e t r a n s i t t h r o u g h t h e i n t e s t i n e t o t h e c o l o n (21)· Expression o f the b a c t e r i a l g a l a c t o s e operon, t h e r e f o r e , w i l l be i n low demand (Table I I I ) , and demand theory p r e d i c t s that i t w i l l be n e g a t i v e l y c o n t r o l l e d . T h i s agrees with the f i n d i n g o f classical repressor control f o r the g a l a c t o s e operon ( 28 ) A r a b i n o s e , on t h e o t h e i n t e s t i n e and i s l i k e l attenuation i n concentration (21). Arabinose i n the colon at r e l a t i v e l y high l e v e l s i m p l i e s t h a t e x p r e s s i o n o f t h e a r a b i n o s e c a t a b o l i c o p e r o n i n t h e b a c t e r i u m w i l l be i n high demand. The p r e d i c t i o n by demand theory o f p o s i t i v e c o n t r o l f o r the a r a b i n o s e o p e r o n i s c o n s i s t e n t with the experimental evidence f o r a c t i v a t o r c o n t r o l o f t h i s system ( 1 4 ) . I n d u c i b l e Gene Movement. Induction o f gene movement a p p e a r s t o be a r e l a t i v e l y r a r e event i n nature. Demand f o r expression o f the m a c h i n e r y f o r movement i s consequently i n low demand and i t s r e g u l a t i o n w i l l be under the c o n t r o l o f a n e g a t i v e - a c t i n g e l e m e n t (see T a b l e I V ) . F o r example, most n a t u r a l i s o l a t e s o f c o l i f o r m organisms a r e l y s o g e n i c f o r one or more temperate phages (29) and s p o n t a n e o u s i n d u c t i o n o f the prophage i s a r e l a t i v e l y i n f r e q u e n t event i n nature (30). These f a c t s imply t h a t the l y t i c f u n c t i o n s o f t h e prophage a r e n o r m a l l y i n low demand, which i s c o n s i s t e n t with the c l a s s i c a l r e p r e s s o r c o n t r o l e s t a b l i s h e d f o r a number o f prophages (31-34). T r a n s p o s i t i o n o f genes a l s o must occur i n f r e q u e n t l y i n nature. Otherwise, the genome o f a bacterium l i k e E. c o l i would have become s c r a m b l e d t o t h e p o i n t where g e n e t i c maps as we know them would not e x i s t . The t r a n s p o s i t i o n machinery w i l l be i n low demand and i t s i n d u c t i o n w i l l be under the c o n t r o l of a n e g a t i v e - a c t i n g element. Again, t h i s i s c o n s i s t e n t w i t h t h e f i n d i n g o f c l a s s i c a l r e p r e s s o r c o n t r o l f o r a number o f transposons (35-38). S i m i l a r a r g u m e n t s c a n be made w i t h r e g a r d t o b a c t e r i a l c o n j u g a t i o n and, a g a i n , t h e r e i s evidence f o r c l a s s i c a l r e p r e s s o r control i n these cases (39-41). The case o f Agrobacterium tumefaciens i s p a r t i c u l a r l y i n t e r e s t i n g . T h i s organism i s w i d e l y found i n n a t u r e . When present a t the s i t e o f a f r e s h wound i n a dicotyledonous p l a n t under appropriate circumstances, the bacterium can t r a n s f o r m t h e normal plant tissue into a d i s o r g a n i z e d tumor. T h i s occurs when s p e c i f i c DNA l o c a t e d on a

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1.

SAVAGEAU

Models

of Gene

Function

23

b a c t e r i a l p l a s m i d becomes i n c o r p o r a t e d i n t o t h e p l a n t genome. T h i s s p e c i f i c DNA a l s o codes f o r a b i o s y n t h e t i c system that causes t h e p l a n t t o produce a r a r e amino a c i d , octopine i n t h i s example. Octopine i n t u r n a c t s as a s p e c i f i c inducer upon the b a c t e r i a t h a t h a r b o r t h e t u m o r - i n d u c i n g p l a s m i d t o c a u s e e x p r e s s i o n o f an o c t o p i n e c a t a b o l i c pathway and e x p r e s s i o n o f a s p e c i f i c system of b a c t e r i a l c o n j u g a t i o n f o r plasmid t r a n s f e r (see R e f s . 39,40). S i n c e o c t o p i n e i s o n l y r a r e l y found i n nature, e x p r e s s i o n o f the octopine c a t a b o l i c system and t h e b a c t e r i a l c o n j u g a t i o n s y s t e m w i l l be i n low demand. Demand theory p r e d i c t s t h a t these systems w i l l be under t h e c o n t r o l o f a n e g a t i v e - a c t i n g e l e m e n t . The e x p e r i m e n t a l e v i d e n c e showing t h a t t h e s e systems are under the c o n t r o l o f a r e p r e s s o r p r o t e i n (40) i s e n t i r e l y c o n s i s t e n t w i t h these e x p e c t a t i o n s . Discussion Our i n t e r e s t i n the i n t e g r a t e d behavior o f complex b i o l o g i c a l s y s t e m s has been p u r s u e d on two l e v e l s . On the f i r s t , we have concentrated on the development of mathematical methods s p e c i f i c a l l y a p p r o p r i a t e f o r complex b i o l o g i c a l systems. On the s e c o n d , we have a p p l i e d t h e s e methods t o a number o f c a s e s r e p r e s e n t i n g s e v e r a l c l a s s e s o f systems. The development o f the power-law formalism, reviewed b r i e f l y i n the f i r s t p o r t i o n o f t h i s paper, began w i t h a c o n s i d e r a t i o n o f the fundamental n o n l i n e a r i t i e s t h a t c h a r a c t e r i z e the kinetic behavior o f b i o l o g i c a l systems at the molecular l e v e l (2,5). From t h i s m o l e c u l a r - b i o l o g i c a l context a "dynamical s y s t e m s " a p p r o a c h to biochemical and g e n e t i c networks was developed (3-7,11,42). The j u s t i f i c a t i o n f o r t h i s f o r m a l i s m i s based s o l i d l y on t h e o r e t i c a l g r o u n d s (5 6 3) as w e l l as agreement w i t h d i r e c t experimental observations (42,9,4)· An a p p r e c i a t i o n o f i t s u t i l i t y i s perhaps best g a i n e d by an e x a m i n a t i o n o f s u c c e s s f u l applications. Numerous examples can be f o u n d e l s e w h e r e (43Μ*.!£·6.·2· £ 4 ) , but the l i m i t a t i o n s o f space have p r e c l u d e d d i s c u s s i n g more t h a n one example, the development o f the demand theory o f gene r e g u l a t i o n . T h i s demand theory i s now supported by experimental e v i d e n c e from more than 40 systems r e p r e s e n t i n g more than a dozen d i f f e r e n t t y p e s o f p h y s i o l o g i c a l f u n c t i o n s . T h i s theory provides a simple u n i f i e d e x p l a n a t i o n f o r what o t h e r w i s e would be u n c o n n e c t e d and d i s p a r a t e o b s e r v a t i o n s . F u r t h e r m o r e , i t p r o v i d e s a wealth o f s p e c i f i c , t e s t a b l e p r e d i c t i o n s t h a t can s e r v e as a g u i d e f o r experimental i n v e s t i g a t i o n (e.g., see R e f s . 49,50 and Table I V ) . T h i s t h e o r y a l s o p r e d i c t s the n a t u r e o f the r e g u l a t o r y mechanisms t h a t govern c e l l - s p e c i f i c f u n c t i o n s i n o r g a n i s m s w i t h d i f f e r e n t i a t e d c e l l types and t h a t these mechanisms w i l l " s w i t c h " i n a c c o r d a n c e w i t h t h e demand r e g i m e d u r i n g t h e p r o c e s s o f d i f f e r e n t i a t i o n (22,5jO. E x p e r i m e n t a l evidence c o n s i s t e n t with these p r e d i c t i o n s i s presented elsewhere (51). 9

f

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

24

BIOCHEMICAL ENGINEERING

In summary, the r e s u l t s p r e s e n t e d i n t h i s p a p e r i l l u s t r a t e the use o f k i n e t i c methods t o achieve fundamental understanding o f gene f u n c t i o n . T h e r e a l s o a r e p r a c t i c a l i m p l i c a t i o n s that have yet t o be f u l l y e x p l o r e d . C l e a r l y , i f one w i s h e s t o o p t i m a l l y e x p l o i t t h e p r o d u c t o f a p a r t i c u l a r gene, then one must know the physiology and n a t u r a l ecosystem o f i t s h o s t organism as i n t i m a t e l y as i t s molecular g e n e t i c s . Acknowledgments T h i s work was s u p p o r t e d i n part by grants from the N a t i o n a l Science Foundation.

Literature cited 1. 2. 3. 4. 5· 6. 7. 8. 9· 10. 11. 12. 13· 14. 15. 16. 17. 18. 19. 20. 21.

Wilkins, J.G. "Manner John Murray: London Savageau, M.A. J. Theoret. Biol. 1969, 25, 365-369. Savageau, M.A. "Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology"; Addison-Wesley: Reading, Mass., 1976. Savageau, M.A. Proc. Natl. Acad. Sci. USA 1979, 76, 5413-5417· Savageau, M.A. J. Theoret. Biol. 1969, 25, 370-379· Savageau, M.A. Curr. Topics in Cell. Reg. 1972, 6, 63-130. Savageau, M.A. J. Theoret. Biol. 1970, 26, 215-226. Savageau, M.A.; Voit, E.O. J. Ferment. Technol. 1982, 60, in press· Kohen, E.; Thorell, B.; Kohen, C.; Solmon, J.M. Adv. Biol. Med. Phys. 1974, 15, 271-297. Savageau, M.A. Math. Biosci. 1980, 48, 267-278. Savageau, M.A. Proc. Natl. Acad. S c i . USA 1979, 76, 6023 -6025. Jacob, F . ; Monod, J . J . Mol. Biol. 1961, 3,318-356. Miller, J . H . ; Reznikoff, W.S. "The Operon"; Cold Spring Harbor Laboratory: Cold Spring Harbor, N.Y., 1978. Englesberg, E.; Wilcox, G. Ann. Rev. Genetics 1974, 8, 219-242. Roberts, J . "RNA Polymerase"; Losick, R.; Chamberlin, M., Eds.; Cold Spring Harbor Laboratory: Cold Spring Harbor, N.Y., 1976; pp. 247-271. Adhya, S. ; Gottesman, M. Ann. Rev. Biochem. 1978, 47,967-996. Rosenberg, M.; Court, D. Ann. Rev. Genetics 1979, 13, 319-353. Yanofsky, C. Nature 1981, 289, 751-758. Platt, T. Cell 1981, 24, 10-23. Savageau, M.A. Proc. Natl. Acad. S c i . USA 1977, 74, 5647-5651. Savageau, M.A. Proc. Natl. Acad. S c i . USA 1974, 71, 2453-2455.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1.

SAVAGEAU

Models

of Gene

Function

22.

25

Savageau, M.A. Proc. 24th Annual North American Meeting of the Society for General Systems Research with the American Association for the Advancement of Science, San Francisco, California, 1980, pp. 125-133. 23. Nixon, S . E . ; Mawer, G.E. Brit. J . Nutrition 1970, 24, 241-258. 24. Savageau, M.A. "Biological Regulation and Development"; Goldberger, R . F . , E d . ; Plenum Press: N.Y., 1979; pp. 57-108. 25. Savageau, M.A. in preparation. 26. DiNocera, P.P.; Blasi, F . ; DiLauro, R.; Frunzio, R.; Bruni, C.B. Proc. Natl. Acad. Sci. USA 1978, 75, 4276-4280. 27. Barnes, W.M. Proc. Natl. Acad. Sci. USA 1978, 75, 4281-4285. 28. Nakanishi, S.; Adhya, S.; Gottesman, M.E.; Pastan, I. Proc. Natl. Acad. Sci. USA 1973, 70, 334-338. 29. Reanney, D. Bacteriol 30. Barksdale, L.; Arden 265-299. 31. Ptashne, M.; Backman, K.; Humayun, M.Z.; Jeffrey, Α.; Maurer, R.; Meyer, B.; Sauer, R.T. Science 1976, 194, 156-161. 32. Scott, J.R. Virology 1970, 41, 66-71. 33. Bertani, L . E . ; Bertani, G. Adv. Genet. 1971, 16, 199-237. 34. Levine, M. Curr. Top. Microbiol. Immunol. 1972, 58, 135-156. 35. G i l l , R . E . ; Heffron, F . ; Falkow, S. Nature 1979, 282, 797-801. 36. Chou, J.; Lemaux, P.G.; Casadaban, M.J.; Cohen, S.N. Nature, 1979, 282, 801-806. 37. Biek, D . ; Roth, J.R. Proc. Natl. Acad. S c i . USA 1980, 77, 6047-6051. 38. Beck, C.F.; Moyed, H . ; Ingraham, J . L . Molec. Gen. Genet. 1980, 179, 453-455. 39. Chilton, M . - D . ; Drummond, M.H.; Merlo, D . J . ; Sciaky, D.; Montoya, A.L.; Gordon, M.P.; Nester, E.W. Cell 1977, 11, 263-271. 40. Klapwijk, P.M.; Schilperoort, R.A. J. Bacteriol. 1979, 139, 424-431. 41. Willetts, N.; Skurray, R. Ann. Rev. Genetics 1980, 14, 41-76. 42. Savageau, M.A. Arch. Biochem. Biophys. 1971, 145, 612-621. 43. Savageau, M.A. J . Mol. Evol. 1974, 4, 139-156. 44. Savageau, M.A. J . Mol. Evol. 1975, 5, 199-214. 45. Savageau, M.A. Nature 1974, 252, 546-549. 46. Savageau, M.A. Nature 1975, 258, 208-214. 47. Savageau, M.A. J . Theoret. Biol. 1979, 77, 385-404. 48. Savageau, M.A.; Jacknow, G. J. Theoret. B i o l . , 1979, 77, 405-425. 49. Shamanna, D . K . ; Sanderson, K . E . J. Bacteriol. 1979, 139, 71-79. 50. Foster, T . J . ; Nakahara, H.; Weiss, Α.Α.; Silver, S. J . Bacteriol. 1979, 140, 167-181. 51. Savageau, M.A. submitted for publication. RECEIVED June 1, 1982

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2

Kinetics

of

Enzyme

Systems

DAVID F. OLLIS University of California, Chemical Engineering Department, Davis, CA 95616

The many circumstances leading to the Henri equation for enzyme conversion of soluble substrates are first noted, followed by some kinetic forms fo hydrolysis. Effect enzyme systems are summarized. Illustrative applications discussed include metabolic kinetics, lipid hydrolysis, enzymatic cell lysis, starch liquefaction, microenvironment influences, colloidal forces, and enzyme deactivation, a l l topics of interest to the larger themes of kinetics and thermodynamics of microbial systems. Enzyme k i n e t i c s i s by now a c l a s s i c a l f i e l d , even i n the arena o f immobilized enzymes, and d e t a i l e d t r a n s i e n t as w e l l as steady s t a t e k i n e t i c models of c e l l u l a r and s u b c e l l u l a r functions have been advanced f r e q u e n t l y which hinge h e a v i l y on the k i n e t i c forms appropriate to s i n g l e enzyme systems. (See l a t e r conference papers of Urabarger, Shuler and Domach, B a i l e y , Agathos and Demain, Marc and Engasser, Costa and Moreira, and Frederickson, f o r examples.) We open t h i s d i s c u s s i o n with a review of causes f o r success and u n c e r t a i n t y regarding the s i n g l e enzyme r a t e equation, f o l l o w i n g which we w i l l touch upon r e s u l t s f o r p a r t i c u l a t e substrates, and c l o s e with some r e s u l t s f o r immobilized enzyme systems. 1.

Soluble

substrates 1

The Henri form f o r r e a c t i o n v e l o c i t y , v, of an enzyme c a t a l y z e d r e a c t i o n was proposed i n 1902 as eqn (1.1):

v

- W ï f s ï

(

1

·

0097-6156/83/0207-0027$07.50/0 © 1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

υ

28

BIOCHEMICAL

ENGINEERING

where ν = maximum v e l o c i t y , Κ = constant, and S = concentra­ t i o n of f r e e (uncomplexed) s u b s t r a t e . T h i s form was l a t e r d e r i v e d by M i c h a e l i s and Menten i n 1913 using an e q u i l i b r i u m assumption i n eqn (1.2a) and an assumed s i n g l e slow step, eqn (1.2b), which y i e l d s form (1.1) above: 2

S + Ε

«k

ES

(1.2a)

Ε + products

(1.2b)

2

ES

->

where Michaelis-Menten:

ν

Κ Ξ

= k E ο 3

max

where Ε = t o t a l (1.3b) ο enzyme c o n c e n t r a t i o n (E + ES)

3 The subsequent Briggs-Haldane treatment recognized that i n general the r a t e constants ( k i , k ) and k could be of a r b i t r a r y r e l a t i v e magnitudes, r a t h e r than only ( k i , k ) » k assumed i m p l i c i t l y by eqns (1.2a,b), l e a d i n g to the form (1.1) again but with Κ and ν ^ given by eqns. (1.4a,b): 2

3

2

3

χ

Briggs-Haldane:

Κ =

(1.4a)

= k E (1.4b) max ο Thus, the constant Κ i s no longer a simple e q u i l i b r i u m constant^ Extensions of form (1.1) a r e apparently endless i n number. For example, f o r a common case of a (two substrate)-(one enzyme) system g i v e n below, ν

Reaction

3

3

D i s s o c i a t i o n Equibrium

Constant

Ε + S i / J ESi

Ki

(1.5a)

Ε + S

K

(1.5b)

2

J ES

ESi + S

2

2

J ESiS

ESi + S ->ESiS 2

ES S

£

2

2

2

Ki

2

Κ

Ρ + E

eqn (1.1) i s again recovered where ν eqns (1.6a,b);

(1.5c) (1.5d) (1.5e) and Κ are i n d i c a t e d i n

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

OLLis

Kinetics

of Enzyme

=

kE S — - — Ki2 + S

Systems

29

2

ν max

substrate

Κ =

(1.6a)

2

Κ

2

1

^ + *

l K l 2

(1.6b)

S2 + K i 2

Thus, i f S2 i s approximately constant as expected f o r S2 = s o l ­ vent or S2 = b u f f e r e d Η or OH , the Henri form of constant parameters ν and Κ w i l l appear to f i t the data f o r S i . S i m i l a r l y , i¥ ?he order of s u b s t r a t e b i n d i n g r e a c t i o n s (5a) and (5b) i s o b l i g a t o r y , form (1.1) i s again obtained (e.g., by e l i m i n a t i o n of eqn (1.5d)). When the second bindin e n t i t y S2 i t s u b s t r a t e but instead an enzyme a c t i v a t o i s again regained with i n h i b i t o r l e v e l as i n d i c a t e d 6y eqns (1.6a,b). The extension of the network i n eqns (1.5 a-e) to m u l t i p l e intermediates i s important i n d e v i s i n g p l a u s i b l e multi-enzyme r a t e forms f o r m i c r o b i a l metabolism. The Henri form obtained i n eqns (1.5a-e) i n v o l v e s three d i f f e r e n t enzyme complexes, a l l e q u i l i b r a t e d with each other "upstream" to the k i n e t i c a l l y slow step (eqn (1.3)). The n e g l i g i b l e f r e e energy changes evident f o r many^of the steps i n the Embden-Meyerhof g l y c o l y t i c sequence (Figure 1) i n d i c a t e that the three r e a c t i o n sequences (1.7a,b,c), a

X

glucose-6-P

£ fructose-6-P ->

(1.7a)

f r u c t o s e - d i - P J · · · J 2(phosphoenolpyruvate)

(1.7b)

pyruvate j l a c t a t e

(1.7c)

and

w i l l behave k i n e t i c a l l y l i k e the simpler r e a c t i o n sequence (1.7d): A (glucose) •> B(fructose-6-phosphate) •+ C(phosphoenolpyruvate) -* D ( l a c t a t e )

(1.7d)

Moreover, the a c t u a l feedback i n h i b i t i o n on the conversion of Β by the ( l a t e r ) products c i t r a t e and ATP (not shown) leads to the yet f u r t h e r s i m p l i f i c a t i o n given by the network below:

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

50

40

< CD

CD

30 Figure 1. Free energy of intermediates of Embden-Myerhoff glycolytic sequence in human erythrocytes. Reproduced, with permission, from Ref. 6. Copyright 1970, Worth Publishers.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

OLLis

Kinetics

of Enzyme

A ( e x t r a c e l l u l a r glucose) 0

membrane permease ( E i )

B(fructoee-6-phoephate)(Si) products ( i n c l . ATP,

31

Systems

phosphofructokinase

citrate)

Thus, the k i n e t i c s of conversions i n metabolic c e l l u l a r sequences, and even i n whole c e l l k i n e t i c s , at or near steady s t a t e may be expected to resemble the k i n e t i c r a t e form appro­ p r i a t e to one or a very small number of s e q u e n t i a l enzyme c a t a ­ l y z e d steps. The i m p l i c a t i o n s of t h i s point i n k i n e t i c models of s t r u c t u r e d c e l l systems are r e f l e c t e d i n l a t e r c o n t r i b u t i o n s i n t h i s conference. The Henri form thu u t i l i t y i n representin Si. The i n t e r p r e t i v e ambiguity accompanying the success of t h i s u n i v e r s a l " f i t t i n g " f u n c t i o n leads us to r e c a l l G i l e a d i ' s c h a r a c t e r i z a t i o n of the Langmuir form, i d e n t i c a l to ( e q n ( l . ) ) i n n o n - b i o l o g i c a l heterogeneous c a t a l y s i s : The Langmuir a d s o r p t i o n isotherm may now be regarded as a c l a s s i c a l law i n p h y s i c a l chemistry. I t has a l l the i n g r e d i e n t s of a c l a s s i c a l equation: i t i s based on a c l e a r and simple model, can be d e r i v e d e a s i l y from f i r s t p r i n c i p l e s , i s very u s e f u l now, about 50 (now 60) years a f t e r i t was f i r s t d e r i v e d and w i l l probably be u s e f u l f o r many years to come, and i s r a r e l y ever a p p l i c a b l e to r e a l systems, except as a f i r s t approximation. A l l r e a c t i o n s , c a t a l y z e d or otherwise, are r e v e r s i b l e at the molecular l e v e l . T h i s f a c t i s most important i n k i n e t i c s when o v e r a l l conversion i s l i m i t e d thermodynamically. For example, the i s o m e r i z a t i o n of glucose to f r u c t o s e by glucose i s o m e r a s e 5

25

G + E

ki k J EXJE + F k-i k-

(1.8)

2

gives (glucose) ^ ( f r u c t o s e ) at e q u i l i b r i u m . Applying the pseudo-steady s t a t e assumption to the s i n g l e intermediate gave eqn (1.9a) ν [G - G*] Π Q) Κ + [G-G*] * m

a

x

a

U

where the parameters ν

,

a

;

and Κ are found i n eqns (1.9b,c) max

Γ

Κ*+1

K Ί r

F

(1.9b)

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

32

κ = [ ΐ ς ^ Π ν ν

κ

]

*

G

**

+

9 K

*ρ G

ENGINEERING

( L E 9 C )

and K* = g l u c o s e / f r u c t o s e e q u i l i b r i u m constant Kp, K

G

= Briggs-Haldane constants f o r f r u c t o s e to glucose and glucose to f r u c t o s e , i . e . ,

Kj, = ( k

e l

+k /k 2

and K

=

Q

- 2

(k^+k^/^

G = glucose c o n c e n t r a t i o n a t e q u i l i b r i u m . Here we note t h a t , even when s t a r t i n g with G » G * , the equation (1.9a) w i l l s t i l l r e f l e c t a r e v e r s i b l e kinetîc form through eqn (1.9c) where Κ = f ( G * ) s a t i s f y eqn (1.1), wit apparent 2. P a r t i c u l a t e substrates The use of enzymes to l y s e c e l l s , hydrolyze f a t emulsions, s o l u b i l i z e proteinaceous c o l l o i d s , l i q u i f y or s a c c h a r i f y s t a r c h g e l s and granules, and degrade v a r i o u s components o f c e l l u l o s i c s u b s t r a t e s i n d i c a t e s that many s u b s t r a t e s a r e present i n a par­ t i c u l a t e form. K i n e t i c forms f o r such enzyme c a t a l y z e d r e a c t i o n r a t e s a r e here noted, and w i l l be r e v i s i t e d i n the subsequent d i s c u s s i o n of immobilized enzyme k i n e t i c s . A f i r s t example i s the h y d r o l y s i s of a uniform s u b s t r a t e , i n the form of a g i v e n t r i g l y c e r i d e emulsion, by a l i p a s e . Thus, the data of Sarda and D e s n e u e l l e * ( F i g u r e 2a,b) i n d i c a t e c l e a r l y that p u r i f i e d p a n c r e a t i c l i p a s e p r e p a r a t i o n s provide a c t i v i t y only when a substrate:water i n t e r f a c e i s present. The corresponding r e a c t i o n v e l o c i t y v s . s u b s t r a t e s u r f a c e area f u n c t i o n (Figure 2a,b) can be d e s c r i b e d by the form (2.1), which i s the analog to (1.1) f o r the case where the i n i t i a l enzyme l e v e l Ε i s much l a r g e r than the i n i t i a l s u b s t r a t e l e v e l ( s u r f a c e area). 7

ν = ν · bfzr]; ν max K+E max L

J>

8

= kS ο

(2.1)

where Ε = f r e e (uncomplexed) enzyme c o n c e n t r a t i o n and ν , Κ = constants as f o r eqn. (1.1). In c o n t r a s t to s o l u b l e s u B s i r a t e s where a s i n g l e r e a c t i o n product i s t y p i c a l l y i d e n t i f i a b l e , m u l t i p l e r e a c t i o n products r o u t i n e l y occur i n p a r t i c u l a t e degra­ d a t i o n and/or enzymatic depolymerizations. A p a r a l l e l / s e q u e n t i a l conversion network appears to be provided f o r t r i g l y c e r i d e s by the data o f Constantin et a l . (Figure 3) which a r e c o n s i s t e n t with the f o l l o w i n g network (2.2): 9

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983. 2

Saturation

LOS 1.5S (0.328 M) 2.0S

3.5S

S

4

0

-

-

-

—

0.1

0.5S

/

Saturation

LOS 1.5S (0.153 M)

1JA

i

I

0.3

ι—ι—τ- ι

Soluble ι Insoluble

Ι

2.0S

I

1

ι—ι 1 0.5 0.7

5

Interfacial Area (Methyl Butyrate) ,10 cm

Figure 2. Variation of the rate of lipase hydrolysis of triacetin and methyl butyrate with the concentration of the substrate. The concentration is expressed as a fraction of the saturation con­ centration (S) and the hydrolysis rate as a percentage of the rate of triolein hydrolysis under optimal conditions. Key: O, impure lipase plus esterolytic activity; A, lipase purified by electrophoresis. Reproduced, with permission, from Ref. 8. Copyright 1965, Academic Press.

0.5S

5

(Triocatin), 10 cm

Interfacial Area 2

34

BIOCHEMICAL ENGINEERING

Hydrolysis, % Figure 3. Liberation of diglycerides, monoglycerides, and glycerol during hydrolysis of a triglyceride by pancreatic lipase in the presence of sodium taurocholate and calcium ions. Key: O, triglyceride; 0, diglyceride; • , monoglyceride; X, glycerol. Reproduced, with permission, from Ref. 8. Copyright 1965, Academic Press

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

Kinetics

OLLIS

of Enzyme

35

Systems

,triglyceride^ diglyceride

monoglyceride

(2.2)

glycerol' The s i m p l i c i t y of k i n e t i c r e s u l t s (Figure 3) i s aided by the presence of s u r f a c t a n t (deoxycholate) and d i v a l e n t c a t i o n Ca which a s s i s t s i n remova^ of f a t t y a c i d product from the r e a c t i o n i n t e r f a c e . Lacking Ca presence, f a t t y a c i d w i l l accumulate at the i n t e r f a c e and compete with enzyme Ε f o r the l i m i t e d s u b s t r a t e surface area; the r e a c t i o n w i l l consequently e x h i b i t product inhibition. F u r t h e r , the extent of t r i g l y c e r i d e decomposition i s s t r o n g l y dependent upo only t r i - t o d i g l y c e r i d present and high enzyme l e v e l s , monoglyceride i s not converted to g l y c e r o l u n t i l the t r i g l y c e r i d e i s consumed. A simple depolymerization of c e l l w a l l m a t e r i a l apparently occurs i n l y s i s of Micrococcus l y s o d e i k t i c u s by lysozyme. The homogenous r e a c t i o n k i n e t i c s of enzyme a t t a c k of using oligomers of t h i s monopolymeric c e l l w a l l example are conveniently studied by using oligomers of the monomer [disaccharide:(GlcNac-MurNac) (N-acetyl-D-glucosamine-N-acetylmuramic a c i d ) ] . The endoenzyme can cleave an oligomer of i u n i t s , at any of the s u s c e p t i b l e bonds measured from a r e f e r e n c e (e.g., non-reducible) end. A model r e a c t i o n network a l l o w i n g f o r such random i n t e r n a l cleavage (but f o r b i d d i n g cleavage of the f i r s t s i t e from e i t h e r end) was proposed by Chipman: 9

10

κ

Ε + S

« J

±

(ES^j

j = 0,1,1

1 1 i + i

(2.3a)

k (ES ).

-

±

C

Aj + S

( i - j )

j = 1, . . . , i

(2.3b)

k [(ES.). -

V

A, + H 0 (2.3c)] k. Α..(+Η 0) V Ε + S (2.3d) *Τ A + S^ Ε + S (2.3e) Here, the (i+2)-mer S^, i s complexed at the j * * s i t e , numbered 0 to i+1, but only b i n d i n g at s i t e s 1< j < i can r e s u l t i n r e a c t i o n , as a s i t e at an end i s u n r e a c t i v e . The model f i t k i n e t i c data from e x p e r i m e n t s s t a r t i n g with (uncleavable) dimer only. Other measures of r e a c t i o n r a t e f o r c e l l l y s i s are t y p i ­ c a l l y more convenient: o p t i c a l d e n s i t y of p a r t i a l l y l y s e d c e l l s ?

1

3

±

2

Jj

± + j

1

11

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

36

BIOCHEMICAL ENGINEERING

i n a whole c e l l r e a c t i o n mixture may s u f f i c e to represent the overall c o n v e r s i o n . The h y d r o l y s i s of starches by amylases i s most conveniently considered i n terms of sugar production ( f o r s a c c h a r i f i c a t i o n ) or v i s c o s i t y r e d u c t i o n ( f o r l i q u e f a c t i o n ) . Starch pastes are c h a r a c t e r i s t i c a l l y p s e u d o p l a s t i c (shear t h i n n i n g ) , and thus s a t i s f y , over an intermediate range of shear r a t e s , a power law r e l a t i o n s h i p between shear s t r e s s , τ, and shear r a t e , γ, of the form (2.4): 2 0 , 2 2

τ = K(^) where

N

Κ = apparent

(2.4) u n i t shear v i s c o s i t y

. Ν = power law inde XT

r

x l =

pseudoplastic

As s t a r c h pastes were hydrolyzed by α-amylase , the para meters Κ and Ν were observed to change with r e a c t i o n progress i n a coupled manner according to the equation (2.5): log Κ - log

- Ν log

(2.5)

Here the p o i n t s (τ^,γ^) have the s i g n i f i c a n c e of being a l i m i t i n g h i g h shear r a t e (and shear s t r e s s ) at which the s o l u t i o n i s pre­ d i c t e d to achieve the Newtonian h i g h shear l i m i t . Thus, i f reducing ends of product were measured to provide an average molecular weight of remaining s t a r c h molecules, i t would be p o s s i b l e to r e l a t e Κ to the extent of r e a c t i o n and, through eqn (2.5), the consequent rheology of the p a r t i a l l y l i q u e f i e d product. (See l a t e r paper of R o l l i n g s , Okos, and Tsao f o r a d i s c u s s i o n of s t a r c h h y d r o l y s i s products.) The a c t i o n of the enzyme rennet on milk, known to d e s t a b l i z e a K-casein and t r i g g e r agglomeration of a m u l t i - c a s e i n m i c e l l a r suspension (a,β,γ,ε,κ) to produce coagulated m i l k f o r cheesemaking, has been shown to produce a r e a c t i o n suspension with power law behavior a l s o described by eqns (2.4-2.5)(Tucznicki and Scott B l a i r ) . * Where production of p a r t i c u l a r mono- or d i s a c c h a r i d e s i s d e s i r e d , employment of an a p p r o p r i a t e exoenzyme, such as 3-amylase i s noted. The r a t e of depolymerization i s again e s s e n t i a l l y an Henri form, unless modified by a product i n h i b i ­ t i o n term. Non-productive b i n d i n g , l e a d i n g to apparent i n h i b i t i o n , occurs f r e q u e n t l y f o r endoenzymes. For example, lysozyme h y d r o l y s i s of poly (GlcNac-MurNAc) y i e l d s dimer (GlcNac-MurNAc)2 which cannot be cleaved (being an end bond), j = 0 , i n eqn 2.3b above), but i t s non-productive b i n d i n g decreases the number of enzyme s i t e s a v a i l a b l e f o r a c q u i r i n g a c l e a v a b l e oligomer or polymer. S i m i l a r l y , the h y d r o l y s i s of ( i n s o l u b l e ) c e l l u l o s e [G] 13

1 1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

Kinetics

OLLis

of Enzyme

Systems

37

to c e l l o b i o s e , Gz i n eqns 2.6a-d and thence t o glucose, G, i n v o l v e s a c e l l o b i o s e noncompetitive b i n d i n g to the c e l l u l a s e ; t h i s i n h i b i t i o n i s r e l i e v e d by c e l l o b i o s e conversion to glucose by β-glucosidase : 9

15

k

[G] + Ej^ ( c e l l u l a s e ) k ->

1

E

l

+

G

Ε

3

E [G] 2

*

E

+

+ G

χ

i

G

2

(2.6a)

(2.6b)

2

c e l l o b i o s e

1 2 (

E (B-glucosidase) + G

E[G]

binding)

2G + E

£

(2.6c) (2.6d)

£

The form of the i n h i b i t i o b i o s e , thus Κ i s unaffecte same K) but the maximal v e l o c i t y i s diminished according t o eqn (2.7): i 1 + (

N

max

=

k

E

3 o

K^

k

3 k

l+î/Κ^

[

1

(

2

'

7

)

C e l l u l o s i c residues c h a r a c t e r i s t i c a l l y c o n s i s t of a mixture of c e l l u l o s e , h e m i c e l l u l o s e , and l i g n i n . Even the i n d i v i d u a l components are heterogeneous: the i n s o l u b l e c e l l u l o s e i t s e l f con­ s i s t s of a s t r u c t u r e d m a t e r i a l of v a r y i n g degrees of c r y s t a l linity. An i l l u s t r a t i v e s t r u c t u r e d substrate d e s c r i p t i o n i n c l u d i n g a k i n e t i c model and supporting data was provided by Ryu, Lee, T a s s i n a r i and Macy. These i n v e s t i g a t o r s modelled the substrate heterogeneity by assuming that the c e l l u l o s e c o n s i s t e d p r i m a r i l y of two phases: "an impermeable, denser, and h i g h l y ordered p a r a c r y s t a l l i n e or amorphous phase." Correspondingly, each phase possesses a d i f f e r e n t r e a c t i v i t y . With S (amor­ phous), S ( c r y s t a l l i n e ) and S ( r e s i d u a l i n e r t , i n c l u d i n g l i g n i n ) making up the t o t a l ceïlulose mass, S , the k i n e t i c model i n c l u d i n g binding of s o l u b l e product Ρ So the enzyme i s the system of r e a c t i o n s given by eqns (2.8a-3): 16

(enzyme adsorption)

k

Ε

ad

E*

(2.8a)

des k

(amorphous conversion)

E* + S

la J k Za

M

„ E*S

k

3 ·>

E*+P

(2.8b)

0

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

38

(crystalline conversion)

E* +S

(inert binding)

E* + S

( s o l u b l e pro­ duct b i n d i n g to s o l u b l e enzyme)

Ε + Ρ

(2.8c)

E*+P

(2.8d)

(2.8e)

EP

These authors determine x-ray d i f f r a c t i o n data; molecular a c c e s s i b i l i t y and surrace area of v a r i o u s l y m i l l e d samples were obtained from i o d i n e adsorption and BET measurements. Degree of c e l l u l o s e p o l y m e r i z a t i o n was determined from viscometry of cadoxen-dissolved s o l u t i o n s , with the s p e c i f i c v i s c o s i t y extrapolated to zero c o n c e n t r a t i o n to obtained the i n t r i n s i c v i s c o s i t y , [η], from which i n turn the v i s c o s i t y average molecular weight M was estimated from the MarkHouwink equation: [η] = 38.5

χ 10

-5 0.76 M J

W

(2.9)

The experimental r e s u l t s supported both the p a r t i t i o n of sub­ s t r a t e i n t o three sub-classes, and the product i n h i b i t i o n as well. Immobilized

Enzymes

The attachment of c a t a l y t i c a l l y a c t i v e s i t e s to m a t e r i a l s which may be e a s i l y recovered from a r e a c t i o n mixture has been the s i n e qua non of most u s e f u l examples of c a t a l y s i s o u t s i d e of enzymology, and t h i s l a t t e r area has begun to f o l l o w s u i t (see f o r example, the s i x Enzyme Engineering C o n f e r e n c e s , as w e l l as s e v e r a l summary t e x t s ). In a p l e a s a n t l y exhaustive review of the k i n e t i c s of immobilized enzyme systems, G o l d s t e i n s e v e r a l years ago assigned "the e f f e c t s of i m m o b i l i z a t i o n on the k i n e t i c behavior of an enzyme" to four s i t u a t i o n s : 17

1 9

"1. Conformational and s t e r i c e f f e c t s : the enzyme may be conformâtionally d i f f e r e n t when f i x e d on a support; a l t e r n a t i v e l y i t may be attached to the s o l i d c a r r i e r i n a way that would render c e r t a i n p a r t s of the enzyme molecule l e s s a c c e s s i b l e to substrate or e f f e c t o r . These e f f e c t s are ( i n 1976) w e l l understood."

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

OLLis

Kinetics

of Enzyme

39

Systems

"2. Partitioning effects: the e q u i l i b r i u m s u b s t r a t e , or e f f e c t o r concentrations w i t h i n the support may be d i f f e r e n t from those i n the bulk s o l u t i o n . Such e f f e c t s , r e l a t e d to the chemi­ c a l nature of the support m a t e r i a l , may a r i s e from e l e c t r o s t a t i c or hydrophobic i n t e r a c t i o n s between the matrix and low-molecular weight species present i n the medium, l e a d i n g t o a modified microenvironment, i . e . , to d i f f e r e n t concentrations of s u b s t r a t e , product or e f f e c t o r , hydrogen and hydroxyl ions, e t c . , i n the domain of the immobilized enzyme p a r t i c l e . "3. Microenvironmental e f f e c t s on the i n t r i n s i c c a t a l y t i c parameters o f the enzyme: such e f f e c t s due t o the p e r t u r b a t i o n of the c a t a l y t i c pathway of the enzymic r e a c t i o n would r e f l e c t events a r i s i n g from the f a c t that enzyme-substrate i n t e r a c t i o n s occur i n a d i f f e r e n t microenvironmen whe i immobi l i z e d on a s o l i d support "4. D i f f u s i o n a l or mass-transfer e f f e c t s : such e f f e c t s would a r i s e from d i f f u s i o n a l r e s i s t a n c e s to the t r a n s l o c a t i o n of s u b s t r a t e , product, or e f f e c t o r to or from the s i t e of the enzymic r e a c t i o n and would be p a r t i c u l a r l y pronounced i n the case of f a s t enzymic r e a c t i o n s and c o n f i g u r a t i o n s , where the p a r t i c l e s i z e or membrane thickness are r e l a t i v e l y l a r g e . An immobilized enzyme f u n c t i o n i n g under c o n d i t i o n s o f d i f f u s i o n a l r e s t r i c t i o n s would hence be exposed, even i n the steady s t a t e , to l o c a l concentrations of s u b s t r a t e product or e f f e c t o r d i f f e r e n t from those i n the bulk s o l u t i o n . " These i n f l u e n c e s have been evaluated s u c c e s s f u l l y , i n d i ­ c a t i n g a pleasant grasp of these fundamental i n f l u e n c e s on enzyme k i n e t i c s . We consider s e v e r a l i l l u s t r a t i v e r e s u l t s . The i n f l u e n c e of the number of covalent couplings t o an enzyme on i t s a c t i v i t y i s shown f o r lysozyme, l i p a s e , and chymotrypsin f o r s o l u b l e enzyme (Figure 4a) and immobilized enzyme (Figure 4 b ) . Here, the s i m i l a r i t y i n a c t i v i t y p a t t e r n changes f o r a l l three enzymes, as the r a t i o of s o l u b l e or i n s o l u b i l i z e d c o u p l i n g groups (Figures 4a and 4b, r e s p e c t i v e l y ) to enzyme i s i n c r e a s e d , suggests c l e a r l y that a l t e r a t i o n of r e l a t i v e enzyme a c t i v i t y upon immobilization (on only the e x t e r n a l surfaces of these polyacrylamide supports) i s governed by conformation or s t e r i c changes e f f e c t e d by the extent of enzyme covalent c o u p l i n g . The microenvironment e f f e c t due to Donnan e q u i l i b r i a i s shown by the now c l a s s i c r e s u l t s (Figure 5) f o r p H - a c t i v i t y p r o f i l e s of chymotrypsin on p o l y c a t i o n i c , and p o l y a n i o n i c sup­ p o r t s vs. that of the s o l u b l e enzyme. Here, the charged s u b s t r a t e p a r t i t i o n i n g i n bulk s o l u t i o n (S ) and i n the porous support (S ) i s given by ο 2 0

(3.1a) where ze = s u b s t r a t e charge, ψ = e l e c t r o s t a t i c p o t e n t i a l of

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

40

BIOCHEMICAL ENGINEERING

8;^

>— E S

MOLA ENZYME LOADING) χ Ι Ο

>>

1.0

I

^

ι­ ο

±

\ \

ο.

χ

Lysozyme^ \

0.01

^

ο Κ 1.0

MAcylated) L( Diazotized)

°\ 3

2

α- -Chymotrysin

V

0.1

-

10

MOLAR RATIO

ο ο \

Lipase >

100

1000

(REGENT/ENZYME)

Figure 4. Top, relative specific activity of immobilized enzyme versus the molar ratio (ratio of immobilized surface coupling groups to enzyme immobilized). Key: · , diazotized lysozyme; X, diazotized lipase; Δ, acylated a-chymotrypsin. Bottom, relative specific activity of modified soluble enzymes versus the molar ratio (ratio of soluble coupling reagent to enzyme). Key: O, diazobenzenesulfonic acid lysozyme; X, diazobenzenesulfonic acid-lipase; | , diazobenzenesulfonic acid-chymotrypsin; Δ, acetic anhydride-chymotrypsin. Reproduced, with permission, from Ref. 20.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

OLLis

Kinetics

of Enzyme

Systems

ι — ι — ι — ι — ι — ι — ι — Γ

Figure 5. Activity-pH curves. Key: O, chymotrypsin; · , a polyanionic ethylenemaleic acid (EMA) copolymer derivative of chymotrypsin, and A, a polycationic derivative, polyornithyl chymotrypsin. Substrate is acetyl-L-tryrosine ethyl ester. Ionic strength is 0.01 mol/L. Reproduced, with permission, from Ref. 19. Copyright 1976, Academic Press, Inc.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

41

42

BIOCHEMICAL ENGINEERING

support, and k = Boltzman constant. With Henri's eqn (1.1) assumed t o apply f o r the a c t u a l i n t e r n a l c o n c e n t r a t i o n S.^ adjacent t o the enzyme, the observed r a t e expressed i n terms of the measurable S value i s s t i l l i n agreement with the Henri form, but the apparent K i s given by eqn (3.1b). f

K

f

= Kexp(zei|;/kT)

(3.1b)

D

as seen from using eqn (3.1a) i n eqn (1.1): ν

max i _

K+S

V

±

ν S max ο Kexp(zei|;/k T) + S B

,~ , ν U-ic;

q

Donnan e q u i l i b r i u m , being an example of charge-charge i n t e r ­ a c t i o n , i s a l s o i n f l u e n c e d b i o n i s t r e n g t h th t M i c h a e l i s constant K' o with i o n i c s t r e n g t h according eq (3.2) K

f

,

= γΚ[1 - K Zm /KI]

l$

(3.2)

c

i n n e r

b u l

where the a c t i v i t y c o e f f i c i e n t r a t i o i s γ = y /y k^ i s the e f f e c t i v e f i x e d charge c o n c e n t r a t i o n i n s i d e the support, and I the bulk s o l u t i o n i o n i c s t r e n g t h . The i n f l u e n c e of c o l l o i d a l f o r c e s on r e a c t i o n s i n v o l v i n g immobilized enzymes a c t i n g on i n s o l u b l e s u b s t r a t e s has r e c e i v e d l e s s a t t e n t i o n , y e t i t appears to o f f e r some c l e a r examples of fundamental phenomena important i n enzyme k i n e t i c s . Datta examined l y s i s of Micrococcus l y s o d e i k t i c u s by s o l u b l e and (polyacrylamide) immobilized lysozyme. He noted that the decrease i n s o l u b l e enzyme a c t i v i t y with decreasing i o n i c strength (Table 1) p a r a l l e l e d the measured decrease i n c e l l l y s i s measured i n flow through a packed bed r e a c t o r of immobilized enzyme. Z

m

2 2

Table l

I o n i c Strength [M]

Soluble Enzyme Activity

2

2

Immobilized Enzyme Rela­ tive activity exp't (theory)

C e l l Surface Potential ψ

(mV)

+83.5mV

ΙΟ"

4

1700

ΙΟ"

3

4000

2.3

(^4.3)

ΙΟ"

2

12000

13.3

(^8.3)

^0

81.0mV -36mV

-37.3mV 22.6 (^8.3) 12000 icf * ( f i r s t numbers a r e experimental r e s u l t s , second ( i n parentheses) are values p r e d i c t e d by p a r t i c l e c o l l e c t o r theory, i n c l u d i n g i n ­ fluence of i n t e r c e p t i o n ( p a r t i c l e s i z e ) and Brownian motion on mass t r a n s f e r of p a r t i c l e s to immobilized enzyme surface.) 1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2. OLLis

Kinetics

of Enzyme

Systems

43

The d e c l i n e i n r a t e with decreasing i o n i c strength i s e v i ­ dently a s s o c i a t e d with a s i g n r e v e r s a l i n net c e l l charge, from a t t r a c t i v e (ψ - +44.5mV, ψ -, - -(36 to 37.3mV)) to r e p u l s i v e (ψ = ¥feï to 83.5mV) as determined from e l e c t r o p h o r e t i c m o b i l i t y measurements. A M i c h a e l i s constant (K) modif i c a t i o n may a l s o be involved (eqn 3.2 above). The agreement between observed r a t e and the c a l c u l a t e d mass t r a n s f e r l i m i t e d r a t e ( l a s t column i n parenthesis) means that the f l u i d mechanical and c o l l o i d a l f o r c e s which a c t to a t t r a c t / r e p e l enzyme and c e l l p a r t i c l e s are, a t the highest i o n i c strengths, dominating the slow step k i n e t i c s , i . e . , that every c e l l which encountered the immobilized enzyme surface was subsequently h y d r o l y z e d . Simil a r l y , the d e c l i n e i n r a t e f o r s o l u b l e enzyme i s to be a s s o c i a ted with a more d i f f i c u l t binding o r lessened substrate a f f i n i t y occasioned i n part by the s h i f t from a t t r a c t i v e to r e p u l s i v e c o l l o i d a l f o r c e betwee The mass t r a n s f e r enzym p a r t i c l e brings a r e l a t i v e l y modest number of hydrolyzable bonds per c e l l p a r t i c l e to the c a t a l y s t . The above lysozyme data i n d i c a t e that the r e a c t i o n r a t e i s e s s e n t i a l l y mass t r a n s f e r c o n t r o l l e d , i . e . , the enzyme can cleave the small number of c e l l w a l l bonds per u n i t volume of c e l l rather r a p i d l y . S o l i d and emulsion p a r t i c l e s of s i m i l a r s i z e , such as c e l l u l a s e p a r t i c l e s or l i p i d emulsion d r o p l e t s , b r i n g a much l a r g e r number of c l e a v a b l e bonds per p a r t i c l e to the immobilized enzyme. Immobilized p a n c r e a t i c lipase shows an observed r e a c t i o n r a t e which i s 10 to 100 times l e s s than that p r e d i c t e d from c o l l o i d a l p a r t i c l e t r a n s port (Figure 6 ) . The p a r t i c l e c o l l e c t i o n e f f i c i e n c y u t i l i z e d i n c a l c u l a t i o n of the p a r t i c l e mass t r a n s f e r c o e f f i c i e n t i s composed of only two important terms, i n t e r c e p t i o n and Brownian motion ( g r a v i t a t i o n a l s e t t l i n g and i n e r t i a l impactions a r e n e g l i g i ble). Thus, the p a r t i c l e mass e f f i c i e n c y of c o l l e c t i o n , η, i s the simple sum of two terms: * ** s

u

r

f

a

c

e

a

22

2 3

2 3

23

η

overall

^Brownian • °·

9(

2

+

^interception )

ΐ Τ Τ Ί Γ e enz ο

2

/

3

+

x

-

5

(

2

d^> enz

(3

3

' >

where d , d ^ are substrate and immobilized enzyme p a r t i c l e d i a ­ meter, r e s p e c l i v e l y , and Ν i s the f l u i d v e l o c i t y e n t e r i n g the enzyme r e a c t o r . The observed r a t e of r e a c t i o n (Figure 6) i s a l s o orders of magnitude higher than the r a t e c a l c u l a t e d by assuming that only a few molecules of product are formed per emulsion p a r t i c l e c o l l i s i o n with the enzyme surface. Thus, p a r t i c l e - c a t a l y s t encounters r e s u l t , on the average, i n the cleavage of thousands to m i l l i o n s of l i p i d bonds per p a r t i c l e - c a t a l y s t c o l l i s i o n event. The above p a r t i c u l a t e examples i n v o l v i n g lysozyme and pan­ c r e a t i c l i p a s e concerned substrates with uniform reactant e

n

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

44

M

^ ^ 2 0 0 - 2 5 0 Mesh 3

ι , - —325 Mesh

s CD

i

10

• #

—50-100 Mesh^ /

1 ^

325 Mesh 3

r

£

«

*

50-100 Mesh Figure 6. Comparison of calculated mass transfer rate and experimentally observed reaction rates at various substrate concen­ trations. Broken lines are calculated values. Experimentally observed values for stain­ less steel are: X, 50-100 mesh; O, 200250 mesh; and Δ, 325 mesh. Reproduced, with permission, from Ref. 23. Copyright 1975, John Wiley and Sons, Inc.

200-250 Mesh

0.1 43

1

0

* ' ' ' ' •' ' ' 0.4 0.8 1.2 1.6 2.0 2.4 2.8 1

É

1

1

Substrate Concentration (Volume %)

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

OLLis

Kinetics

of Enzyme

45

Systems

s t r u c t u r e : Micrococcus l y s o d e i k t i c u s ( p r o c a r y o t i c ) and t r i b u t y r i n , r e s p e c t i v e l y . More complex p a r t i c u l a t e s t r u c t u r e s provide a v a r i e t y of hydrolysable bonds per p a r t i c l e , l e a d i n g to a greater d i f f i c u l t y i n reaching a d e s c r i p t i o n of enzyme h y d r o l y t i c kinetics. Examples here i n c l u d e e u c a r y o t i c c e l l w a l l s (e.g., yeast, with c r o s s l i n k e d mannan and glucan components), and the c e l l u l o s i c substrates discussed i n the e a r l i e r s e c t i o n . Enzyme immobilization leads always to the need to consider d i f f u s i o n a l l i m i t a t i o n s , as the l a t t e r can give r i s e to r a t e l i m i t a t i o n s and d i s g u i s e s . The general k i n e t i c r e s u l t s are w e l l e s t a b l i s h e d , and we touch on only a few i l l u s t r a t i v e examples i n t h i s short paper; d i f f u s i o n a l l i m i t a t i o n s , enzyme e l e c t r o d e design, and polystep conversions. Internal d i f f u s i o n a l r e s i s t a n c e i s widely appreciated now, and t e s t s f o r freedom fro used i n k i n e t i c s t u d i e s i n t r u s i o n s i s i l l u s t r a t e d with c o n s i d e r a t i o n of an immobilized dual system: glucose oxidase (E^) and c a t a l a s e (E«) a r e used to o x i d i z e glucose (G) to o x i d i z e d glucose ( G ^ ) , and to decompose ox hydrogen peroxide ( H 0 ) : v

G

+

0

2

G

Î E

H

2

2

ox

+

H

2°

( 3

2°2

2

t

2°2

H

-

1 2°2

+

(

4 a )

3

,

4

b

)

(In a developing commercial process, the o x i d i z e d glucose i s reduced subsequently to f r u c t o s e using a t h i r d c a t a l y s t . ) The enzymes E^ and E« are both d e a c t i v a t e d by hydrogen peroxide, l e a d i n g to a d i f f u s i o n - r e a c t i o n s i t u a t i o n which changes slowly i n time. K i n e t i c equations f o r t h i s system have been widely studied; the equations (3.5 a,b,c,d,e,f) used r e c e n t l y by Chang a r e c h a r a c t e r i s t i c of the l i t e r a t u r e phenomena examined: 2 6

27

[G = glucose, A = oxygen, Β = i ^ C ^ , and Ρ = o x i d i z e d glucose] Glucose consumption r a t e (by oxidase ν

-

V

l•

Γ

E

ox

/ ( 1 + K

G

/ C

G

+

(ox)) :

V a> c

( 3

-

5 a )

Peroxide conversion r a t e (by c a t a l a s e ( c a ) ) : = V

z

- k

Ε C ca ca D

(3.5b)

Oxidase d e a c t i v a t i o n : dE O

X

dt

- - k

0

3

C E_ Β ox B

(3.5c)

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

46 Catalase

activity:

dE dt

= -k.C^E 4 Β ca

Product formation dP dt

=

(3.5d) (at pseudo-steady s t a t e ) :

^dG dt

(3.5e)

In commercial l a r g e s c a l e c a t a l y t i c conversions, a c t i v i t y maintenance i s important. C a l c u l a t i o n s by C h a n g i n d i c a t i n g the glucose oxidase a c t i v i t y p r o f i l e s vs. d i s t a n c e i n the c a t a l y s t p e l l e t are shown i n Figure 7 f o r v a r i o u s c a t a l a s e enzyme loadings 27

l

20

9

0 = / R

k

Ε /D ca ca A i n F i g s . 7a (t=0), 7b (t=100), 7d(t=150), 73(t=20C0, and 7f(t=300). Lack of any c a t a l a s e (φ = 0, F i g s . 7a-3, curve a) r e s u l t s i n the most r a p i d d e a c t i v a t i o n of Ε , while the highest E^ l o a d i n g , case glucose oxidase system i s probably the best studied example of c a t a l y s t a c t i v i t y maintenance. E v a l u a t i o n of system behavior, based upon H e n r i - r e l a t e d r e a c t i o n s (3.5a, 3.5b) and d e a c t i v a t i o n s (eqns 3.5c, 3.5d) o c c u r r i n g simultaneously with i n t e r n a l (eqns 3.5a,b) d i f f u s i o n and e x t e r n a l mass t r a n s f e r pre­ sents as complete a k i n e t i c a n a l y s i s as i s c o n v e n t i o n a l l y a v a i l ­ able i n other w e l l studied commercial examples of c a t a l y s i s . A second a p p l i c a t i o n of immobilized enzymes i n v o l v e s enzyme e l e c t r o d e s . An i l l u s t r a t i v e example of k i n e t i c fundamentals i s provided by the urease electrode,which uses a urease membrane to cleave urea i n t o bicarbonate and ammonium i o n , coupled to an ammonium i o n s p e c i f i c pontentiometric e l e c t r o d e . As with the glucose oxidase/catalase example above, the homogeneous phase k i n e t i c s can be a p p l i e d to describe the response of the immobi­ lized urease: 2

2

2 8

i n "planar" membrane: d i f f u s i o n + r e a c t i o n of urea s u b s t r a t e :

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

OLLis

Kinetics

of Enzyme Systems

47

Figure 7. Activity profiles for glucose oxidase (E ) coimmobilized with catalase (Eg) in an initially uniform concentration. The glucose oxidase loading is constant; the catalase loading increases as reflected by increased Thiele modulus, = R V Ε,ο/DSo, from Curve a (E = 0) to Curve d (E (max)). Dimensionless time appears at the lower right-hand corner of each graph (27). t

s

M0

t0

American Chemical Society Library 1155 16th St., N-W.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983. Washington, D.C. 20036

BIOCHEMICAL ENGINEERING

48

d

P

2

k kE S

g

3

Q

s ^ 2 " (1+KS) (1+K- [NH +]

=

( 3

°

4

'

6 a )

production of ammonium i o n product ,2 +, 2k-KE S r M H

v;

+ (

n«)(i«'[HH^i)

with boundary c o n d i t i o n s (at steady

d[NH+] —j

d

V

d

~ = L( s αζ Z

. V

0

( 3

·

6 b )

state)

s

= 0 =— d z

=

z

D

at ζ = L (ammonium i o n electrode)

(3.6c)

)

(3.6d)

ζ

(externa - ν surface)

dNHT = k

( [ N H

l M H

(

3

6

β

)

N H4 ^ " îlb> · 4 -d^ Using publisheddata of L a i d l e r et a l . , the c a l c u l a t e d ammonium ion concentration p r o f i l e i s presented i n Figure 8 f o r v a r i o u s urease loadings i n the t h i n "planar" membrane g e l surrounding the t i p of the ammonium i o n e l e c t r o d e . These r e s u l t s c o n t a i n u s e f u l design information. I f ^e wish to use the e l e c t r o d e to measure substrate (urea), the NH^ s i g n a l a t the ammonium e l e c t r o d e sur­ face (z/L = 1.0, F i g . 8) should be independent of Ε , thus we should produce an e l e c t r o d e with Ε > 20-30 mg urease per ml of g e l . I f we wish t o detect an i n h i b i t o r , then we should load the enzyme membrane e l e c t r o d e very l i g h t l y (e.g., Ε = 2 mg/ml) so that a 50% a c t i v i t y inhibition,corresponding to E^ = Ε /2, produces a considerable drop i n NH^ s i g n a l . The experimental voltage response o f an urease enzyme e l e c t r o d e with v a r i o u s urease loadings was determined by G u i l b a u l t and M o n t a i v o ; F i g . 9 i n d i c a t e s that the i n i t i a l l o a d i n g of 20-30 mg c a l c u l a t e d above i s i n reasonable agreemen£ with the experimental r e s u l t s (note that c a l c u l a t i o n gives NH^ (Z=0) while measurement i s reported as ammonium i o n e l e c t r o d e voltage.) Many other sub­ stances have been analyzed experimentally with s i m i l a r enzyme e l e c t r o d e probes ( G u i b a u l t ) , i n d i c a t i n g major p o t e n t i a l f o r analogs of eqns (3.6a-e). A

2 9

30

3 2

Summary The k i n e t i c s of s o l u b l e and immobilized enzymes, involved i n r e a c t i o n s of s o l u b l e and i n s o l u b l e substrates appears to be s u f f i c i e n t l y w e l l studied over the l a s t 20 years that r e a c t o r design procedures based on fundamental k i n e t i c s r a t e equations may be executed with considerable confidence. The a p p l i c a t i o n o f such emzyme k i n e t i c s forms to s t r u c t u r e d models of m i c r o b i a l metabolism has a l s o progressed, as t h i s book documents.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

OLLis

Kinetics

0

0.1

of Enzyme

0.2

0.3

Systems

0.4

49

0.5

0.6

0.7

0.8

0.9

1.0

DIMENSIONLESS THICKNESS Figure 8. Influence of enzyme loading (mg enzyme/cc gel) on product profiles for 50μ membrane; bulk urea concentration, 0.0833 M; bulk ammonium ion, negligible (10 M). Reproduced, with permission, from Ref. 28. Copyright 1972, Plenum Publishing Corp. 1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

50

τ

1

1

1

1

Γ

UREASE (mg//tgel) Figure 9. Comparison of experimental and calculated electrode steady-state responses versus enzyme loading. Key: Δ, experimental data (L = 350μ, bulk urea = 0.0833 M, bulk ammonium ion negligible); O, calculation from model given in text (L = 50μ, bulk urea = 0.0833 M, bulk ammonium ion negligible (10 M). Reproduced, with permission, from Ref. 28. Copyright 1972, Plenum Publishing Corp. 1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

OLLIS

Kinetics

of Enzyme

Systems

51

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

18. 19. 20.

21. 22. 23. 24.

Henri, V. Comptes Rendus Acad. Sci., Paris, 1902, 135, 916. Michaelis, L; Menten, M. L., Biochem. Ζ., 1913, 333, 49. Briggs, G. E.; Haldane, J. B. S. Biochem. J., 1925, 19, 338. Dixon, M.; Webb, E. C. "Enzymes", Academic Press, 1964; Chapter IV). Gileadi, E. (ed), "Electrosorption", Plenum Press, New York, 1967. Lehninger, A. L. "Biochemistry", Worth Publishers, New York, 1970, p. 327. Sarda, L.; Desnuelle, P. Biochim. Biophys. Acta, 1958, 30, 513. Wills, E. D. Adv. in Lipid Research, 1965, 3, 219. Constantin, M. J.; Pasero L.; Desnuelle P Biochim Biophys. Acta, 1960 Chipman, D. M. Biochemistry, , , Chipman, D. M.; Pollock, J . J.; Sharon, N. J. Biol. Chem., 1968, 243, 481. Cruz, Α., Russel; W. B.; Ollis, D. F. AIChE J., 1976, 22, 832. Whitaker, J . "Enzymology of Foods", John Wiley and Sons, New York. Tuczinski, W.; Scot Blair, G. W. Nature, 167, 216, 367. Howell, J . Α.; Stuck, J . D. Biotech. Bioeng., 1975, 17, 873. Ryu, D. D. Y.; Lee, S. F . ; Tassinari, T.; Macy, C. "Effect of Compression Million on Cellulose Structure and on Enzyma­ tic Hydrolysis Kinetics", private communication, 1981. "Enzyme Engineering I", L. B. Wingard (ed.), Plenum Press, 1972; II, Pye Ε. K. and L. B. Wingard (eds), Plenum Press, New York, 1974; III, Pye Ε. K. and Weetall, H. H. (eds), Plenum Press, New York, 1977; IV, Brown, G. and Mannecke, G. (eds), Plenum Press, New York; V, Plenum Press, New York, 1980; VI, 1982 (in press). Zaborsky, O. "Immobilized Enzymes", CRC Press, 1973; Chibata, (ed), "Immobilized Enzymes: Research and Development", Kodansha Press, Tokyo, 1978. Goldstein, L. "Adv. In Enzymology, XLIV, (K. Mosbach (ed.)), Academic Press, New York, 1976, pp. 397-443. Datta, R.; Ollis, D. F., "Immobilized Biochemicals and Affinity Chromatography, (R.B. Dunlap (ed.)), Plenum Ρress, New York, 1974, p. 293; "Adv. in Enzymol.", XLIV, pp. 444450 (K. Mosbach (ed.)). Wharton, C. M.; Crook, Ε. M.; Brocklehurst, K. Eur. J. Biochem., 1968, 6, 572. Datta, R., PhD Thesis, Princeton Univ., 1974. Lieberman, R.; Ollis, D. F . , Biotech. Bioengig, XVII, 1401 (1975). Bailey, J . B.; Ollis, D. F. "Biochemical Engineering Funda­ mentals", McGraw H i l l , 1977, p. 469.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

52

BIOCHEMICAL ENGINEERING

25.

Fratzke, A. R.; Lee, Y. Y.; Tsao, G. T. G.V.C./AIChE - Joint Meeting, Munich, 1974, 4, F2-1. 26. Prenosil, J . F., Biotech. Bioeng., 1979, 21, 89; Buchholz, K.; Godelman, . Biotech. Bioeng., 1978, 20, 1201; Reuss, M.; Buchholz, K. Biotech. Bioeng., 1975, 17, 211. 27. Chang, T. MSE Thesis, Univ. of California, Davis, March, 1982. 28. Ollis, D. F.; Carter, R. "Kinetic Analysis of a Urease Elec­ trode: in "Enzyme Engineering II", F. K. Pye and L. B. Wingard (eds), Plenum Publishing Corp., New York, 1972, p. 271. 29. Hoare, J . G.; Laidler, K. J. J . Am. Chem. Soc., 1950, 72, 2487; Wall, M. C . ; Laidler, K. J. Arch. Biochem. Biophys., 1953, 43, 299; Wall, M. C . ; Laidler, K. J., Arch. Biochem. Biophys., 1953, 43 307 30. Guilbault, G. C. an 1970, 92, 2533. 31. Wills, E. D. Adv. In Lipid Research, 1965, 3, 197. 32. Guilbault, G. C. "Biochemical Engineering II, A. Constantinides, W. R. Vieth and K. Venkatasubraminian (eds), Ann. Ν. Y. Acad. Sci., 1981, 309, 285. RECEIVED

July 7, 1982

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

3 Optimization of Fermentation Processes Through the Control of In Vivo Inactivation of Microbial Biosynthetic Enzymes SPYRIDON N. AGATHOS and ARNOLD L. DEMAIN Massachusetts Institute of Technology, Department of Nutrition and Food Science, Fermentation Microbiology Laboratory, Cambridge, MA 02139 Prolonged productio by in vivo stabilizatio As a model system we have focused on the gramicidin S synthetase complex in Bacillus brevis. Our group previously reported an O -dependent loss of total biosynthetic activity preventable by anaerobiosis. We further found this inactivation to be independent of aerobic energy-yielding metabolism and of de novo protein synthesis through inhibitor studies. However, retardation of inactivation was achieved upon addition of utilizable carbon sources to aerated cell suspensions, the degree of stabilization being proportional to the ease of uptake and to the concentration of each C-source. Dithiothreitol contributed to retardation and partial reversal of the inactivation. These results suggest that the in vivo inactivation may be due to an energy deficiency at the end of exponential growth with a concomitant exposure of sulfhydryl groups on the synthetases to autoxidation. 2

Important commodity chemicals are c u r r e n t l y being produced by microorganisms i n a v a r i e t y of fermentation and bioconversion processes. The e f f i c i e n t production of these substances r e q u i r e s considerable enzyme l e v e l s c a t a l y z i n g the b i o s y n t h e s i s of metabol i t e s , as w e l l as good c a t a l y t i c a c t i v i t i e s and adequate operat i o n a l s t a b i l i t i e s . T h i s i s c e r t a i n l y true of both primary and secondary metabolites. U n t i l r e c e n t l y , most work aimed a t o p t i m i z i n g production of valuable secondary metabolites such as a n t i b i o t i c s has c o n s i s t e d of environmental and genetic approaches a f f e c t i n g almost e x c l u s i v e l y the l e v e l s and c a t a l y t i c a c t i v i t i e s of the relevant b i o s y n t h e t i c enzymes, rather than t h e i r o p e r a t i o n a l s t a b i l i t y . Environmental manipulations have included: (a) the a d d i t i o n o f appropriate precursors; (b) the d i s r u p t i o n of r e g u l a t o r y mechanisms

0097-6156/83/0207-0053$06.00/0

© 1983 American Chemical Society In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

54

BIOCHEMICAL ENGINEERING

c o n t r o l l i n g the i n i t i a t i o n of a n t i b i o t i c s y n t h e s i s , such as r e p r e s s i o n and i n h i b i t i o n of t h e i r synthetases. For example, carbon c a t a b o l i t e r e g u l a t i o n i s r e l i e v e d through a d d i t i o n of a slowly u t i l i z e d carbon source at the beginning of a batch fermentation or through the slow a d d i t i o n of the otherwise r e a d i l y consumed carbon source i n various fed-batch type o p e r a t i o n s . S i m i l a r l y , n i t r o g e n and phosphate r e g u l a t i o n are bypassed e i t h e r through r e s t r i c t i o n of the r e s p e c t i v e N- or P- source or through a d d i t i o n of a slowly metabolized a l t e r n a t i v e source of those n u t r i e n t s . Feedback i n h i b i t i o n of a n t i b i o t i c synthetases has been minimized by approp r i a t e b i o r e a c t o r design, e.g., a d i a l y s i s c u l t u r e i n which the end product i s continuously removed; (c) f i n a l l y , the s p e c i f i c growth r a t e of the a n t i b i o t i c - p r o d u c i n g microorganism i s optimized during the idiophase (e.g., through l i m i t a t i o n of a key n u t r i e n t , pH c o n t r o l , etc.) s i n c e i n i t i a t i o n and maintenance of i d i o l i t e production i s favored a Genetic s o l u t i o n s t problem regu l a t o r y mechanisms have a l s o been a p p l i e d s u c c e s s f u l l y f o r the e f f i c i e n t production of secondary m e t a b o l i t e s . Mutation and s e l e c t i o n f o r s u p e r i o r producing mutants can account f o r much of the success of the modern a n t i b i o t i c i n d u s t r y . However, even with s u p e r i o r producer s t r a i n s and r a t i o n a l environmental s t r a t e g i e s f o r adequate expression and a c t i v i t y of the synthetases, these b i o s y n t h e t i c enzymes u s u a l l y decay q u i c k l y during the idiophase. Thus, the i n v i v o i n a c t i v a t i o n of b i o s y n t h e t i c enzymes i s widespread and appears to be a l i m i t i n g f a c t o r i n the prolonged production of a n t i b i o t i c s and r e l a t e d secondary m e t a b o l i t e s . Despite i t s importance, i n v i v o enzyme i n a c t i v a t i o n of secondary metabolism has not received any a t t e n t i o n as a d i s t i n c t b i o l o g i c a l phenomenon, although a fundamental understanding of the process(s) could hold the key to i t s successf u l circumvention as i s the case with other types of c e l l u l a r enzyme r e g u l a t i o n . We have reasoned that a novel approach to prolong the product i o n phase of secondary metabolites should be based on an attempt to prevent or r e t a r d the process of in v i v o i n a c t i v a t i o n of the enzymes (synthetases) c a t a l y z i n g t h e i r formation i n fermentations. Such an attempt would r e q u i r e an understanding of the chemical nature of the i n a c t i v a t i o n . T h i s knowledge could be subsequently t r a n s l a t e d i n t o process development and c o n t r o l i n a c t u a l ferment a t i o n s , which, f o r the most p a r t , are c a r r i e d out i n batch r e a c t o r s . If the object of the fermentation i s the recovery of the enzymes f o r f u r t h e r use i n a c e l l - f r e e system or the a c q u i s i t i o n of a c t i v e whole c e l l s f o r repeated use i n a f i x e d bed-type b i o r e a c t o r , the prevention or r e t a r d a t i o n of the i n a c t i v a t i o n process would ensure both an adequate margin of time for primary h a r v e s t i n g and a longer h a l f - l i f e of the a c t i v i t y f o r the b i o c a t a l y s t s i n the c e l l s . The purpose of t h i s communication i s to i l l u s t r a t e the p o t e n t i a l of the above-mentioned approach by f o c u s i n g on our

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

3.

AGATHOS AND

DEMAIN

Optimizing Fermentation

55

i n v e s t i g a t i o n of the in v i v o i n a c t i v a t i o n of the enzyme (synthetase) complex r e s p o n s i b l e f o r the formation of g r a m i c i d i n S (GS), a c y c l i c peptide a n t i b i o t i c i n B a c i l l u s b r e v i s ATCC 9999. This i n v e s t i g a t i o n represents the f i r s t attempt, to our knowledge, t o understand and to c o n t r o l in v i v o i n a c t i v a t i o n of a synthetase i n v o l v e d i n the production of a secondary metabolite. The choice of GS s y n t h e s i s , as our model system, was i n f l u e n c e d by the r e l a t i v e l y l a r g e amount of i n f o r m a t i o n i n the l i t e r a t u r e about the enzymology of GS formation, the p a r t i c i p a t i o n of only two polyenzymes i n i t s b i o s y n t h e s i s and the existence of a c e l l - f r e e b i o s y n t h e t i c system. Also the p a t t e r n of appearance and disappearance of the enzyme complex (GS synthetase) i s t y p i c a l of a l a r g e number of a n t i b i o t i c fermentations. In a d d i t i o n , the producing organism, B a c i l l u s b r e v i s , i s a non-filamentous, r a p i d l y growing prokaryote and only a s i n g l e a n t i b i o t i c i s produced i n t h i s fermentation. I n v e s t i g a t o r s have appearanc s o l u b l e GS synthetases at the end of exponential growth, they r a p i d l y disappear as the c e l l p o p u l a t i o n moves i n t o s t a t i o n a r y phase (12,L3) ( F i g - 1)· These changes have beeen observed using the assay which measures the t o t a l synthetase a c t i v i t y as w e l l as both L - o r n i t h i n e and L-phenylalanine-dependent ATP-PPi exchange r e a c t i o n s (assays f o r the i n d i v i d u a l heavy and l i g h t GS synthetases r e s p e c t i v e l y ) . F r i e b e l and Demain (.4,5.) found that i n a c t i v a t i o n of s o l u b l e GS synthetase i n v i v o i s oxygen-dependent and i r r e v e r s i b l e . They a l s o found that N gas prevented in v i v o i n a c t i v a t i o n of the enzyme complex under otherwise fermentation c o n d i t i o n s . However, under these c o n d i t i o n s no GS was produced, presumably due to the need of oxygen f o r ATP production i n t h i s aerobic organism. I t i s u s e f u l to review b r i e f l y some of the current motions on i n v i v o i n a c t i v a t i o n of m i c r o b i a l enzymes: 2

In Vivo Enzyme I n a c t i v a t i o n . Enzyme l e v e l s i n microorganisms are known to be c o n t r o l l e d through r e g u l a t i o n of the r a t e of t h e i r s y n t h e s i s ( i n d u c t i o n / r e p r e s s i o n ) whereas enzyme a c t i v i t i e s are c o n t r o l l e d by non-covalent b i n d i n g of v a r i o u s ligands ( a c t i v a t i o n / i n h i b i t i o n ) . However, through s t u d i e s that have focused almost e x c l u s i v e l y on the disappearance of enzymes of primary metabolism, i t i s now apparent that an a d d i t i o n a l type of enzyme r e g u l a t i o n i s o p e r a t i v e i n microorganisms, i . e . , the c o n t r o l of enzymatic a c t i v i t y by s e l e c t i v e i n a c t i v a t i o n . This i n a c t i v a t i o n of p a r t i c u l a r enzymes i s widespread among microorganisms, i s brought about by s e v e r a l mechanisms, and i s observed under s p e c i f i c p h y s i o l o g i c a l c o n d i t i o n s (2,LI). In v i v o i n a c t i v a t i o n i s defined as the i r r e v e r s i b l e l o s s of an enzyme's c a t a l y t i c a c t i v i t y i n the c e l l . This d e f i n i t i o n i s designed to c o n t r a s t i n a c t i v a t i o n from i n h i b i t i o n , which i s the r e v e r s i b l e l o s s of enzyme a c t i v i t y through u s u a l l y non-covalent b i n d i n g of an i n h i b i t o r that can be d i a l y z e d o r d i l u t e d away to r e s t o r e a c t i v i t y . I n v i v o enzyme i n a c t i v a t i o n can

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

56

BIOCHEMICAL ENGINEERING

GROWTH

(Klett)

4

5

6

7

8

9

FERMENTATION TIKE (hours) Figure 1. Dynamics of appearance and disappearence of GS synthetases. Key: O, growth; GS; and A, total GS biosynthetic activity (Synthetase scale).

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

3.

AGATHOS AND

DEMAIN

Optimizing

Fermentation

57

be classified into modification inactivation, which involves usually a covalent modification of the protein molecule and dégradât ive inactivation, which involves cleavage of at least one peptide bond of the enzyme protein. The in vivo inactivation of microbial enzymes i s usually observed as the cells approach or enter stationary phase i n a batch reactor. It occurs mainly at a point i n which the microbe's nutritional/energetic state changes upon exhaustion or nutrients or a shift in carbon or nitrogen source. Possibly, i t i s a general regulatory mechanism aimed at phasing out a particular enzyme when a metabolic shift renders i t wasteful of metabolites and/or directly harmful to the c e l l . Materials and Methods The culture used i thes experiment Bacillu brevi ATCC 9999. The preparation o tion of growth were as previously (9) determined by the biuret method (6). In order to study the i n vivo disappearance of GS synthetase, we have used a system that exhibits inactivation kinetics i n short-term experiments. The system u t i l i z e s frozen and thawed c e l l s of IJ. brevis harvested after growth i n yeast extract-peptone (YP) medium in a 180-1 fermentor and frozen at -20°C immediately after harvesting. Small batches of cells were thawed just before performing i n vivo inactivation studies according to the methodology of Friebel and Demain (4). In brief, these cells are agitated under a i r i n buffer for various periods of time in the presence of appropriate compound vs. nitrogen-covered controls, crude cell-free extracts are subsequently prepared using lysozyme, and the extracts are assayed by the overall GS synthetase assay (incorporation of L-[ H]ornithine into GS). 3

Results and Discussion A typical kinetic pattern of the in vivo loss of GS synthetase in our frozen-thawed c e l l system i s shown i n Figure 2. The enzyme survives over 8 hours under nitrogen gas, but i s usually lost at the end of 2-3 hours under conditions of agitation at 250 rpm, 37°C i n a i r (simulated aerobic fermentation conditions). The time scale should not be taken as an absolute measure of the enzyme's survival, because the rate of the inactivation depends upon the previous growth history of the c e l l s . Therefore, comparisons are made only between experiments performed with c e l l s from the same batch of c e l l s . Lack of Inactivation by Energy-yielding Cellular Metabolism. We f i r s t examined whether the dependence of synthetase inactivation on oxygen reflects a requirement for aerobic energy-yielding metabolism. Some enzymes are inactivated i n vivo i n the presence of 0 due to the operation of energy-yielding circuits i n the c e l l , 2

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

Figure 2. Typical kinetic pattern of in vivo inactivation of GS synthetase complex in frozen-thawed cells of B. brevis. Standard conditions for inactivation: agitation at 250 rpm, 37°C under air, vs. N -covered control. t

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

3.

AGATHOS AND

DEMAIN

Optimizing

59

Fermentation

such as glycosis, the c i t r i c acid cycle, electron transport, etc (11)· Especially i n Bacillus s u b t l l i s , i t has been demonstrated that inhibitors of such energy-yielding pathways prevent the i n vivo inactivation of aspartase transcarbamylase, a process requiring oxygen and entry into the stationary phase (15). In our case, inhibitors of glycolysis (NaF), the c i t r i c acid cycle (malonate) and oxidative phosphorylation (DNP), i n concentrations known to inhibit their respective metabolic c i r c u i t s , were not effective i n preventing enzyme inactivation (Table I)·. Therefore, i t appears as i f the inactivation i s not due to energy-yielding metabolic c e l l a c t i v i t y . Table I. Effect of Energy Metabolism Inhibitors on in vivo Stabilit

a

Atmosphere

Additive

Activity

Nitrogen Air Air Air Air Nitrogen Nitrogen Nitrogen

None None 50 mM NaF 50 mM Malonate 0.2 mM DNP 50 mM NaF 50 mM Malonate 0.2 mM DNP

100 4 2 0 6 77 85 103

%

Incubation with shaking for 90 min at 250 rpm, 37°C.

Independence of Inactivation from Protein Synthesis. A similar experiment was carried out to determine whether the inactivation was dependent upon protein synthesis. Conceivably the process of in vivo synthetase inactivation could be enzymatic, involving the mediation of an enzyme that i s derepressed at some point during late exponential growth i n actively growing cultures of 1J. brevis, e.g., a protease with an unusual requirement for oxygen or an oxygenase or an unknown "inactivase". Nevertheless, when a protein synthesis inhibitor (chloramphenicol) was included i n the aerated c e l l suspensions of our system i n a concentration known to inhibit de novo protein synthesis i n IJ. brevis, no prevention or slowdown of the inactivation process was noted, thus suggesting that the process i s not protein-synthesis dependent. Carbon Source-mediated Retardation of Inactivation. As mentioned previously, a shift in C-metabolism i s one of the physiological conditions most commonly associated with in vivo inactivation of

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

60

BIOCHEMICAL ENGINEERING

m i c r o b i a l enzymes. I t might be assumed that as B. b r e v i s moves i n t o the s t a t i o n a r y phase, the o p e r a t i o n of the ITS synthetase f o r continued formation of the a n t i b i o t i c from i t s c o n s t i t u e n t amino a c i d s becomes wasteful of p r o t e i n p r e c u r s o r s . Thus enzyme i n a c ­ t i v a t i o n may spare b u i l d i n g blocks and energy and may be brought about by s i g n a l s of p r o g r e s s i v e d e p l e t i o n of carbon and energy source and/or the i n t r a c e l l u l a r ATP p o o l . To determine whether carbon sources have any e f f e c t on i n a c t i v a t i o n of GS synthetase, v a r i o u s u t i l i z a b l e ( g l y c e r o l , f r u c t o s e , i n o s i t o l ) and n o n u t i l i z ­ able (glucose, s o r b i t o l ) carbon sources were added to f r o z e n thawed c e l l suspensions a g i t a t e d under a i r . As shown i n Table I I , s e v e r a l C-sources were able to p a r t i a l l y s t a b i l i z e the enzyme. Table I I . Effect o Stabilit

Atmosphere

Additive

Nitrogen Air Air Air Air Air Air

None None 1% G l y c e r o l 1% Fructose 1% Glucose 1% I n o s i t o l 1% S o r b i t o l

a

O v e r a l l synthetase specific activity "g GS 1 Lmg-hr J

Γ

7.8 0.5 7.0 5.4 3.6 3.1 0.4

I n c u b a t i o n with shaking f o r 90 min at 250 rpm,

Activity (%)

100 6 90 69 46 40 5 37°C.

The best s t a b i l i z a t i o n was obtained with g l y c e r o l , followed by f r u c t o s e , glucose, and i n o s i t o l i n decreasing order of e f f e c t . S o r b i t o l was i n c l u d e d i n t h i s experiment s i n c e i t i s not a source of carbon f o r growth but i s known to s t a b i l i z e at high concentra­ t i o n s ("20%) some c e l l - f r e e enzymes. In our case i t was i n a c t i v e . The r e s u l t s suggest that in v i v o synthetase s t a b i l i z a t i o n by c a r ­ bon sources i s l i n k e d with the u t i l i z a t i o n of these compounds by the c e l l s under the c o n d i t i o n s of a e r a t i o n used here. Studies by A s a t a n i and Kurahashi ÇI) have revealed that there e x i s t systems of a c t i v e uptake f o r both g l y c e r o l and f r u c t o s e i n Β· b r e v i s . The uptake of g l y c e r o l i s c o n s i d e r a b l y f a s t e r than that of f r u c t o s e and they are both c a t a b o l i z e d through the g l y c o l y t i c (EMP) path­ way. The same workers have reported that glucose, while not able to support growth as sole C-source f o r B^. b r e v i s , can d i f f u s e

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

3.

AGATHOS AND

DEMAIN

Optimizing

61

Fermentation

p a s s i v e l y and very slowly i n t o the c e l l s and, once i n s i d e , i t can be c a t a b o l i z e d through the EMP pathway. In our frozen-thawed c e l l s we are e v i d e n t l y experiencing increased p e r m e a b i l i t y of the c e l l membrane to glucose as a r e s u l t of the freeze-thaw treatment. I n o s i t o l has been found by Vandamme and Demain (14) to be a poor source of carbon f o r t h i s organism. Our r e s u l t s i n d i c a t e that there i s a d i r e c t r e l a t i o n s h i p between magnitude of the s t a b i l i ­ z a t i o n e f f e c t brought about by the C-sources i n question and t h e i r u t i l i z a t i o n . This c o r r e l a t i o n favors the idea of a metabolic b a s i s f o r the observed s t a b i l i z a t i o n in v i v o . I t i s p o s s i b l e that the c e l l s of B^. b e v i s are starved f o r a C- (and energy) source at the point of the in v i v o i n a c t i v a t i o n and that such n u t r i e n t s must be added to r e t a r d the i n a c t i v a t i o n process o c c u r r i n g under a i r . An experiment was c a r r i e d out i n which 1% g l y c e r o l was added to a c e l l suspension a f t e r i t had been subjected to i n a c t i v a t i n g con d i t i o n s ( i . e . , shaking i n a c t i v a t e d synthetase g l y c e r o l , demonstrating that g l y c e r o l i s e f f e c t i v e i n r e t a r d i n g synthetase i n a c t i v a t i o n i n a i r but cannot restore a c t i v i t y a f t e r i t has been l o s t . Table I I I . F a i l u r e of Carbon Source to R e - a c t i v a t e i n a c t i v a t e d GS Synthetases

Atmosphere

Additive

Nitrogen Air Air

None None None, i n i t i a l l y ; 1% g l y c e r o l added after inactivation

a

O v e r a l l Synthetase specific activity Ug GS L mg'hr J

Γ

Τ

10.3 0.4 0.4

I n c u b a t i o n with shaking f o r 90 min at 250 rpm,

37°C.

Given the immediate i m p l i c a t i o n s of a simple step, such an a d d i t i o n or p u l s i n g of carbon source f o r prolonged p r e s e r v a t i o n of the synthetase a c t i v i t y i n whole c e l l s , f u r t h e r experiments were conducted over s e v e r a l hours, to examine the time course of the enzyme a c t i v i t y i n the presence of s e v e r a l l e v e l s of g l y c e r o l . Figure 3 shows that p r o g r e s s i v e l y higher l e v e l s of carbon source from 1 to 4% are able to p r o p o r t i o n a t e l y r e t a r d the i n a c t i v a t i o n

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

62

process. In the same experiment, the d i s s o l v e d oxygen (D.O.) conc e n t r a t i o n s were a l s o monitored i n t e r m i t t e n t l y i n the v e s s e l s cont a i n i n g v a r i o u s g l y c e r o l l e v e l s . I t can be seen ( F i g . 3) that there e x i s t s a c o r r e l a t i o n between enzyme a c t i v i t y , l e v e l s of Csource and D.O. concentration. The r e t e n t i o n of enzyme a c t i v i t y i s g e n e r a l l y compatible with "lower" D.O. l e v e l s . T h i s could mean that the lower D.O. l e v e l s are maintained, at l e a s t p a r t l y , through increased r e s p i r a t o r y a c t i v i t y i n the e a r l i e r domains of such time-course experiments, and t h a t , i n the presence of C-source such as g l y c e r o l , r e s p i r a t o r y a c t i v i t y d e p l e t i n g the D.O. i n the c e l l suspension i s maintained f o r a longer period of time thus preventing premature 0 -mediated i n a c t i v a t i o n . I t i s a l s o p o s s i b l e that the catabolism of the C-source i s required to continue f u r n i s h i n g both ATP (a co-substrate and p o s s i b l e p o s i t i v e a l l o s t e r i c e f f e c t o r of the enzyme' s t r u c t u r a l i n t e g r i t y ) well reduced p y r i d i n e n u c l e o t i d e s retarding i n a c t i v a t i o n below) , c o r r e l a t i o n of D.O. with remaining l e v e l of enzyme a c t i v i t y i s a s i g n i f i c a n t r e s u l t not only because i t immediately suggests ways of engineering i n t e r v e n t i o n (e.g., through a c o n t r o l l e d regime of D.O. during production phase) i n a batch a n t i b i o t i c fermentation to achieve optimal GS production, but a l s o because i t might suggest a general model of regulatory a c t i o n of oxygen upon enzymes i n aerobic microorganisms producing secondary metabolites. A case i n point i s the secondary metabolic process of cyanogènesis (producion of HCN) by Pseudomonas species described by C a s t r i c and h i s colleagues £ 2 , 3 2 which i s a l s o subject to oxygen-mediated i n a c t i v a t i o n . I t i s p o s s i b l e that oxygen becomes harmful to b i o s y n t h e t i c enzymes of secondary metabolism i n o b l i g a t e aerobes at the point of C- and energy source d e p l e t i o n p a r t l y by v i r t u e of the f a c t that D.O. l e v e l s are kept low only during aerobic C-source catabolism. A p o s s i b l e mechanistic scheme that would l i n k d i r e c t l y the C-source catabolism with the molecular events c o n s t i t u t i n g the i n a c t i v a t i o n of the sytnthetase v i a oxygen, could be formulated as f o l l o w s : the a c t u a l target of the i n a c t i v a t i o n could w e l l be l a b i l e s u l f h y d r y l (SH-) a c t i v e groups on the enzyme s u r f a c e . According to Laland and Zimmer (8) i t seems that at l e a s t seven SH- groups are d i r e c t l y required f o r a c t i v i t y and p o s s i b l y some more are involved i n ensuring the s t r u c t u r a l i n t e g r i t y of the enzyme macromolecule. I t i s then p l a u s i b l e to assume that while such SH- groups are s u s c e p t i b l e to a u t o x i d a t i o n by D.O. the presence of an a c t i v e l y metabolized C-source could lead to a low i n t r a c e l l u l a r redox p o t e n t i a l which i s conducive to maintaining the i n t r a c e l l u l a r p r o t e i n c y s t e i n e residues i n the SH- ( i . e . , reduced) s t a t e . Conceivably NAD(P)H produced under such cond i t i o n s may be coupled to regeneration of SH- groups on the enzyme v i a t h i o l interchange ( n u c l e o p h i l i c s u b s t i t u t i o n ) with g l u t a t h i o n e (reduced) or lipoamide or t h i o r e d o x i n . For example, g l u t a t h i o n e , the most abundant i n t r a c e l l u l a r t h i o l i n most types of c e l l s may interchange with the enzyme as shown i n Figure 4. 2

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

AGATHOS A N DDEMAIN

0

Optimizing

1

2 time

Fermentation

3 4 [ hr ]

5

Figure 3. Time course of specific activity of G S synthetase under air in the presence of various levels of utilizable carbon source (glycerol). Shown also are the corre­ sponding levels of dissolved oxygen (DO). Standard conditions for inactivation: agitation at 250 rpm, 3TC. Glycerol levels: M, 4%; A, 2%; Δ, 1%; O, 0%.

S Enz'i + GSH S

SH Enz' -h GSSG ^SH

^ ^ GSH reductase

n a d p*

Stabilizer compound

nad ρ

—>

—>

—>

—>

H

Τ

Figure 4. Hypothetical scheme illustrating the action of a stabilizer compound (e.g., utilizable carbon source) on an enzyme containing O -sensitive SH— groups. GSH, reduced glutathione; GSSG, oxidized glutathione. t

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

64

BIOCHEMICAL ENGINEERING

I n a c t i v a t i o n Through Autoxidation o f S u l f h y d r y l Groups. To examine f u r t h e r the p o s s i b i l i t y that SH- groups are o x i d i z e d and i n a c t i v a t e d by 0 i n v i v o we checked the e f f e c t of an organic t h i o l (DTT) on the a c t i v i t y of the synthetase i n long-term e x p e r i ments. Because hydrogen peroxide and superoxide f r e e r a d i c a l s are generated during most o x i d a t i o n s of organic t h i o l s , such as DTT, i n a i r (10), such reagents cannot be used as a d d i t i v e s i n f o r c i b l y aerated c e l l suspensions, but only under N gas. Results from long-term incubations are shown i n Figure 5. The experiment was c a r r i e d out i n a way which only assumes a l a c k of forced 0 transf e r to a l l c e l l suspensions [both experimental (with DTT) and c o n t r o l s (without DTT)]. This was achieved through a p a r t i a l atmosphere of N gas i n rubber-capped v i a l s , which, however, permit the gradual entry of a i r l a t e r i n the i n c u b a t i o n . DTT at 15 mM preserved p r a c t i c a l l y the e n t i r e i n i t i a l a c t i v i t y of the enzyme during 16 hours of incubation v e s s e l (no DTT) had l o s the slow r e t u r n to a e r o b i o s i s i n the c o n t r o l v e s s e l s (no DTT) lead to a u t o x i d a t i o n and i n a c t i v a t i o n f a s t e r than i n the v e s s e l s cont a i n i n g DTT. S t i l l another approach to determine the p o s s i b l e involvement of SH- groups as t a r g e t s of o x i d a t i v e i n a c t i v a t i o n of the enzyme was to incubate c e l l s , having already been exposed to various degrees of 0 ~dependent i n a c t i v a t i o n , under N i n the presence of d i t h i o t h r e i t o l (DTT). I f the hypothesis i s c o r r e c t then the synthetase a c t i v i t y should increase under these c o n d i t i o n s . I t i s of course assumed that the postulated SH- a u t o x i d a t i o n has led to s u l f u r d e r i v a t i v e s of the enzyme, which are amenable to r e d u c t i o n back to the t h i o l s t a t e (SH-) i n the presence of excess d i t h i o t h r e i t o l . An i n i t i a l experiment along these l i n e s i s shown i n Figure 6. I t can be noted that moderate r e a c t i v a t i o n was achieved even from s t a t e s that assume t o t a l l o s s of a c t i v i t y under air. In t h i s experiment a 45-minute a d d i t i o n a l incubation of the p r e v i o u s l y exposed c e l l suspensions was c a r r i e d out under N i n the presence of 15 mM DTT. The r e s u l t s of t h i s experiment s t r o n g l y i m p l i c a t e SH- groups on the synthetase as the a c t u a l t a r g e t s of the 0 ~dependent i n a c t i v a t i o n . 2

2

2

2

2

2

2

2

Conclusions I t seems that u t i l i z a b l e C-sources are able to r e t a r d i n v i v o i n a c t i v a t i o n of the synthetases of GS and i t a l s o appears as i f the i n a c t i v a t i o n i s brought about by a u t o x i d a t i o n of SH- groups on the enzyme complex. Moreover the l o s s of synthetase a c t i v i t y i s , at l e a s t p a r t i a l l y , r e v e r s i b l e through e x t e r n a l l y added d i t h i o threitol. These r e s u l t s throw considerable l i g h t on the process of i n v i v o i n a c t i v a t i o n of the b i o s y n t h e t i c enzyme complex c a t a l y z i n g the formation of GS i n B^. b r e v i s . We b e l i e v e that these f i n d i n g s not only suggest f r e s h ways of optimizing the GS ferment a t i o n by c o n t r o l l i n g the r a t e of synthetase i n a c t i v a t i o n , but

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

3.

AGATHOS A N DDEMAIN

Optimizing

65

Fermentation

%

0

4

8

12 16 time [ hr J

20

24

Figure 5. Long-term incubation of frozen-thawed cells of B . brevis under N in the presence and absence of an organic thiol (DTT). Standard conditions: agitation at 250 rpm, 37°C. Key: O, N present; Δ, N + 15 mM DTT present. t

t

a

% S.a.

Figure 6. Effect of DDT on specific activity of GS synthetase at various degrees of prior exposure to standard inactivating conditions (air, 250 rpm, 37°C). The subsequent incubation of the cell suspensions was under N in the presence of 15 mm DTT at 37°C for 45 min. Key: O, air only; Δ, air, then N, + 15 mM DTT. g

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

66

BIOCHEMICAL ENGINEERING

a l s o that such knowledge should be d i r e c t l y a p p l i c a b l e to the e f f i c i e n t production of c l o s e l y r e l a t e d a n t i b i o t o c s of commerical s i g n i f i c a n c e , such as b a c i t r a c i n . The methodology o u t l i n e d i n t h i s i n v e s t i g a t i o n and p o s s i b l y s p e c i f i c f i n d i n g s may a l s o be exendable to d i f f e r e n t processes c a l l i n g f o r i n v i v o s t a b i l i z a t i o n of b i o s y n t h e t i c enzymes, p a r t i c u l a r l y o f oxygen-labile enzymes i n a e r o b i c organisms. Furthermore a fundamental understanding o f the i n v i v o i n a c t i v a t i o n of such synthetases appears to hold the pro­ mise f o r a more r a t i o n a l i n t e r v e n t i o n on the part of the biochemi­ c a l engineer i n making e f f i c i e n t use o f the b i o s y n t h e t i c p o t e n t i a l of a wide v a r i e t y of i n d u s t r i a l l y s i g n i f i c a n t microorganisms. While the immediate b e n e f i t from such an understanding would be an extended production phase i n batch fermentations, t h i s knowledge should a l s o be c e n t r a l i n designing a l t e r n a t i v e w h o l e - c e l l pro­ cesses (e.g., immobilized c e l l r e a c t o r s ) i n which keeping the enzymes " a l i v e " i n t h e i could be the optimal approac batch t o a continuous process. Acknowledgements We thank the Greek M i n i s t r y of Coordination and Planning f o r a NATO Science Fellowship f o r S. N. Agathos.

Literature Cited 1. Asatani, M.; Kurahashi, K. J. Biochem. (Tokyo) 1977, 81 813-822. 2. Castric, P.Α.; Ebert, R.F., Castric K.F. Current Microbiol. 1979, 287-292. 3. Castric, P.Α.; Castric K.F.; Meganathan, R. "Hydrogen Cyanide Metabolism," Conn, E . E . , Knowles, C . J . , Vennesland, B., Wissing F . , Eds.; Academic Press: New York, in press. 4. Friebel, T . E . ; Demain, A.L. J. Bacteriol. 1977a, 130, 1010-1016. 5. Friebel, T . E . ; Demain, A.L. FEMS Microbiol. Lett. 1977b, 1, 215-218. 6. Gornall, S.G.; Bardawill, C . J . , David, M.M. J. Biol. Chem. 1949, 177, 751-766. 7. Holzer, H. Trends Biochem. Sci. 1976, 1, 178. 8. Laland, S.;, Zimmer, T. Essays Biochem. 1973, 9, 31. 9. Matteo, C.C.; Glade, M.; Tanaka, Α.; Piret, J.: Demain, A.L. Biotechnol. Bioeng. 1975 17, 129-142. 10. Misra, H.P. J. Biol. Chem. 1974, 249, 2151. 11. Switzer, R.L. Ann. Rev. Microbiol. 1977, 31, 135. 12. Tomino, S.; Yamada, M.; Itoh, H.; Kurahashl, K. Biochemistry 1967, 6, 2552. 13. Tzeng, C H . ; Thrasher, K.D.; Montgomery, J.P.; Hamilton, B.K.; Wang, D.I.C. Biotechnol. Bioeng., 1975, 17, 143.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

3.

AGATHOS A N D D E M A I N

Optimizing

Fermentation

14. Vandamme, E . J . ; Demain, A.L. Antimicrob. Agents Chemother. 1976, 10, 265-273. 15. Waindle, L.M.; Switzer, R.L. J. Bacteriol. 1973, 114, 517. RECEIVED

June 1, 1982

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4

Microbial Regulatory Mechanisms: Obstacles and Tools for the Biochemical Engineer H. E. UMBARGER Purdue University, Department of Biological Sciences, West Lafayette, IN 47907

The integration of metabolic activity of bacterial cells with extent to which for industrial purposes. Since the mechanisms underlying this integration are genetically controlled, they can be often bypassed or compensated by judicious selection of mutants. The general physiological and molecular patterns of regulatory mechanisms that should be considered in the use of mutant methodology are briefly reviewed. Examples of the way such knowledge can be exploited to obtain valine-and isoleucine-producing strains are described. There i s today a widespread a p p r e c i a t i o n of the f a c t that metabolic pathways i n microorganisms are remarkably w e l l i n t e grated with the growth process. I t i s f u r t h e r remarkable that t h i s i n t e g r a t i o n i s p o s s i b l e under a broad range o f environmental conditions — c o n d i t i o n s that vary both chemically and p h y s i c a l l y . This i n t e g r a t i o n r e s u l t s from c o n t r o l s exerted i n two ways: one, the c o n t r o l of enzyme a c t i v i t y , and the other, the c o n t r o l of enzyme amount. ( S t r i c t l y speaking, t h i s l a t t e r category should a l s o i n c l u d e c o n t r o l of the amount o f other macromolecules, such as the ribosomal p r o t e i n s , ribosomal and t r a n s f e r RNA, and membrane components.) L e t me consider the p h y s i o l o g i c a l patterns found to a f f e c t enzyme a c t i v i t y , which I l i k e to c a l l the c o n t r o l of metabolite flow. (Throughout t h i s a r t i c l e , the words " c o n t r o l " or " r e g u l a t i o n " are meant to connote f a c t o r s a f f e c t i n g b i o l o g i c a l functions that can be modulated, i n contrast to a f a c t o r that has consequences on b i o l o g i c a l f u n c t i o n . An analogy with a domestic water supply would be an adjustable valve that can be manipulated, i n contrast to an o b s t r u c t i o n i n the supply l i n e . ) Broadly speaking, there are three b a s i c patterns a f f e c t i n g the c o n t r o l o f metabolite flow (Table I ) . The simplest i s endproduct i n h i b i t i o n i n which the endproduct o f a pathway i s an 0097-6156/ 83/0207-0071 $ 0 6 . 5 0 / 0 © 1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

72

BIOCHEMICAL ENGINEERING

Table I P h y s i o l o g i c a l Patterns o f C o n t r o l o f Metabolite Pattern En dp r ο duct inhibition

I n h i b i t i o n of threonine deaminase by i s o l e u c i n e

(1)

Qoli)

S t i m u l a t i o n o f l a c t a t e dehydro­ genase by f r u c t o s e - l , 6 - d i p h o s phate

Compensatory modulation

Reference

Example

(E.

Precursor activation

Flow

(Streptococcus

fecalis)

S t i m u l a t i o n o f carbamylphosphate synthetase by o r n i t h i n e (E.

(2)

(1)

coli)

i n h i b i t o r of the i n i t i a l enzyme o f the pathway. The i n h i b i t i o n of threonine deaminase i s a w e l l known example to which I r e f e r l a t e r i n t h i s a r t i c l e (1). There are v a r i a t i o n s on t h i s general theme i n which m u l t i p l e endproducts may act i n concert or synerg i s t i c a l l y upon a s i n g l e enzyme c a t a l y z i n g the f i r s t step i n a common pathway o r i n which a segment of a s i n g l e pathway i s con­ t r o l l e d by an intermediate i n h i b i t i n g an e a r l i e r step [e.g., the i n h i b i t i o n o f phosphofructokinase of Escherichia coli by phosphoenolpyruvate ( 2 ) ] . The reverse of endproduct i n h i b i t i o n i s precursor a c t i v a t i o n . Although i t i s more d i f f i c u l t to c i t e examples i n b i o s y n t h e t i c pathways, an example i s found i n the a c t i v a t i o n of c e r t a i n micro­ b i a l l a c t a t e dehydrogenases by fructose-l,6-diphosphate. Finally, there i s another p a t t e r n o f enzyme a c t i v a t i o n that I would c a l l compensatory modulation of a c t i v i t y . The example that i s p a r t i c u ­ l a r l y w e l l s t u d i e d i s the a c t i v a t i o n of carbamyl phosphate synthe­ tase o f E. coli by o r n i t h i n e (3). This enzyme forms carbamyl­ phosphate needed f o r both pyrimidine n u c l e o t i d e b i o s y n t h e s i s and a r g i n i n e b i o s y n t h e s i s . The enzyme i s i n h i b i t e d by UMP, an i n d i ­ cator of the g l o b a l pyrimidine p o o l . However, an ample supply o f carbamylphosphate f o r a r g i n i n e b i o s y n t h e s i s i s assured by o r n i ­ thine s t i m u l a t i n g the enzyme and antagonizing the UMP-mediated i n h i b i t i o n . O r n i t h i n e , o f course, i s an intermediate that would appear only when the a r g i n i n e supply was low. This c l a s s i f i c a t i o n o f r e g u l a t o r y patterns implies nothing with respect to the mechanisms by which r e g u l a t i o n was achieved. The common mechanisms that have been recognized i n c o n t r o l l i n g carbon flow are c l a s s i f i e d i n Table I I . We can recognize mecha­ nisms that are s p e c i f i c i n that they are r e l a t e d to the s p e c i f i c r o l e the modulated enzyme plays and mechanisms that are general i n that they may a f f e c t many enzymes o r pathways that are not func­ t i o n a l l y r e l a t e d o r have l i t t l e to do with the p h y s i o l o g i c a l r o l e of the enzyme.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

UMBARGER

Microbial

Regulatory

Mechanisms

Table I I Enzymic Mechanisms Underlying C o n t r o l of Metabolite Flow Example i n E. coli

Mechanism

Référer

S p e c i f i c mechanisms: Binding at catalytic site

Inhibitio o asparagine synthetase by asparagine

(4)

Binding at regulatory

I n h i b i t i o n of threonine deaminase by i s o l e u c i n e and i t s antagonism by valine

(

Enzyme modification

A d e n y l y l a t i o n of glutamine synthetase

(

Protein-protein interaction

S t i m u l a t i o n of α-subunit of tryptophan synthase by β-subunit

(

Energy charge

Retardation of aspartokinase I I I a c t i v i t y at low energy charge

(

Reducing potential

I n h i b i t i o n of pyruvate dehydrogenase a t low NAuVNADH r a t i o s

(

Substrate availability

None known

site

General mechanisms:

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

74

BIOCHEMICAL ENGINEERING

The simplest of these mechanisms would be the a c t i o n of an i n h i b i t o r b i n d i n g at the a c t i v e s i t e . The i n h i b i t i o n of succinate dehydrogenase by oxaloacetate can be looked upon as such an exam­ p l e (10). It may be that t i g h t b i n d i n g of a product may a l s o play a r o l e i n r e g u l a t i n g the a c t i v i t y of an enzyme (11). The i n h i b i ­ t i o n of asparagine synthetase by asparagine i n microorganisms provides a l i k e l y candidate f o r r e g u l a t i o n by t i g h t binding of product (4). Obviously more complex would be those enzymes on which a separate regulatory s i t e has been developed f o r b i n d i n g of e i t h e r a s t i m u l a t o r y or an i n h i b i t o r y l i g a n d that i s p h y s i o l o g i c a l l y r e l a t e d to the f u n c t i o n but not i t s e l f s t o i c h i o m e t r i c a l l y r e l a t e d to the c a t a l y t i c events. When such a l i g a n d i s an i n h i b i t o r , i t would be an example of what Monod and Jacob (12) had defined as an a l l o s t e r i c i n h i b i t o r i n contrast to the previous example which they defined as i s o s t e r i c regulatory process hav s y n t h e t i c pathways. However, i n r e f e r r i n g to binding of a r e g u l a ­ tory l i g a n d to a d i s t i n c t r e g u l a t o r y s i t e , I would not wish to imply a common mechanism by which the i n h i b i t i o n or the s t i m u l a ­ t i o n occurs. There probably are s e v e r a l mechanisms i n v o l v e d , and at the l e v e l of enzyme s t r u c t u r e there i s seldom complete agree­ ment among a l l i n v e s t i g a t o r s regarding the p r e c i s e d e t a i l s . At the present time, we can c i t e more examples of enzyme m o d i f i c a t i o n o c c u r r i n g as r e g u l a t o r y mechanisms i n animal metabo­ l i s m than we can i n m i c r o b i a l metabolism. In animal metabolism, phosphorylation by p r o t e i n kinases a f f e c t s many enzymes (13). There are examples of phosphorylation of b a c t e r i a l p r o t e i n s , but, with few exceptions, the r o l e or even the i d e n t i t y of the p r o t e i n i s unknown. One example that has been s t u d i e d i s the i s o c i t r a t e dehydrogenase of E. coli, which i s phosphorylated when the c e l l i s s h i f t e d from glucose to acetate as the carbon source and which thereby undergoes a very r a p i d decrease i n a c t i v i t y (14). The b e s t - s t u d i e d example of m o d i f i c a t i o n of an enzyme i s that of the a d e n y l y l a t i o n and deadenylylation of glutamine synthase of E. coli, which, i n e f f e c t , serves to i n h i b i t and to a c t i v a t e the enzyme (6). To some extent, the idea of p r o t e i n - p r o t e i n i n t e r a c t i o n s a f f e c t i n g the a c t i v i t y of b a c t e r i a l pathways may s t i l l be hypo­ thetical. In yeast, we can c i t e at l e a s t one c l e a r l y important example. That i s the i n h i b i t i o n of o r n i t h i n e transcarbamylase upon binding to arginase, an enzyme induced by adding a r g i n i n e to the medium (15). This p r o t e i n - p r o t e i n i n t e r a c t i o n thus prevents a f u t i l e c y c l e i n which o r n i t h i n e , formed from exogenous a r g i n i n e , would be converted back to a r g i n i n e . There are i n v i t r o models that can be c i t e d i n b a c t e r i a l metabolism that demonstrate the f e a s i b i l i t y of such a mechanism, i n which an a c t i v i t y of one pro­ t e i n i s markedly enhanced upon b i n d i n g to another. For example, the conversion of s e r i n e and i n d o l e to tryptophan i s slowly c a t a ­ l y z e d by the α subunit of tryptophan synthase alone but i s

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

UMBARGER

Microbial

Regulatory

Mechanisms

75

stimulated some 30-fold upon b i n d i n g to 3-subunit dimers. Under the category o f general c o n t r o l s , I have l i s t e d energy charge and reducing p o t e n t i a l , which could be looked upon as spe­ c i a l cases of substrate a v a i l a b i l i t y . The energy charge e x p e r i ­ ments of Atkinson (16) have demonstrated s e v e r a l examples of i n v i t r o response to energy charge, but i t i s s t i l l d i f f i c u l t to assess the i n v i t r o s i g n i f i c a n c e of such a response to energy charge, s i n c e c e l l s do have a remarkable c a p a c i t y f o r maintaining the energy charge w i t h i n rather narrow l i m i t s (17). Similarly, the extent to which a p y r i d i n e n u c l e o t i d e - l i n k e d r e a c t i o n proceeds can be modulated by the NAD/NADH (or NADP/NADPH) r a t i o (9). The question i s whether these r a t i o s can be so changed i n the growing c e l l to be e x p l o i t e d as a r e g u l a t o r y mechanism. One can a n t i c i p a t e that the f l u x through a pathway might be l i m i t e d not by some r a t e - l i m i t i n th beginnin withi the pathway but by the the pathway i s s u p p l i e d supply s t r a t e i s modulated, such a mechanism might play a r e g u l a t o r y r o l e . That a l i m i t a t i o n i n supply can have important consequences on the extent that a pathway might f u n c t i o n w i l l become c l e a r i n the d e s c r i p t i o n of the development o f an i s o l e u c i n e - p r o d u c i n g strain later i n this a r t i c l e . However, i n the sense of the word " r e g u l a t i o n " as used here, t h i s example would not be considered a r e g u l a t o r y mechanism. Just as p h y s i o l o g i c a l patterns of c o n t r o l over metabolite flow can be recognized, so can p h y s i o l o g i c a l patterns of c o n t r o l over the amount of enzyme. Table I I I l i s t s a convenient c l a s s i f i ­ cation. C l e a r l y , the amount o f enzyme a t any time i s a summation of the amount formed and the amount destroyed. Two s p e c i f i c patterns c o n t r o l l i n g formation might be recognized: repression by endproducts and i n d u c t i o n by substrate or a precursor. I t should be s t r e s s e d that the terms " r e p r e s s i o n " and " i n d u c t i o n " are o p e r a t i o n a l and should carry no connotations regarding the mechanisms. In a d d i t i o n , there are general mechanisms c o n t r o l l i n g l a r g e r groups o f enzymes or groups o f pathways. One general mechanism i s involved i n r e p r e s s i n g the formation of carbon- and energyy i e l d i n g pathways when there i s a good carbon and energy source ( t h i s i s b e t t e r known as c a t a b o l i t e repression) (27). An analagous c o n t r o l mechanism i s r e l a t e d to the n i t r o g e n supply, and many i n d u c i b l e c a t a b o l i c pathways y i e l d i n g ammonia are repressed when there i s already an adequate n i t r o g e n supply (21). Another important c o n t r o l mechanism i s that r e l a t e d to growth r a t e . At high growth rates i n a r i c h medium, the ρrotein-forming apparatus (ribosomes, tRNA, etc.) i s high, whereas the enzymes forming the small molecule b u i l d i n g blocks are repressed to an extent much greater than that accounted f o r by the presence o f the endproducts i n the medium (22). Recent s t u d i e s by Neidhardt and h i s colleagues (23) have revealed a newly recognized c l a s s of enzymes i n E. coli that are induced at e l e v a t e d temperatures.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

76

BIOCHEMICAL ENGINEERING Table I I I P h y s i o l o g i c a l Patterns o f Regulation of P r o t e i n Amount T y p i c a l examples

Pattern

Reference

E f f e c t on Enzyme Formation Specific: Repression by endproducts

Repression o f arginine biosyn­ t h e t i c enzymes

(18)

Induction by substrates or precursors

Induction of lac operon

(19)

Histidase induction i n glucose-containing, N ^ - f r e e media

(21)

General: Related to carbon suppl Related to n i t r o g e n supply

(K.

aerogenes)

Related to growth r a t e

Derepression of the protein synthesizing system at f a s t growth rates

(22)

Related to temperature

"Thermometer" p r o t e i n s , which increase o r decrease i n amount with growth temperature

(23)

The s t a b i l i z a t i o n of glutamine phosphoribosylpyrophosphate amidotransferase of

(24)

E f f e c t on Enzyme D e s t r u c t i o n Specific: S t a b i l i z a t i o n by l i g a n d s

B.

subtilis

by

substrates General: Starvation of c e l l s f o r carbon or n i t r o g e n

Increased p r o t e i n turn­ over with onset o f starvation

(25)

Serine protease i n h i b i ­ I n h i b i t i o n of protease (26) activity t o r of ±. υ· B. subtilis *The examples c i t e d are found i n E. coli, except where i n d i c a t e d . Ό

*

S

^

^

»

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

UMBARGER

Microbial

Regulatory

Mechanisms

77

F i n a l l y , the degradation of an enzyme by p r o t e o l y s i s can be modulated i n s p e c i f i c ways through substrate o r product s t a b i l i z a t i o n (24). These would c o n s t i t u t e s p e c i f i c c o n t r o l s over enzyme destruction. I t i s a l s o known that, when c e l l s are starved f o r amino a c i d s , n i t r o g e n , o r energy, there i s increased turnover o f many c e l l p r o t e i n s (25). Such a c o n t r o l might be considered a general one. Some of the mechanisms underlying the p h y s i o l o g i c a l responses l i s t e d i n Table I I I are given i n Table IV. Enzyme d e s t r u c t i o n , which w i l l not be considered f u r t h e r , occurs o f course by proteol y t i c breakdown and, i n that i t can be impeded by ligands ( e i t h e r substrates o r i n h i b i t o r s ) that bind to the p r o t e i n , could be subj e c t to a s p e c i f i c c o n t r o l . P r o t e o l y s i s might be enhanced by f a c t o r s that a c t i v a t e proteases o r r e l e a s e protease i n h i b i t o r s . Such an enhancement might be considered a general c o n t r o l over p r o t e o l y t i c breakdown. The formation o f p r o t e i n regulate , e i t h e r by a f f e c t i n g formation o f mRNA ( t r a n s c r i p t i o n ) or i t s u t i l i z a t i o n as template ( t r a n s l a t i o n ) . In turn, t r a n s c r i p t i o n can be c o n t r o l l e d i n two ways. One i s a c o n t r o l o f i n i t i a t i o n of t r a n s c r i p t i o n ( i . e . , whether the RNA polymerase forms an i n i t i a t i o n complex). The other i s a c o n t r o l over how f a r a polymerase t r a v e l s and whether i t proceeds i n t o a s t r u c t u r a l gene or not ( i . e . , whether a t t e n u a t i o n o f t r a n s c r i p t i o n o c c u r s ) . T r a n s l a t i o n a l c o n t r o l would more l i k e l y be achieved by c o n t r o l l i n g r i b o some b i n d i n g to the mRNA, although mechanisms a f f e c t i n g ribosome t r a v e l are conceivable. Among the molecular mechanisms c o n t r o l l i n g the i n i t i a t i o n of t r a n s c r i p t i o n i n b a c t e r i a that might be considered s p e c i f i c mechanisms o f c o n t r o l are those that i n v o l v e a negative c o n t r o l element, or the repressor of the o r i g i n a l model of Jacob and Monod (44). Two kinds o f c o n t r o l were envisioned i n that model. One i n v o l v e d a repressor p r o t e i n that was a c t i v e only i n the presence o f the endproduct of the pathway. The b e s t - s t u d i e d example i s the product of the trpR gene, which becomes a c t i v e only a f t e r b i n d i n g to tryptophan. The b i n d i n g o f the a c t i v a t e d repressor t o the operator s i t e s o f the trp operon, of the aroH gene, o r o f the trpR gene and the binding o f RNA polymerase to the corresponding promoters are mutually e x c l u s i v e (28). The inverse o f t h i s p a t t e r n i s the i n a c t i v a t i o n of the repressor p r o t e i n by the substrate^ (or a d e r i v a t i v e ) . The b e s t - s t u d i e d example o f t h i s p a t t e r n i s the i n a c t i v a t i o n o f the lac repressor by i t s b i n d i n g o f a l l o l a c t o s e , a d e r i v a t i v e o f l a c t o s e formed by the a c t i o n o f 8-galactosidase on l a c t o s e (29). Although i t was considered as one p o s s i b i l i t y by Jacob and Monod (44) i n t h e i r formulation o f a model f o r c o n t r o l o f gene expression, r e g u l a t i o n by p o s i t i v e c o n t r o l elements was considered a l e s s l i k e l y mechanism f o r c o n t r o l of gene expression. There have been s e v e r a l examples described i n which p o s i t i v e c o n t r o l

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

78

BIOCHEMICAL ENGINEERING Table IV Molecular

Basis of Regulation

Mode o f C o n t r o l

of P r o t e i n Formation T y p i c a l Examples

Reference

Transcriptional Control C o n t r o l of T r a n s c r i p t i o n I n i t i a t i o n Specific: Negative C o n t r o l Elements trp

A c t i v a t e d by endproducts

Repression

I n a c t i v a t e d by substrat or precursor

operon by a l l o l a c t o s e

of the

(28)

P o s i t i v e C o n t r o l Elements A c t i v a t e d by s u b s t r a t e or precursor

Induction of acetohydroxy isomeroreductase by acetohydroxy acids

( I n a c t i v a t i o n by endproduct)

None known

(30)

General: P o s i t i v e C o n t r o l Elements A c t i v a t e d by cAMP

Dependence of lac operon i n d u c t i o n on cAMP-CRP i n t e r a c t i o n

(31)

A c t i v a t e d by temperature

Dependence of s e v e r a l heat-induced p r o t e i n s on the htp gene product

(32)

σ-Like p r o t e i n s

S h i f t o f RNA polymerase s p e c i f i c i t y by B a c i l l i during s p o r u l a t i o n

(33)

[ppGpp-mediated regulation]

I n h i b i t i o n of RNA polymerase b i n d i n g to rrn promoters. Enhancement of polymerase pausing i n rrn opérons

(34)

[Nitrogen-mediated regulation]

(35)

The glnG-dependent a c t i v a - (36) t i o n of genes i n v o l v e d i n catabolism of n i t r o g e n c o n t a i n i n g compounds

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

UMBARGER

Microbial

Regulatory

79

Mechanisms

Table IV, cont'd. Control of Transcription

Termination

General: p-Dependent

termination

trpt* terminator of trp operon t

p-Independent

termination

Transient terminâtion polymerase pausing

R 1

terminator

a t end

of λ

Termination o f t r a n s c r i p t i o n at the end of leader sequence f o r amino a c i d b i o s y n t h e t i c operon i n rmB

(37) (38) (39)

operon

Specific: A n t i t e r m i n a t i o n by s p e c i f i c proteins

λ Ν gene-dependent t r a n s c r i p t i o n beyond the tp2 terminator

(41)

A n t i t e r m i n a t i o n by ribosome h a l t at s p e c i f i c codon

Attenuation o f ilv, trp, his, and other amino a c i d b i o s y n t h e t i c codons

(39)

Binding o f small r i b o somal p r o t e i n s a t r i b o ­ some b i n d i n g s i t e f o r the rbsL (str) operon

(42)

Control of T r a n s l a t i o n SpecificMasking of ribosomal b i n d i n g s i t e s by p r o t e i n binding By p e r t u r b a t i o n of secondary s t r u c t u r e of message

The masking o f erm (43) (erythromycin r e s i s t a n c e ) ribosome b i n d i n g s i t e by retarded t r a n s l a t i o n o f the erm leader t r a n s c r i p t

General: (Amino a c i d supply)

None known

(Inhibition)

None known

Mechanisms enclosed i n ( ) may be h y p o t h e t i c a l , s i n c e no examples have been reported. Mechanisms enclosed i n [ ] remain unexplained, i . e . , p r e c i s e mechanism i s unknown.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

80

BIOCHEMICAL ENGINEERING

provides the primary c o n t r o l over expression of a gene. One ex­ ample i s the p o s i t i v e c o n t r o l element ( u p s i l o n , the product of the ilvY gene) required f o r the i n d u c t i o n of acetohydroxy a c i d isomeroreductase, the i n d u c i b l e enzyme i n the i s o l e u c i n e and va­ l i n e b i o s y n t h e t i c pathway of E. coti (30). ( I t should be pointed out that some regulatory elements can play both a p o s i t i v e and a negative c o n t r o l r o l e . An example i s the araC gene product r e ­ q u i r e d f o r i n d u c t i o n of the a r a b i n o s e - u t i l i z i n g pathway (45). In the absence of arabinose, i t acts as a negative c o n t r o l element or repressor, and i n i t s presence i t acts as a p o s i t i v e c o n t r o l element.) Again, the inverse of t h i s p a t t e r n , i n a c t i v a t i o n of a p o s i t i v e c o n t r o l element by the endproduct of a pathway, might provide a mechanism f o r r e p r e s s i o n . However, t h i s w r i t e r i s aware of no example of such a mechanism. Several of the general c o n t r o l formatio * to be achieved by a f f e c t i n no reason to assume tha genera diated v i a p o s i t i v e or negative c o n t r o l elements of broad s p e c i f i ­ c i t y , and i t may be that many are. A w e l l - s t u d i e d example of a p o s i t i v e c o n t r o l element a f f e c t i n g many c a t a b o l i c systems i n bac­ t e r i a i s the i n t e r a c t i o n between cAMP and i t s binding p r o t e i n (CAP), which allows binding of CAP to the DNA near the promoters of c e r t a i n c a t a b o l i c enzymes, a f t e r which RNA polymerase can more r e a d i l y bind (31). The heat-induced p r o t e i n s r e c e n t l y demon­ s t r a t e d i n E. coli by Neidhardt's group may be considered another example (23). The i n d u c t i o n of these enzymes appears to be depen­ dent upon a p o s i t i v e c o n t r o l element s p e c i f i e d by the htp gene (32). Another kind of c o n t r o l has been found to be important i n the B a c i l l i and might be important i n other organisms as w e l l . This i s a c o n t r o l of l a r g e numbers of genes by a l t e r i n g the s p e c i ­ f i c i t y of RNA polymerase by the binding of d i f f e r e n t sigma (σ) f a c t o r s (33). Thus, during the s p o r u l a t i o n phase, the 55-kd σ f a c t o r that i s predominantly bound to RNA polymerase i s replaced by a 29-kd σ f a c t o r which allows some of the s p o r e - s p e c i f i c genes to be expressed. To date, at l e a s t four d i f f e r e n t σ f a c t o r s have been i d e n t i f i e d i n B. siibtiUs. Two other general regulatory mechanisms have been s t u d i e d that appear to a f f e c t t r a n s c r i p t i o n i n i t i a t i o n . Neither, however, are w e l l enough understood to decide whether they might c o n s t i t u t e unique mechanisms or are s p e c i a l cases of p o s i t i v e c o n t r o l e l e ­ ments that exert a g e n e r a l i z e d c o n t r o l r o l e . One i s the ppGppmediated r e g u l a t i o n that impedes s t a b l e (ribosomal and t r a n s f e r ) RNA formation and, at l e a s t i n v i t r o , stimulates t r a n s c r i p t i o n of many b i o s y n t h e t i c and c a t a b o l i c opérons. While ppGpp does prevent RNA polymerase binding to s t a b l e RNA promoters, the pronounced e f f e c t of ppGpp on s t a b l e RNA formation cannot s o l e l y be explained on t h i s b a s i s alone (see below) (34,35). The other i s the c o n t r o l that i s an e f f e c t of n i t r o g e n l i m i t a t i o n and leads to the expression of genes involved i n r e l e a s i n g NH3 from n i t r o g e n -

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

UMBARGER

Microbial

Regulatory

Mechanisms

81

containing compounds (36). The glnG gene i s somehow i n v o l v e d , but whether that product i s a p o s i t i v e c o n t r o l element a c t i n g i n a way analogous to that by which cAMP bound to CAP acts on carbon and energy producing pathways i s not c l e a r . Table IV a l s o l i s t s some o f the f a c t o r s that c o n t r o l t r a n s c r i p t i o n termination. T r a n s c r i p t i o n termination plays two r o l e s . One, of course, i s the termination that occurs a short distance beyond the end of a given s t r u c t u r a l gene or beyond the end of the operon. The other i s a termination that serves to attenuate the t r a n s c r i p t or to terminate t r a n s c r i p t i o n at a s i t e upstream of that at which the maximal-sized t r a n s c r i p t i s terminated (39). I t i s the modulation of the l a t t e r kind o f t r a n s c r i p t i o n termination that provides an important mechanism of t r a n s c r i p t i o n a l c o n t r o l . T r a n s c r i p t i o n termination i s s i g n a l l e d by e i t h e r p-dependent or p-independent sequence i th (and RNA) Th l a t t e r e a d i l y recognized as region y i e l d stem and loop s t r u c t u r e y sequenc of s e v e r a l u r i d i n e residues i n which t r a n s c r i p t i o n i s terminated (46). p-Dependent termination s i t e s seem to be c h a r a c t e r i z e d by t r a n s c r i p t s with more weakly base-paired stem and loop s t r u c t u r e s near the termination s i t e i n the t r a n s c r i p t s and with l e s s p r e c i s e p o i n t s of termination than those found i n p-independent terminat i o n s i t e s (47,48). C l o s e l y r e l a t e d to the s i t e s of p-dependent and p-independent termination s i t e s are s i t e s at which pausing o f RNA polymerase occurs. Pausing i s a l s o apparently c h a r a c t e r i s t i c of termination s i t e s , but the " r u l e s " f o r polymerase pausing are even l e s s c l e a r than those f o r termination (40,49). Polymerase pausing and t r a n s c r i p t i o n termination can thus a f f e c t the extent to which the DNA downstream of the pausing or termination s i t e are t r a n s c r i b e d independently of the t r a n s c r i p t i o n i n i t i a t i o n event. That pausing or termination can be modul a t e d allows a c o n t r o l of the process. I t i s an enhancement by ppGpp o f polymerase pausing at a s i t e e a r l y i n ribosomal RNA opérons that may account f o r the s t r i k i n g e f f e c t that t h i s nucleot i d e has on the s y n t h e s i s of s t a b l e RNA over and above that which occurs a t the polymerase b i n d i n g step (40). The prolonged pausing of polymerase progress at a s p e c i f i c p o i n t has been termed " t u r n s t i l e " attenuation. S i m i l a r l y , when termination at a s i t e w i t h i n an operon or a t the end o f a leader region i s a f f e c t e d by a s p e c i f i c r e g u l a t o r y s i g n a l , an e f f i c i e n t c o n t r o l can be achieved. One of the most s t u d i e d c o n t r o l s over a p-dependent termination i s that which occurs at the XtRl s i t e and i s prevented by the λ Ν gene product (41). L i k e the a c t i v i t y of ρ i t s e l f , the a c t i v i t y of the Ν gene product i s dependent on the elongation subunit of RNA polymerase s p e c i f i e d by the E. coli, nusA gene. I t might be a n t i c i p a t e d that a t t e n u a t i o n of t r a n s c r i p t i o n by a s p e c i f i c a n t i t e r m i n a t i n g p r o t e i n i s a general p a t t e r n that w i l l be found to occur frequently i n m i c r o b i a l systems.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

82

BIOCHEMICAL ENGINEERING

Another c o n t r o l over termination that has been e x t e n s i v e l y s t u d i e d i s the attenuation of t r a n s c r i p t i o n at the end of the leader regions of s e v e r a l amino a c i d b i o s y n t h e t i c opérons (or genes) i n E. coli and r e l a t e d organisms (39). The primary i n d i c a t i o n that such a mechanism i s involved i n the c o n t r o l of an amino a c i d b i o s y n t h e t i c pathway i s an endproduct r e p r e s s i o n that i s dependent on the amino a c i d being t r a n s f e r r e d to i t s cognate tRNA at an ample r a t e . Thus, derepression of the h i s t i d i n e biosynthet i c pathway can be achieved by any mechanism that reduces the i n t r a c e l l u l a r l e v e l of h i s t i d y l tRNA, f o r example, by l i m i t i n g the supply of h i s t i d i n e i t s e l f or by l i m i t i n g the a c t i v i t y of the h i s t i d y l tRNA synthetase (51). Thus f a r , the amino a c i d b i o s y n t h e t i c genes c o n t r o l l e d i n t h i s way are c h a r a c t e r i z e d by the presence of a leader region between the promoter and the s t r u c t u r a l gene (52,53) The leader i s t r a n s c r i b e d at a frequenc polymerase a v a i l a b i l i t t i o n i n i t i a t i o n i t s e l f i s c o n t r o l l e d by the trp repressor). The leader t r a n s c r i p t c a r r i e s the information f o r a short peptide that i s unusually r i c h i n the amino a c i d ( s ) f o r which the pathway i s concerned. Whether RNA polymerase stops at the end of the leader or proceeds i n t o the s t r u c t u r a l gene i s dependent upon whether a ribosome can t r a n s l a t e the leader t r a n s c r i p t to the stop codon (amino a c i d excess) or i s s t a l l e d at a codon f o r the amino a c i d for which the pathway i s concerned (amino a c i d l i m i t a t i o n ) . The mechanism underlying termination i s that competing secondary s t r u c t u r e s of the leader t r a n s c r i p t are s e l e c t e d by the extent of ribosomal t r a v e l and that one of these a l t e r n a t i v e secondary s t r u c t u r e s contains a t y p i c a l ρ (rho)-independent termination s i g ­ nal. The general features have been studied best i n the amino a c i d b i o s y n t h e t i c opérons of s e v e r a l Enterobacteriaceae (39). Although the nature of the b a c t e r i a l c e l l makes p o s s i b l e spec i f i c c o n t r o l over t r a n s c r i p t i o n i n ways that cannot be achieved i n eukaryotic systems, c o n t r o l of gene expression at the l e v e l of t r a n s l a t i o n i s a l s o important i n b a c t e r i a . Control of t r a n s l a t i o n i s achieved p r i m a r i l y by the prevention of ribosomal binding. Such a c o n t r o l might be achieved by masking the binding s i t e e i t h e r by s p e c i f i c b i n d i n g by p r o t e i n s or by the secondary s t r u c ture of the message i t s e l f . The b e s t - s t u d i e d examples are the ribosomal p r o t e i n s (54). Although the genes f o r a l l ribosomal p r o t e i n s have not yet been examined, the general pattern that seems to be emerging i s that one of the ribosomal p r o t e i n s s p e c i f i e d by a m u l t i c i s t r o n i c , ribosomal p r o t e i n operon prevents message t r a n s l a t i o n by binding at the t r a n s l a t i o n a l s t a r t s i t e on the message. The b a s i s for the s p e c i f i c binding i n the case of r i b o somal p r o t e i n s S4 and S7 i s that the RNA i n the v i c i n i t y of the ribosomal s t a r t s i t e has a s t r u c t u r e s t r o n g l y homologous to that of the region on 16S RNA that binds to S4 (or to S7) during r i b o some assembly (42). The c o n t r o l over the erythromycin r e s i s t a n c e gene, which

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

UMBARGER

Microbial

Regulatory

Mechanisms

83

s p e c i f i e s a ribosomal methylase, i s a l s o achieved by i n t e r f e r i n g with t r a n s l a t i o n of the message (43). Masking of the ribosome masking s i t e i s not by a p r o t e i n binding to i t but by a secondary s t r u c t u r e o c c u r r i n g i n the message whenever a t r a n s l a t i n g ribosome i s able to t r a n s l a t e the peptide s p e c i f i e d by the leader sequence (as could occur only i f already modified ribosomes were f u n c t i o n ing i n the presence of erythromycin or i f normal ribosomes were f u n c t i o n i n g i n the absence of erythromycin). The ribosome binding s i t e of the methylase message would be opened when the t r a n s l a t i n g ribosome s t a l l e d i n the e a r l y part of the leader (as could occur i f unmodified, s e n s i t i v e ribosomes were f u n c t i o n i n g i n the presence of erythromycin). This mechanism, a f f e c t i n g a c c e s s i b i l i t y of a ribosome b i n d i n g s i t e i s thus reminiscent of the c o n t r o l of formation of a t r a n s c r i p t i o n termination s i t e by the t r a n s l a t i o n of the leader sequence of l amin a c i d b i o s y n t h e t i described above. These examples are a small sample of many that could be c i t e d that make i t q u i t e c l e a r that m i c r o b i a l metabolism i s r a t h e r r i g i d l y c o n t r o l l e d f o r the primary f u n c t i o n of the microbe: to grow and reproduce i t s e l f as e f f i c i e n t l y as p o s s i b l e . These are what I would term obstacles to the biochemical engineer who may wish to e x p l o i t a p a r t i c u l a r enzyme r e a c t i o n or a p a r t i c u l a r pathway to a f u n c t i o n that may w e l l be detrimental to the primary f u n c t i o n of the organism. However, i n every case, the c o n t r o l mechanisms that c o n s t i t u t e these o b s t a c l e s are g e n e t i c a l l y cont r o l l e d and, t h e r e f o r e , are subject to mutation. To the extent that mutations can be s e l e c t e d that are advantageous to the engineer without being l e t h a l to the organism, these c o n t r o l mechanisms can be considered " t o o l s to be manipulated and c a r e f u l l y honed. It i s , however, sometimes d i f f i c u l t to e x p l o i t the capacity of an organism to perform a u s e f u l biochemical transformation. Often Nature has s e l e c t e d organisms i n which the s t r i c t u r e s found i n most organisms are modified, and the organism occupies a unique niche. Such organisms, i f discovered, can serve u s e f u l f u n c t i o n s . Just such organisms are those that are c u r r e n t l y being used i n the Japanese amino a c i d fermentation i n d u s t r y . In most cases, the organisms have been i s o l a t e d and i d e n t i f i e d by e m p i r i c a l research and screening procedures. In some cases, the b a s i s f o r the nonnormal formation of amino a c i d s can be explained post facto, but seldom does i t appear that these organisms were developed by a preconceived, r a t i o n a l approach. I would t h e r e f o r e l i k e to c i t e and analyze what I think provides an exception. The e x c e p t i o n a l case i s one i n which the i n v e s t i g a t o r s j u d i c i o u s l y combined e m p i r i c a l and r a t i o n a l approaches to prepare an organism capable of producing l a r g e amounts of the amino a c i d i s o l e u c i n e . The p r o j e c t was performed by i n v e s t i g a t i o n at the Tanabe Seiyeku Company i n Osaka, Japan, and i n v o l v e d the organism Serratia marcescens (55). Before review of t h i s work, i t i s necessary to consider b r i e f l y s e v e r a l aspects of the pathways by which 11

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

84

i s o l e u c i n e and the c l o s e l y r e l a t e d amino a c i d , v a l i n e , are formed. Figure 1 shows these pathways. An important feature i s that the four steps l e a d i n g to v a l i n e are c a t a l y z e d by enzymes that are a l s o needed f o r i s o l e u c i n e formation. In a d d i t i o n , a f i f t h enzyme, threonine deaminase, i s r e q u i r e d i n most p l a n t s and micro­ organisms f o r the formation of α-ketobutyrate. Several d e t a i l s of the pathways are given i n the legend. Also shown i n Figure 1 i s the arrangement of the s t r u c t u r a l genes found i n E. coli. I t should be pointed out that a l l of the genes, except those f o r the two v a l i n e - i n s e n s i t i v e acetohydroxy a c i d synthases, are contained i n the ilv gene c l u s t e r at the 84minute region of the E. coli chromosome. I t might t h e r e f o r e be a n t i c i p a t e d that an E. coli s t r a i n c a r r y i n g a plasmid with the ilv gene c l u s t e r would be an e x c e l l e n t overproducer of v a l i n e . (If the chromosomal ilv fragment derived fro th K-12 s t r a i of E. coli i t would hav would be expressed. Se more e f f e c t i v e i f the i n s e r t e d DNA c a r r i e d an ilvA lesion, i . e . , was threonine deaminase negative. Overproduction of v a l i n e would be expected, s i n c e the v a l i n e pathway derives i t s carbon e x c l u ­ s i v e l y from a key intermediate i n the c e n t r a l metabolic route, pyruvate. Flow i n t o the pathway would then never be r e s t r i c t e d as long as ample carbon source was present. An analogous c o n d i t i o n f o r i s o l e u c i n e overproduction would not be expected to a r i s e i f the corresponding plasmid c o n t a i n i n g an ilvA s t r u c t u r a l gene mutation l e a d i n g to a feedback negative threonine deaminase were to be employed. As can be seen i n Figure 2, carbon flow i n t o the i s o l e u c i n e pathway i s dependent not only on the supply of pyruvate but a l s o on threonine, an endproduct i t s e l f , and the s y n t h e s i s of which i s a l s o s t r i n g e n t l y r e g u l a t e d . It i s doubtful whether threonine could be formed f a s t enough i n an otherwise normal c e l l to e x p l o i t f u l l y the high l e v e l expres­ s i o n of the ilv genes c a r r i e d on a plasmid as d e s c r i b e d here. The procedures followed by Komatsubara and h i s coworkers i l l u s t r a t e s w e l l how t h i s k i n d of o b s t a c l e can be circumvented. The sequence of manipulations employed by Komatsubara et a l . (55) i s summarized i n Figure 3. The simplest step was to i s o l a t e a d e r i v a t i v e o f the parent S. maroeeoens s t r a i n , 8000, that was derepressed f o r the ilvGEDA operon and c a r r i e d a l e s i o n i n the ilvA gene that allowed the formation of an i s o l e u c i n e - i n s e n s i t i v e (feedback negative) threonine deaminase ( T D ) . This kind of i s o ­ l a t i o n had e a r l i e r been accomplished by the s e q u e n t i a l s e l e c t i o n of an aminobutyrate-resistant s t r a i n (derepressed) followed by s e l e c t i o n of an i s o l e u c i n e hydroxamate-resistant d e r i v a t i v e (feed­ back r e s i s t a n t ) (58). The i n v e s t i g a t o r s were more fortunate i n the s e l e c t i o n of s t r a i n GIHVL-r6426, which arose as an i s o l e u c i n e hydroxamate-resistant s t r a i n a f t e r mutagenesis by n i t r o s o g u a n i dine, a mutagen known f o r causing c l o s e l y l i n k e d mutations i n the same c e l l . The p r e c i s e nature of the mutation a l l o w i n g derepres­ s i o n was not e s t a b l i s h e d , but, i n analogy with what has been y

r

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Ο

L-Threonjne

3

AHSU

3

3

Ο

3

CH

I

AHSm

—ι—-pi

H

a - Aceto - a hydroxybutyrate

2

CH

CH -C-C-COO"

3

a-Acetolactate

CH

CH -C-C-C00~

Ο OH

Β AHSI

I—; 1

IR

IR

3

Ο Ο

3

2

Y

A

D

OH

DH ι

Ο -CH-C-COO"

E

CH

2

3

ÇH

q

a

e

G G G Gp

a-Keio-βmethy I valerate

3

CH -CH-C-COO"

CH, a-Ketoisovalerate

3

CH

ι—:—ι—;—ι—; —ι ; ι—; —ι—I, t i *ι "i I I ι ι TD DH TrB AHSU

C

CH α,β-Dihydroxy/3-methylvolerote

ι

CH

CH -C-CH-COO" 3

3

CH α,β-Dihydroxyisovalerate

CH -C-CH-COO~

Η Η Ο Ο

TrB

TrC TrB 3

NH

3

3

2

TD (ilvA), threonine deaminase; AHS I (ilvB) and AHS III (ilvHI), valine-inhibited acetohydroxy acid jynthases; AHS II (ilvG), valine-insensitive acetohydroxy acid synthase; IR (ilvC), acetohydroxy acid isomeroreduc~' tase; DH (ilvD), dihydroxy acid dehydrase; TrB (ilvE), transaminase B; TrC, transaminase C. In E. coli strain K-12, ilvG exhibits no activity owing to a polar lesion in the ilvO region of the gene. Certain frameshift mutations in ilvO result in ilvG expression and increased downstream expression. Control of the ilvGEDA operon occurs by attenuation at ilvGa of transcripts initiated at the promoter ilvGp. A putative 32-residue leader peptide, rich in isoleucirte, leucine, and valine is specified by ilvGe. The ilvY product, μ, is a positive control element needed for induction of ilvC by the substrates of its product, IR.

L- Isoleucine

CH

ι

CH

CH -CH-CH-COO" 3

ι

CH L- Valine

3

NH CH, -CH-CH-COO"

IR Figure 1. Biosynthesis of isoleucine and valine. The enzymes catalyzing the indicated steps are abbreviated, and the corresponding structural genes (where known) are indicated in parentheses as follows.

CH -CH - CH-COO"

3

TD-*-NH

a-Ketobutyrote

CH -CH-C-COO

3

Pyruvote

3

CH -C-COO'

3

CH -C-COO Pyruvate

AHSU

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

!

h a t e

BJdapB

Dihydrodipicolinic acid

Aspartic wVAjr ' semialdehyde

L-Lysine

cJ/ysA

meso-diaminopimelate

LL-Diaminopimelate

Ε I dapE

N-succinyl-LLdiaminopimelate

DjcfapC or D

N-succinyl- '' L-Aspartate r> Aspartyl metLM "~f"* P P

4.

UMBARGER

Microbial

Regulatory

87

Mechanisms

THREONINE AND ISOLEUCINE PRODUCING STRAINS (Komatsubara et a l . ) AECrl74

N-ll

uth ilvA

KNr31

uth ilvA

uth ilvA

?(Met-leaky)

? (Met-leaky)

r

lysC (AK )

?(Met-leaky) 0.3 g T h r / 1

r

lysC (AK )

T-570

HNr21

T-693

uth ilvA

uth ilvA

r

r

r

thrA (AK HD )

uth ilvA

r

thrA (AK HD )

?(Itet-leaky)

ileS

11 g T h r / 1

r

lysC (AK ) lyeCo ?

8 g Thr/1

r

r

thrA (AK HD )

île S 25 g T h r / 1 HNr59

E-60

uth ilvA thrA (HD ) ileS r

5 g Thr/1

uth ilvA thrA (HD ) ileS thrB/C r

T-803 r

GIHVL-r6426 r

ilvA (TD ) ilvGa ? Mu-910

uth

3.5 g I l e / 1 8000

uth ilvA (TD ) ilvGa ? ?(Met-leaky) r

lysC (AK ) lysCo ? r

r

thrA (AK HD )

ileS 25 g I l e / 1

Figure 3. The development of an isoleucine-producing strain from S. marcescens strain 8000. Key: φ, phage-mediated transduction; M , nitrosoguanidine mutagenesis. See text for details.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

88

BIOCHEMICAL ENGINEERING

learned about the c o n t r o l of the ilvGEDA operon i n E. coli, i t is most l i k e l y a mutation a f f e c t i n g the attenuator (ilvGa), thereby a b o l i s h i n g the m u l t i v a l e n t c o n t r o l of the p a r e n t a l s t r a i n . That ilvGy the s t r u c t u r a l gene f o r the v a l i n e - i n s e n s i t i v e acetohydroxy a c i d synthase, was derepressed assured that acetohydroxy a c i d i s o meroreductase would be h i g h l y induced by s u b s t r a t e , even though i t s s t r u c t u r a l gene, ilvC i s not part of the derepressed operon. The r e s i s t a n t mutant was shown to excrete up to 3.5 gm of i s o l e u cine per l i t e r i n a minimal medium c o n t a i n i n g 150 gm of sucrose as carbon source. That t h i s l e v e l was l i m i t e d by a v a i l a b i l i t y of threonine was l a t e r demonstrated by the f a c t that t r a n s f e r of the two l i n k e d ilv mutations to a s t r a i n overproducing l a r g e q u a n t i t i e s of threonine r e s u l t e d i n a much b e t t e r i s o l e u c i n e producer. The steps used to develop the threonine producer were complex and are a l s o o u t l i n e d i F i g u r 3 Th f i r s t f thes step the i s o l a t i o n of n i t r o s o g u a n i d i n l i z e threonine as a n i t r o g e (59) was i n the uth gene, which s p e c i f i e s threonine dehydrogenase. To obtain an organism even l e s s able to break down exogenous t h r e o nine, mutagenesis to y i e l d an i s o l e u c i n e - r e q u i r i n g s t r a i n l a c k i n g threonine deaminase was employed. When preformed threonine was added to f u l l y grown c u l t u r e s of the r e s u l t i n g s t r a i n , D-60, the r a p i d disappearance noted with the o r i g i n a l parent s t r a i n was no longer observed (59). S t r a i n D-60 was then used to s e l e c t mutants r e s i s t a n t to the threonine analog, 3-hydroxynorvaline, f o l l o w i n g n i t r o s o g u a n i d i n e mutagenesis (60,61). Three kinds of r e s i s t a n t s t r a i n were saved for subsequent use. One of these (HNr31) had an incomplete but undefined b l o c k i n methionine b i o s y n t h e s i s , which may have accounted f o r the s m a l l amount o f threonine that was accumulated from homoserine being funneled i n t o the threonine pathway. The other two mutants produced much g r e a t e r amounts of threonine. One, s t r a i n HNr21, appeared to contain a s i n g l e mutation i n the thrA gene, which s p e c i f i e s the b i c e p h a l i c enzyme, a s p a r t o kinase I-homoserine dehydrogenase I (Figure 2). Normally, both of these a c t i v i t i e s are i n h i b i t e d by threonine. The mutation i n s t r a i n HNr21 a b o l i s h e d the threonine s e n s i t i v i t y f o r both a c t i v i ties. This l o s s of feedback c o n t r o l r e s u l t e d i n an overproduction of threonine to an extent of 11 gm of threonine per l i t e r . The other s t r a i n , HNr59, a l s o had a thrA l e s i o n , but t h i s one appeared to a b o l i s h only the threonine s e n s i t i v i t y of the homoserine dehydrogenase. There was another mutation i n the same s t r a i n which appeared to be i n the ileS gene. I f so, i t undoubtedly caused the corresponding gene product, i s o l e u c y l tRNA synthetase, to have a reduced a f f i n i t y f o r i t s s u b s t r a t e . Such an enzyme would l e a d to reduced l e v e l s o f i s o l e u c y l tRNA and derepressed l e v e l s of the thr operon and the ilvGEDA operon. Since the mutant was an ilvA mutant, the concomitant derepression of the ilvGEDA operon was of no consequence. However, the iVoA mutation made i t necessary f o r the s t r a i n to be grown i n the presence of exogenous i s o l e u c i n e and may 9

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

UMBARGER

Microbial

Regulatory

Mechanisms

89

have reduced the e f f e c t i v e n e s s of the l o w - a f f i n i t y i s o l e u c y l tRNA synthetase i n causing a derepression of the threonine b i o s y n t h e t i c enzymes. In an attempt to enhance threonine production, steps were taken to r e p l a c e the thrA gene mutation a f f e c t i n g only homoserine dehydrogenase I a c t i v i t y i n s t r a i n HNr59 with that of s t r a i n HNr21, which a f f e c t e d both aspartokinase I and homoserine dehydrogenase I a c t i v i t i e s . This t r a n s f e r was accomplished by i n t r o ducing a thrB (or C) mutation i n HNr59, to y i e l d s t r a i n E-60 (62). This s t r a i n then served as r e c i p i e n t f o r phage-mediated transduct i o n with s t r a i n HNr21 as donor. The r e s u l t i n g s t r a i n , T-570, contained the doubly i n s e n s i t i v e aspartokinase I-homoserine dehydrogenase I a c t i v i t i e s of s t r a i n HNr21 but had not l o s t the c l o s e l y l i n k e d ileS l e s i o n of s t r a i n E-60 (or i t s parent, HNr59). Surprisingly, this strain did t produc q u i t h threonin did s t r a i n HNr21. Attempts were t h e r e f o r threonine pathway by enhancing the a c t i v i t y of the l y s i n e - s e n s i t i v e aspartokinase. This was accomplished by s e l e c t i n g n i t r o s o guanidine- induced mutants r e s i s t a n t to aminoethylcysteine (61). One of these s t r a i n s , AECrl74, was probably another doubly mutated s t r a i n with a l y s i n e - i n s e n s i t i v e aspartokinase that was a l s o derepressed. The derepression might have been e i t h e r an "up" promoter or an operator mutation i n the lysC gene (as i s suggested i n Figure 3). This s t r a i n accumulated 7 gm of threonine per l i t e r . Mutagenesis to threonine auxotrophy y i e l d e d s t r a i n N - l l , which allowed i n t r o d u c t i o n of the thrA gene and ileS genes of s t r a i n T-570 by phage-mediated t r a n s d u c t i o n (62). The r e s u l t a n t s t r a i n , T-693, produced up to 25 gm of threonine per l i t e r and provided e x a c t l y the k i n d of background that might feed carbon i n t o an i s o l e u c i n e pathway that had l o s t both feedback and r e p r e s s i o n c o n t r o l . This i n t r o d u c t i o n was p o s s i b l e because s t r a i n T-693 c a r r i e d the o r i g i n a l ilvA l e s i o n of s t r a i n D-60. Phage grown on s t r a i n G1HVL-6426 was t h e r e f o r e used to render s t r a i n T-693 i s o l e u c i n e independent. In so doing, both the feedback r e s i s t a n c e of threonine deaminase and the derepression of the ilvGEDA operon were introduced. The r e s u l t i n g s t r a i n , T-803, produced up to 25 gm of i s o l e u c i n e per l i t e r . The carbon flow i n t o the u n c o n t r o l l e d threonine pathway had thus been almost comp l e t e l y d i v e r t e d to i s o l e u c i n e production with only about 3 gm of threonine now being formed by s t r a i n T-803. This r a t h e r i n v o l v e d example serves perhaps as an i n t e r e s t i n g model f o r the way e m p i r i c a l l y generated mutations can be r a t i o n a l l y manipulated to y i e l d u s e f u l organisms. In the example c i t e d , the u s e f u l t o o l of using analogs to s e l e c t s t r a i n s with a l t e r e d c o n t r o l c i r c u i t s was i n v a l u a b l e . There were r e a l l y no unexpected mutations, yet there was no way to p r e d i c t which combination of l e s i o n s would have supplemented each other to have y i e l d e d such p r o l i f i c overproducers. I t may be that the maximally e f f e c t i v e combination was not obtained i n s t r a i n T-803, and i t i s l i k e l y

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

90

BIOCHEMICAL ENGINEERING

that the i n v e s t i g a t o r s t r i e d many more combinations than those that were reported. I n v e s t i g a t o r s are undoubtedly now being tempted to e x p l o i t the use o f recombinant DNA technology to produce s t r a i n s with cert a i n biochemical a c t i v i t i e s enhanced. The lesson the model system described here has f o r such i n v e s t i g a t o r s i s t h a t , i n a d d i t i o n to r e q u i r i n g elevated enzyme a c t i v i t i e s , i t i s a l s o necessary to assure that the c e l l can provide the substrates o r the carbon r e quired f o r the enhanced pathway to f u n c t i o n . The other lesson i s that s t r a i n development w i l l remain l a r g e l y an e m p i r i c a l process but that empiricism w i l l be more r e a d i l y harnessed i f the i n v e s t i g a t o r has a thorough knowledge o f the physiology and biochemist r y o f the process.

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Umbarger, H. E. Scienc Kotlarz, D.; Buc, H. Biochim. Biophys. Acta 1977, 484, 35-48. Anderson, P. M.; Marvin, S. V. Biochemistry 1969, 9, 171-8. Cedar, H.; Schwartz, J . H. J. Biol. Chem. 1969, 244, 4112-21. Hoffler, J . G.; Burns, R. O. J . Biol. Chem. 1978, 253, 124551. Ginsburg, A.; Stadtman, E. R. "The Enzymes of Glutamine Metabolism"; Prusinev, S.; Stadtman, E. R., Ed.; Academic: New York, 1973; p. 9. Crawford, I. P.; Yanofsky, C. Proc. Natl. Acad. Sci. USA 1958, 44, 1161-70. Klungsøyr, L.; Hagemen, J . H . ; Fall, L . ; Atkinson, D. E. Biochemistry 1968, 7, 4035-40. Shen, L. C.; Atkinson, D. E. J . Biol. Chem. 1970, 245, 597478. Pardee, A. B.; Potter, V. R. J . Biol. Chem. 1948, 176, 1085-94. Koch, A. L. J. Theoret. Biol. 1967, 15, 75-102. Monod, J.; Jacob, F. Cold Spr. Harbor Symp. Quant. Biol. 1961, 26, 389-401. Krebs, E. G.; Beavo, J . A. Annu. Rev. Biochem. 1979, 48, 923-59. Garnak, M.; Reeves, H. C. J. Biol. Chem. 1979, 254, 7915-20. Pennincky, M.; Simon, J . P.; Wiame, J . M. Eur. J. Biochem. 1974, 49, 429-42. Atkinson, D. E. Biochemistry 1968, 7, 4030-34. Chapman, A. G.; Fall, L . ; Atkinson, D. E. J . Bacteriol. 1971, 108, 1072-86. Vogel, R. H.; McLellen, W. L.; Hirvonen, A. P.; Vogel, H. J . "Metabolic Pathways," 3rd ed.; Vogel, H. J., Ed.; Academic: New York, 1971, vol. 5, p. 464. Pardee, A. B.; Jacob, F . ; Monod, J. J . Mol. Biol. 1959, 1, 165-78. Nakada, D.; Magasanik, B. J . Mol. Biol. 1964, 8, 105-27.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

4.

UMBARGER

Microbial

Regulatory

Mechanisms

21.

Privai, M. J.; Magasanik, B. J . Biol. Chem. 1971, 246, 628896. 22. Pedersen, S.; Bloch, P. L.; Reeh, S.; Neidhardt, F. C. Cell 1978, 14, 179-90. 23. Herendeen, S. L.; VanBogelen, R. Α.; Neidhardt, F. C. J . Bacteriol. 1979, 139, 185-94. 24. Turnbough, C. L., Jr.; Switzer, R. L. J . Bacteriol. 1975, 121, 115-20. 25. Goldberg, A. L.; St. John, A. C. Annu. Rev. Biochem. 1976, 45, 747-803. 26. Millet, J.; Gregoire, J . Biochimie 1979, 61, 385-91. 27. Magasanik, B. Cold Spring Harbor Symp. Quant. Biol. 1961, 26, 249-56. 28. Squires, C. L.; Lee, F. D.; Yanofsky, C. J . Mol. Biol. 1975, 92, 93-111. 29. Jobe, Α.; Bourgeois 30. Biel, A. J.; Umbarger, H. E. J. Bacteriol. 1981, 146, 718-24. 31. Zubay, G.; Schwartz, D.; Beckwith, J . Proc. Natl. Acad. Sci. USA 1970, 66, 104-10. 32. Neidhardt, F. C.; VanBogelen, R. A. Biochem. Biophys. Res. Commun. 1981, 100, 894-900. 33. Haldenwang, W. G.; Lang, N.; Losick, R. Cell 1981, 23, 61524. 34. Hamming, J.; Ab, G.; Gruber, M. Nucl. Acids Res. 1980, 8, 3947-63. 35. Kingston, R. E.; Nierman, W. C.; Chamberlin, M. J . J . Biol. Chem. 1981, 256, 2787-97. 36. Backman, K.; Chen, Y.-M. ; Magasanik, B. Proc. Natl. Acad. Sci. USA 1981, 78, 3743-47. 37. Wu, A. M.; Christie, G. E.; Platt, T. Proc. Natl. Acad. Sci. USA 1981, 78, 2913-17. 38. Court, D.; Brady, C.; Rosenberg, M.; Wulff, D. L.; Behr, M.; Mahoney, M.; Izumi, S. J . Mol. Biol. 1980, 38, 231-54. 39. Yanofsky, C. Nature 1981, 289, 751-58. 40. Kingston, R. E . ; Chamberlin, M. J . Cell 1981, 27, 523-31. 41. Greenblatt, J.; Li, J . J . Mol. Biol. 1981, 147, 16-20. 42. Nomura, M.; Yates, J . L.; Dean, D.; Post, L. E. Proc. Natl. Acad. Sci. USA 1980, 77, 7084-88. 43. Horinouchi, S.; Weisblum, B. Proc. Natl. Acad. Sci. USA 1980, 77, 7079-83. 44. Jacob, F . ; Monod, J . Cold Spring Harbor Symp. Quant. Biol. 1961, 26, 193-211. 45. Englesberg, E . ; Wilcox, G. Annu. Rev. Genet. 1974, 8, 219-42. 46. Christie, G. E.; Farnham, P. J.; Platt, T. Proc. Natl. Acad. Sci. USA 1981, 78, 4180-84. 47. Calva, E . ; Burgess, R. R. J . Biol. Chem. 1980, 255, 11017-22. 48. Platt, T. Cell 1981, 24, 10-23. 49. Farnum, P. J.; Platt, T. Nucl. Acids Res. 1981, 9, 563-77.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

92

50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62.

ENGINEERING

Umbarger, H. E. "Transfer RNA: Biological Aspects"; S ö l l , D.; Abelson, J . N.; Schimmel, P. R., Ed.; Cold Spring Harbor Laboratory: Cold Spring Harbor, New York, 1980; p. 453. Johnston, H. M.; Barnes, W. M.; Chumley, F. G.; Bossi, L.; Roth, J . R. Proc. Natl. Acad. Sci. USA 1980, 77, 508-12. Bertrand, Κ.; Korn, L . ; Lee, F . ; Platt, T . ; Squires, C. L . ; Squires, C.; Yanofsky, C. Science 1975, 189, 22-26. Zurawski, G.; Elseviers, D.; Stauffer, G. V.; Yanofsky, C. Proc. Natl. Acad. Sci. USA 1978, 75, 5988-92. Yates, J . L.; Nomura, M. Cell 1981, 24, 243-9. Komatsubara, S.; Kisumi, M.; Chibata, I. J . Gen. Microbiol. 1980, 119, 51-61. Leathers, T. D.; Noti, J.; Umbarger, H. E. J. Bacteriol. 1979, 140, 251-60. Cassan, M.; Boy, E.; Borne F Patte J C J Bacteriol 1975, 123, 391-99 Kisumi, M.; Komatsubara, ; Sugiura, ; , Bacteriol. 1972, 110, 761-3. Komatsubara, S.; Murata, K.; Kisumi, M.; Chibata, I. J. Bacteriol. 1978, 135, 318-23. Komatsubara, S.; Kisumi, M.; Murata, K.; Chibata, I. Appl. Environ. Microbiol. 1978, 35, 834-40. Komatsubara, S.; Kisumi, M.; Chibata, I. Appl. Environ. Microbiol. 1979, 38, 777-82. Komatsubara, S.; Kisumi, M.; Chibata, I. Appl. Environ. Microbiol. 1979, 38, 1045-51.

RECEIVED

June 1, 1982

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

5

Mathematical Models of the Growth of Individual Cells Tools for Testing Biochemical Mechanisms

M. L. SHULER and M. M. DOMACH Cornell University, School of Chemical Engineering, Ithaca, NY 14853 The rationale for and development of mathematical models fo potential use o coli in ascertaining the plausibility of basic biological hypotheses is illustrated with respect to the control of the initiation of DNA synthesis and with respect to ammonium ion assimilation. Mechanisms postulated on the basis of in vitro enzymology can be tested for in vivo compatibility using the model. The transient behavior of single-cells to step-up and step-down in glucose or ammonium ion is shown to result in oscillatory responses and hysterisis. Methods to construct population models from single-cell models are discussed. Population models are important to engineering analysis and in relating data for experiments with large populations to the responses of a "typical cell". Why S i n g l e - C e l l Models? The b a s i c conceptual u n i t i n microbiology i s the s i n g l e c e l l . Although m i c r o b i o l o g i s t s and biochemists work with l a r g e populat i o n s of c e l l s , the goal i s g e n e r a l l y to understand the behavior of a " t y p i c a l " c e l l . There i s very l i t t l e d i r e c t data on the growth of i n d i v i d u a l c e l l s - and what data e x i s t s i s o f t e n of* questionable value because the c o n d i t i o n s r e q u i r e d f o r observat i o n s may lead to "unnatural responses". Thus, the behavior o f the " t y p i c a l " c e l l must be i n f e r r e d from the aggregated behavior of the t o t a l p o p u l a t i o n . B i o l o g i s t s u s u a l l y are i n t e r e s t e d i n a s i n g l e aspect of c e l l growth (e.g. p r o t e i n s y n t h e s i s ) . Cells c o n t a i n a complex, n o n l i n e a r , h i g h l y regulated s e r i e s of chemical r e a c t i o n s . Human l o g i c c o n s i s t s of a few l i n e a r s t e p s . I t i s e s s e n t i a l l y impossible f o r the unaided mind to i n t e r r e l a t e p r o t e i n s y n t h e s i s , DNA r e p l i c a t i o n , n u t r i e n t t r a n s p o r t , e t c . i n t o a coherent conceptual model of a c e l l . 0 0 9 7 - 6 1 5 6 / 8 3 / 0 2 0 7 - 0 0 9 3 $ l 1.50/0 © 1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

94

BIOCHEMICAL ENGINEERING

Computer models of s i n g l e c e l l s act as an a i d In b u i l d i n g such conceptual models. Because such models make q u a n t i t a t i v e p r e d i c t i o n s - p r e d i c t i o n s which are experimentally v e r i f i a b l e they serve as good v e h i c l e s to r e v e a l e r r o r s i n e i t h e r b a s i c mechanisms or the manner i n which they are i n t e g r a t e d i n the conceptual model. Population models can be constructed from ensemb l e s of s i n g l e - c e l l models. Such models may be u s e f u l a i d s i n r e l a t i n g the behavior of whole populations to biochemical mechanisms w i t h i n a t y p i c a l c e l l . S i n g l e - c e l l models are p a r t i c u l a r l y w e l l s u i t e d to the conceptual and experimental needs of b i o l o gists. S i n g l e - c e l l models are a l s o of importance to biochemical engineers. The motivation i s d i f f e r e n t from b i o l o g i s t s . Engineers are i n t e r e s t e d i n manipulating a population of c e l l s ; such manipu l a t i o n i s f a c i l i t a t e d b mathematical models that can p r e d i c t the response of the populatio ronment. H i s t o r i c a l l y i n biosystems has sprung from a need to model populations of cells. Population models have inherent l i m i t a t i o n s - l i m i t a t i o n s that can be circumvented by using ensembles of s i n g l e - c e l l models. Population Models. To understand why s i n g l e - c e l l models are u s e f u l i t i s important to review previous attempts at modeling populations. The h i s t o r y and philosophy of modeling as w e l l as the v i r t u e s and f a u l t s inherent i n previous models has been w e l l described i n the l i t e r a t u r e . Among these a r t i c l e s are those by Tsuchiya, F r e d r i c k s o n , & A r i s (1); P a i n t e r & Marr (2); Van Uden (3); G a r f i n k e l , eit a l . (4); F r e d r i c k s o n , Megee, & Tsuchiya (5); N y i r i (6); Boyle & Berthouex (7) ( f o r waste t r e a t ment) ; F r e d r i c k s o n (8) ( f o r s t r u c t u r e d models o n l y ) ; and Bailey (9). One method of c l a s s i f y i n g models i n v o l v e s the concept of " s t r u c t u r e " . Structured models have the inherent a b i l i t y to des c r i b e the p h y s i o l o g i c a l s t a t e of a microorganism or a c u l t u r e of such c e l l s . Unless the p h y s i o l o g i c a l s t a t e can be s p e c i f i e d , the dependence of a c u l t u r e on i t s previous h i s t o r y cannot be accounted f o r . Such dependence on h i s t o r y i s known to be important C5). T y p i c a l l y , s t r u c t u r e i s added to a model by c o n s i d e r i n g the c e l l or c u l t u r e to c o n s i s t of two or more components (e.g. n u c l e i c a c i d s and p r o t e i n , etc.) or to d i s t i n g u i s h between separate c e l l s on the b a s i s of s i z e or age. Any model not i n c o r p o r a t i n g the foregoing p r i n c i p l e i s u n s t r u c t u r e d — f o r example, the well-known Monod model. I t has been shown that unstructured models are a p p l i c a b l e only i n b a l anced growth s i t u a t i o n s (10), which, according to Campbell's (11) d e f i n i t i o n , r e q u i r e s that each component of the c u l t u r e be accumulated at the same r a t e . Unstructured models are never general, give very l i t t l e i n s i g h t i n t o c e l l u l a r mechanisms, and cannot be used to describe l a g and d e c l i n e phases i n batch growth, t r a n s i e n t

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

5.

SHULER AND

DOMACH

Models of Cell

Growth

95

response i n chemostats, or growth i n m u l t i s t a g e continuous c u l t u r e . I f the formation of a product i s dependent on c e l l h i s t o r y and i s not growth a s s o c i a t e d , then an u n s t r u c t u r e d model w i l l be u n s u i t a b l e . Unstructured models have been widely used, however, and have been s u c c e s s f u l when a p p l i e d to the commonly o c c u r r i n g balanced growth s i t u a t i o n s of e x p o n e n t i a l phase batch c u l t u r e and steady-state s i n g l e - s t a g e d continuous c u l t u r e . Two of the f i r s t s t r u c t u r e d models proposed were those by Williams (_L2, 13) and Ramkrishna, F r e d r i c k s o n , & Tsuchiya (14). Both models were d e t e r m i n i s t i c and d e a l t with a nonsegregated b i o mass. A nonsegregated model i s one which does not recognize exp l i c i t l y the e x i s t e n c e of i n d i v i d u a l c e l l s . For example, the contents of a fermenter can be thought of as c o n s i s t i n g of two p h a s e s — o n e b i o t i c and the other a b i o t i c . The b i o t i c phase can then be t r e a t e d as a homogeneous e n t i t y Nonsegregated models of course, cannot make any the e f f e c t s of c e l l geometr easy to handle mathematically, and the o v e r a l l biomass and i t s major components can be determined e x p e r i m e n t a l l y with reasonable accuracy. I t i s obvious to anyone who has m i c r o s c o p i c a l l y examined mic r o b i a l c u l t u r e s that c e l l s are i n d i v i d u a l s and can vary g r e a t l y i n observable p r o p e r t i e s such as c e l l s i z e . Only segregated mode l s can capture t h i s p r o p e r t y . Such models c o n t a i n s t r u c t u r e i n the sense that changes are allowed i n the d i s t r i b u t i o n of s t a t e s among the p o p u l a t i o n i n response to the e x t e r n a l environment. Examples of models u s i n g age as a measure of the index of a c e l l ' s stage i n c l u d e those by Von F o e r s t e r (15); Trucco (16); Yakovlev, et a l . (17); F r e d r i c k s o n & Tsuchiya (18); Kozesnik (19); and Lebowitz & Rubinow (20). C e l l s i z e can a l s o be u t i l i z e d as suggested by Koch & Schaechter (21) and Eakman, et a l . (22). In the above examples only one parameter was used as an index of s t a t e ; i t would be impossible to i n s e r t any i n f o r m a t i o n about biochemical mechanisms i n t o the model. Models which i n c l u d e both s t r u c t u r e and segregation lead to mathematical equations which are extremely d i f f i c u l t to s o l v e even with the a i d of modern high-speed computers. B a i l e y and co-workers (23, 24, 25) have made progress i n circumventing some of these problems. Nonetheless i t appears impossible to prepare p o p u l a t i o n models which would c o n t a i n a h i g h l e v e l of s t r u c t u r e (say more than f i v e components) and s e g r e g a t i o n , and which s t i l l are mathematically tractable. Population models which c o n t a i n both a h i g h - l e v e l of s t r u c ture and segregation are d e s i r a b l e . Such models have the potent i a l to make accurate p r e d i c t i o n s of t r a n s i e n t responses - such p r e d i c t i o n s are important not only f o r process c o n t r o l but may be u s e f u l i n d e s i g n i n g c y c l e d - r e a c t o r s which can have product y i e l d s greater than comparable s t e a d y - s t a t e c u l t u r e s (26, 27). There i s a l s o p r e l i m i n a r y evidence that under some circumstances only a small sub-population of c e l l s produce most of the product (24);

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

96

BIOCHEMICAL ENGINEERING

thus the manipulation of the d i s t r i b u t i o n of sub-populations can be p r e d i c t e d only i f a structured-segregated model i s a v a i l a b l e . Tanner (28) has made persuasive arguments f o r the need f o r more s o p h i s t i c a t e d models t o optimize the design of commercial fermentation processes. He has s t a t e d that commercial fermentat i o n processes have not been s i g n i f i c a n t l y optimized "because there a r e no simple, g e n e r a l , and accurate mathematical models f o r p r e d i c t i n g the c a s u a l e f f e c t s of c o n t r o l v a r i a b l e changes". Furt h e r , he claims that "the establishment of j u s t one of these prof i l e s [pH, temperature, n u t r i e n t , e t c . ] t o optimize a batch f e r mentation i s a n e a r l y impossible task t o perform d i r e c t l y on a process". The use of mathematical models i n c o n j u n c t i o n with modern q u a n t i t a t i v e o p t i m i z a t i o n procedures could circumvent much of the experimental work. The need f o r a good model of b a c t e r i a l growth which could accommodate product formation has been w e l l recognized (e.g. 6^, 23 s u f f i c i e n t l y general t A way to generate h i g h l y structured-segregated models which are mathematically t r a c t a b l e i s to b u i l d p o p u l a t i o n models u s i n g an ensemble of s i n g l e - c e l l models. Such an approach can avoid the generation of i n t e g r a l - d i f f e r e n t i a l equations which are so computationally d i f f i c u l t to s o l v e . Thus, s i n g l e - c e l l models f i l l c e r t a i n r e a l needs of both b i o l o g i s t s and engineers. The advantages of s i n g l e - c e l l models compared to normal p o p u l a t i o n models a r e : 1. e x p l i c i t accounting of c e l l geometry and i t s p o t e n t i a l e f f e c t s of n u t r i e n t t r a n s p o r t ; 2. the a b i l i t y to p r e d i c t temporal events during the d i v i sion cycle; 3. the a b i l i t y to consider the e f f e c t s of s p a t i a l arrangements w i t h i n a c e l l ; 4. and the ease i n which d e t a i l s about biochemical pathways and t h e i r i n t e g r a t i o n and metabolic c o n t r o l can be i n c l u d e d . These advantages make s i n g l e - c e l l models p a r t i c u l a r l y w e l l - s u i t e d to t e s t i n g the p l a u s i b i l i t y of hypotheses about metabolic mechanisms. S i n g l e - c e l l models i n v i t e complexity. T h e i r main disadvantage i s that s i n g l e - c e l l models represent only a " t y p i c a l " c e l l and are adequate r e p r e s e n t a t i o n s of the growth of c e l l populations only i f the moments o f d i s t r i b u t i o n of c e l l u l a r p r o p e r t i e s higher than the f i r s t - o r d e r can be ignored. The l a s t disadvantage i s circumvented by u s i n g an ensemble of s i n g l e - c e l l models t o b u i l d a p o p u l a t i o n model ( i . e . each s i n g l e - c e l l represents some small f r a c t i o n of the t o t a l p o p u l a t i o n ) . I d e a l Model. Having discussed why s i n g l e - c e l l models may be u s e f u l , what c h a r a c t e r i s t i c s should such models have? The f o l l o w ing f e a t u r e s are important: 1. the model must be c o n s i s t e n t with experimentally confirmed observations over a wide v a r i e t y of growth c o n d i t i o n s ,

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

5.

SHULER A N D DOMACH

Models

of Cell

Growth

97

2. the model must have a s t r u c t u r e which can e a s i l y allow the i n c o r p o r a t i o n o f p o s t u l a t e d biochemical mechanisms, 3. the parameters o f the model must be determined d i r e c t l y from independent experiments o r estimated by an o b j e c t i v e s e r i e s of r u l e s (no a d j u s t a b l e parameters), 4. the e f f e c t of c e l l geometry and shape on n u t r i e n t uptake must be included (the e x t e r n a l environment must be e x p l i c i t l y accounted f o r ) , 5. the model must allow f o r the i n c l u s i o n o f randomness i n key metabolic systems, 6. the model must not i n c l u d e a r t i f i c i a l c o n s t r a i n t s such as growth must be e x p o n e n t i a l , the c e l l must maintain a given shape, the c e l l w i l l d i v i d e when the amount of given component doubles, etc., 7. the only s i g n a l t r a t i o n s of v a r i o u s biochemica 8. the model must be mathematically t r a c t a b l e . The model should be a model - not a c o l l e c t i o n of phenomenological equations based on curve f i t s . Examples of S i n g l e - C e l l Models One of the f i r s t examples of i n d i v i d u a l - c e 1 1 models i s that suggested by Von B e r t a l a n f f y (see 1). In h i s model growth was a r e s u l t of competition between the process o f n u t r i e n t a s s i m i l a t i o n and endogenous metabolism. N u t r i e n t uptake was p o s t u l a t e d t o be p r o p o r t i o n a l t o the c e l l ' s surface area and the c o n c e n t r a t i o n of n u t r i e n t i n the a b i o t i c environment and the r a t e of endogenous metabolism was p o s t u l a t e d to be p r o p o r t i o n a l t o c e l l mass. Heinmets (35) suggested i n 1966 a model f o r a s i n g l e c e l l (or the nucleus of an e u c a r y o t i c c e l l ) that incorporated 19 d i f f e r e n t i a l equations. The model contained an amino a c i d p o o l , a n u c l e o t i d e pool f o r RNA s y n t h e s i s , a general i n t r a c e l l u l a r metabolic p o o l , t o t a l p r o t e i n , RNA polymerase, genes f o r s y n t h e s i s of v a r i o u s RNA's, m-RNA (2 t y p e s ) , r-RNA, and t-RNA. The model could respond to step changes i n the e x t r a c e l l u l a r n u t r i e n t p o o l s . The main purpose o f the model was t o examine how a c e l l would change from normal t o abnormal growth. The mechanistic scheme r e f l e c t s the general understanding of c e l l u l a r biochemistry i n 1965 but d i f f e r s somewhat from the present conception of the c e l l . The constants chosen were a r b i t r a r y , and the model was not formulated t o any s p e c i f i c organism, and no attempt was made t o compare the p r e d i c t i o n s t o a c t u a l experimental data. E f f e c t s of c e l l geometry and s i z e on n u t r i e n t uptake were not considered. The c e l l d i v i s i o n hypothesis depends on an imposed c r i t e r i o n to do with the concent r a t i o n s of i n t r a c e l l u l a r components. C e l l d i v i s i o n i s not a " n a t u r a l " response of the model. Davison (36) has solved Heinmets' model with only the d i g i t a l computer and has compared the r e s u l t s with two experimental s i t u a t i o n s . The f i r s t was the

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

98

BIOCHEMICAL ENGINEERING

recovery of an IS. c o l i f o r Mg s t a r v a t i o n , and the second was the e f f e c t of s p l i t r a d i a t i o n doses on Chinese Hamster c e l l s . In both cases reasonable q u a l i t a t i v e p r e d i c t i o n s were obtained from the model. Another example of s i n g l e - c e l l model i s that proposed by Simon (37) i n 1973. He considered only steady-state balanced growth. His model c e l l contained enzymes involved i n d i v i s i o n i n i t i a t i o n , i n the formation of DNA p r e c u r s o r s , and i n RNA synthesis. DNA s y n t h e s i s was i n i t i a t e d when a c r i t i c a l m a t e r i a l accumulated to a t h r e s h o l d value; DNA i n i t i a t i o n caused a l l the t h r e s hold m a t e r i a l to be consumed. Each p r o t e i n s y n t h e s i s r a t e was made p r o p o r t i o n a l to the degree of genome a c t i v a t i o n . The r a t i o of c e l l volume to p r o t e i n was considered constant, and volume growth was forced to be e x p o n e n t i a l . The surface to volume r a t i o was considered constant (a c y l i n d e r without ends) The e f f e c t s of the a b i o t i c environmen value of the growth r a t required to d i v i d e when the amount of each component i s doubled. I n i t i a l c e l l s i z e could be p r e d i c t e d . A short general q u a l i t a t i v e comparison of the model to experimental observations was given; the model was found to be s a t i s f a c t o r y f o r the parameters compared. Weinberg, Z e i g l e r , & L a i n g (38) and Z e i g l e r & Weinberg (39) have attempted to construct a model of an IS. c o l i c e l l . They have considered how the v a r i o u s components of the c e l l might be aggregated. T h e i r c e l l contains e x p l i c i t concentrations f o r c e l l w a l l , DNA, m-RNA, t-RNA, ribosomes, p r o t e i n , amino a c i d s , w a l l prec u r s o r s , n u c l e o t i d e s , ATP, and ADP are shown (38, 39) along with a pool c a l l e d glucose which i n c l u d e s glucose and other small metabolites made from glucose. They c l a i m that t h e i r model of a c e l l d i f f e r s from others i n that the a b s t r a c t i o n i n v o l v e d i n model formulation a r i s e s from the aggregation of v a r i a b l e s r a t h e r than the s e l e c t i o n of subsystems. D i f f e r e n c e and Boolean equations were used to d e s c r i b e the system. Hyperbolic ("saturation k i n e t i c s " ) r a t e forms were not used; f o r example, the r a t e of product i o n of amino a c i d s from glucose was made p r o p o r t i o n a l to the product of glucose, ATP, and enzyme 2 c o n c e n t r a t i o n s . Enzyme a c t i v i t y was modified to simulate an a l l o s t e r i c enzyme by use of Boolean equations. T h e i r c e l l was constrained to grow exponent i a l l y i n volume. A mechanism f o r i n i t i a t i o n of DNA r e p l i c a t i o n was included but none f o r c e l l d i v i s i o n . From the above papers (38, 39) i t i s not c l e a r whether n u t r i e n t uptake was e x p l i c i t l y accounted f o r or not. They (39) d e s c r i b e how they evaluated r a t e constants from the data i n the l i t e r a t u r e . A d i r e c t comparison to experimental data was made (38) f o r s h i f t experiments between v a r i o u s media; r-RNA and DNA concentrations were s a t i s f a c t o r i l y p r e d i c t e d by the model i f feedback c o n t r o l s were i n c l u d e d . Another approach to p r e d i c t i n g the response of a " t y p i c a l " c e l l to a s h i f t i n media has been suggested by Bremer and co-work-

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

5.

SHULER AND

DOM

ACT

Models

of

Cell

Growth

99

ers (40, 41, 42)· They have made extensive measurements of RNA metabolism and p r o t e i n s y n t h e s i s i n IS. c o l i and have c o r r e l a t e d t h e i r r e s u l t s with phenomenological expressions. These expressions coupled with s i m i l a r r e l a t i o n s h i p s suggested by other workers (e.g. Cooper and Helmstetter (43)) allow r a t h e r accurate c a l c u l a t i o n of c e l l s i z e and composition f o r u n r e s t r i c t e d growth i n media of v a r i o u s compositions. These expressions appear to be u n s a t i s f a c t o r y f o r growth r e s t r i c t e d by a l i m i t i n g n u t r i e n t as glucose (41). The above expressions do not e x p l i c i t l y depend on the e x t e r n a l environment; the growth r a t e which a media w i l l support must be known beforehand. These expressions are r e a l l y c o r r e l a t i o n s r a t h e r than a t r u e model. They are l i m i t e d to a narrow range of growth c o n d i t i o n s and are not p o t e n t i a l l y as general as the other models d i s c u s s e d . Another type of s i n g l e - c e l Nishimura and B a i l e y (24) c e l l mass and DNA content are e x p l i c i t l y recognized. Rules con cerning DNA r e p l i c a t i o n and the timing of i n i t i a t i o n DNA s y n t h e s i s are imposed on the c e l l ; the r u l e s are d e r i v e d from the observat i o n s of Cooper and Helmstetter (43) and Donachie (44). The s i n g l e - c e l l model was e s s e n t i a l l y the b a s i s f o r the c o n s t r u c t i o n of a p o p u l a t i o n model - a formulation among the most general c u r r e n t l y a v a i l a b l e . The main l i m i t a t i o n of the model i s i t s i n a b i l i t y to permit an e x p l i c i t c a l c u l a t i o n of each c e l l ' s growth r a t e i n terms of the e x t e r n a l environment and the c e l l ' s p h y s i o logical state. Ho and Shuler (45) proposed a mathematical model f o r the growth of an i n d i v i d u a l bacterium i n c o r p o r a t i n g feedback c o n t r o l of n u t r i e n t uptake. T h i s simple model could p r e d i c t the growth p a t t e r n f o r a c e l l of a given shape (filamentous, b a c i l l u s , or s p h e r i c a l ) . The model c e l l contained four components (ammonium ion, glucose, p r e c u r s o r s , and macromolecules). An a n a l y t i c a l s o l u t i o n was p o s s i b l e f o r filamentous c e l l s , but numerical s o l u t i o n s were r e q u i r e d f o r other c e l l shapes.t More r e c e n t l y Shuler, Leung, and Dick (46) have presented a more complete model f o r the growth of a s i n g l e - c e l l of E s c h e r i c h i a c o l i B/r A. The model contained 14 components. A l l of the c e l l ' s components were included i n one of the model components. The model c e l l r e l i e d on chemical concentrations as c o n t r o l s i g n a l s so that the growth p a t t e r n , timing of DNA s y n t h e s i s , c e l l shape, c e l l s i z e , c e l l composition, and c e l l d i v i s i o n could be considered n a t u r a l responses to e x p l i c i t changes (e.g. glucose concentration) i n the e x t e r n a l environment. An attempt was made to evaluate k i n e t i c parameters from independent measurements on e x p o n e n t i a l l y growing c e l l s . Four parameters, having to do with c e l l envelope tThe example c i t e d i n Equation B9-B14 of Ho and Shuler (45) i s f a u l t y . However, i t i s easy to demonstrate that the c o n c l u s i o n i s c o r r e c t . D e t a i l s of the c o r r e c t e d example are a v a i l a b l e upon request.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

100

and c r o s s - w a l l formation were taken as a d j u s t a b l e . model i s being f u r t h e r developed.

T h i s prototype

The C o r n e l l S i n g l e - C e l l Model The prototype model has been revamped. The base model has 20 components; the a d d i t i o n a l components are necessary to allow an accurate d e s c r i p t i o n of the systems a l l o w i n g the i n c o r p o r a t i o n of ammonium i o n i n t o amino a c i d s , to allow more accurate estimates of c e l l u l a r energy expenditures, and to allow a more complete s i m u l a t i o n of systems c o n t r o l l i n g t r a n s c r i p t i o n and t r a n s l a t i o n . Some of the parameters i n the prototype model (46) were c a l c u ­ l a t e d based on c e l l dimensions obtained f o r c e l l s f i x e d i n osmium t e t r o x i d e ; these have been r e c a l c u l a t e d u s i n g s i z e parameters obtained from g l u c o s e - l i m i t e d chemostat c u l t u r e with g l u t e r aldehyde-fixed c e l l s . F i g u r e 1 and Tables I to IV d e s c r i b e the current model. J u s t i f i c a t i o n of parameter values have been given elsewhere (4650). Almost a l l parameters were estimated from independent measurements on e x p o n e n t i a l l y growing c e l l s or c e l l - f r e e systems. Values f o r η2 and η (parameters a s s o c i a t e d with the r a t i o of envelope used f o r extension and c r o s s - w a l l formation) were r e ­ quired to be p o s i t i v e but were otherwise considered a d j u s t a b l e . Values f o r and K p ^ were adjusted w i t h i n the range of 0 to 3

A2

0.05

gm/cc of c e l l volume.

Values f o r η 2 , r\

39

, and

K

p

| > A 2

were estimated by comparing data to model p r e d i c t i o n s at y = 0.95 hr and μ = 0.5 h r " . A parameter f o r u n i d e n t i f i e d energy consumption, 6^ was i n c l u d e d to make the p r e d i c t e d growth y i e l d 1

1

9

1

at μ = 0.95 hr match experimental measurements. Values f o r iIF* * * * ZMi» l * experimental growth data f o r μ < 0.95 hr but were evaluated independently of the model's p r e ­ d i c t i o n s . A l l parameters were set based on g l u c o s e - l i m i t e d growth o n l y . No f u r t h e r adjustments were made f o r p r e d i c t i o n of ammonium i o n - l i m i t e d growth. The model makes reasonable p r e d i c t i o n s of the dependence of c e l l s i z e , c e l l shape, c e l l composition, growth r a t e , and the timing of c e l l u l a r events on e x t e r n a l concentrations of glucose. Results f o r g l u c o s e - l i m i t e d growth are given elsewhere (47, 50). The c u r r e n t model makes use of recent observations of F r a l i c k (51), Messer, et a l . (52) , and Fayet & Louarn (53) to construct a mechanism f o r the c o n t r o l of the i n i t i a t i o n of DNA s y n t h e s i s . The scheme i s i l l u s t r a t e d i n Figure 2. The dnaA gene which i s l o c a t e d near the o r i g i n makes a gene product (RP) which represses the t r a n s c r i p t i o n of the 0-RNA gene. I n i t i a t i o n r e ­ q u i r e s 0-RNA as a primer. An a n t i - r e p r e s s o r (ARP) i s made which i n a c t i v a t e s RP. Experimental evidence f o r ARP e x i s t s (51), and there are i n d i c a t i o n s that ARP production i s r e l a t e d to c e l l envelope formation (54). In the model we have made the r a t e of K

P

Z

a n
δ

(5)

ε Ρ2 + ω

+ .. .

δ Α Τ Ρ -> δ ( Α 0 Ρ

(6)

3 ει»Ρι + $ι*Α + ... -> Ρι»

+ ...

δ

2

2

3

Ό

•> P 2

Χ + ... + Ρ

3

r

2

(7)

Macromolecule Formation ΎιΡι Μι + ...

(8)

Ύ2?2

(9)

Ύ3Ρ3 J

J

£ Μ Μ

2

+ ...

3

+ ...

ρ ι

(11) γ 5A2 J

Μ

5

ρΐ(

A d d i t i o n a l D i r e c t Reductant Use Transport of ions Membrane recharge leakage

to o f f s e t

H

ρι

(ADP

ρ

ρ 3

ΑΤΡ -> δ

ATP

ΑΤΡ

Μ

->

(ADP

ρ

y

(ADp

->-

V

(

A

D

P

(ADP ΑΤΡ -+ δ Μ3

+ +

ν

+ +

p

i>

p

i>

p

i>

p

i>

+ + +

3

δ

Μ/

δ

Μ

W

(ADP + Ρ.) i

δ (ΑΟΡ

ρ 3

δ

+ ...

-V

Α

ρ 2

V

Ύ^Ρ*

Α2

Α

Μ (10)

ΑΤΡ -* δ

Α2

Τ

-> δ

Ρ

Mit

Α Τ Ρ 5

+

->

ω

r

V

(ADP

+

(ADP

+

ΐ Ο Ν *>* -

W

I0N

+

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

H 2

°

SHULER

5.

Table I ,

AND

DOMACH

Models

of Cell

103

Growth

continued.

Additional Biosyntheti SO" -> S

=

ω

8 0 ι +

Χ + SO

Mass use

ω

Β Ι ( )

A d d i t i o n a l ATP Coupling PG formation

ό ATP -> 6 „ ( A D P + P.)

Χ

+

M J * - M^*

D

PG

Non-Specified Size linked

-> [ S ]

PG

i

ATP Use oyATP -* δ (ΑΟΡ + P ) γ

±

* Coupled to e i t h e r phosphate bond energy or o x i d a t i v e r e a c t i o n s . Products of o x i d a t i o n i n c l u d e pmf and reducing e q u i v a l e n t s . ** 0X* **RED * l * reduced c e l l mass, r e s p e c t i v e l y . M

=

u

n

r

e

c

u

c

e

(

a n c

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING TABLE I I :

Equations D e s c r i b i n g nent i n the C e l l .

the Rate of Change of Each Compo­

The symbols are the same as l i s t e d i n Figure A d d i t i o n a l symbols used a r e :

1 and Table I .

μ, k, η = maximum r a t e s of synthesis of the macromolecules, p r e ­ c u r s o r s , and enzymes, r e s p e c t i v e l y V = maximum transport r a t e Κ = s a t u r a t i o n constants = decomposition r a t e s i R = r a t e of transport F = number of f o r k s i n DNA molecule Ν = number of DNA o r i g i n s ο S c e l l u l a r surfac V = volume RI = mass of i d l i n g ribosomes moles acetate formed 7 L moles glucose d i s s i m i l a t e d GD = number of genes coding f o r s t a b l e RNA synthesis P = density f = p r o p o r t i o n a l i t y constant between Mi* and c e l l surface area SL = septum length CL = length of c y l i n d r i c s e c t i o n of the c e l l W = c e l l width SEPF = mass of septum IF = i n i t i a t i o n f a c t o r s f o r p r o t e i n synthesis RP = repressor p r o t e i n ARP = a n t i - r e p r e s s o r p r o t e i n (P/0) = maximum P/0 r a t i o max k

When S and D are used as s u b s c r i p t s , they denote r a t e of synthesis and r a t e of degradation r e s p e c t i v e l y . A and C as sub­ s c r i p t s r e f e r to anabolism and catabolism. dAi it

_ " V

r/

c

s

-

α

ι

[

(

d P l

\

ΐΓ>

/

d P l

N

ι

(

5

- -dT>

] D

,dGLN

N

a

(

- i,GLN ^r>

/ 1 Λ

(

1

)

s

NET

,dM . 5

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

(2)

SHULER A N D DOMACH

5.

Models

of Cell

105

Growth

Table I I , continued. .dATP dt

K

,dP!

;

rf i

s d M 2

ν

RTI dt

[1 »

,dPG

s

l d t >

-

GLN ^ t

f

- "a!'V

s

+

< ω

ΐΟΝ

(3)

W~dt>

+

g

s

+

ω

Ο

dP Ρ

3

ν

δ

+

ω

(dATP/dt). + dX/dt(P/0) S max •180 4 + (12 - 4·Ζ)(Ρ/0) max

(dA /dt), 2

/ Ζ =μ

dA

(4)

3

(dMWdt)

^

2

(7) A

L»

GLN/V dt

" "A

SxGUI

+

A /V 2

G L N / V

«ΡχΑ,

+

A

(8a) l

/

V

2

Pi/V

Ai/V . W

+

A

l

/

V

W

+

P

GLN l

/

V J L

K

G L N

+ (GLN/V)^ (8b)

s ι · r. ( d t )

,dGLN.

Term i s equivalent t o glutamine d r i v e n Glutamate Synthase

Continued on next page.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

106

dp *

Term i s equal to net Ρ χ formation,

N

("^~")

E

T

» where the f i r s t

term r e f e r s to Αχ i n c o r p o r a t i o n v i a glutamate ( d t

V

** T h i s term i s equivalent t o : e [ ( ^ f )

-

2

S t

dehydrogenase,

T h i s term i s equivalent t o :

1 D

ει

*(~ΠΓ*) S

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

SHULER A N D DOMACH

5.

Models

of Cell

107

Growth

Table II, continued. y

dMi

(12)

dM

2

RTI = P2 dt

iPG

P /V 2

^

P

P

^

* ^ 1 P G

+

PG/

7

\LIF rr K

k

iIF

TM

2

+

[ (

dMi/dtv Μ

•GD Mi

l

RTI (dMi/dt)

RTI1

S

ι

rdM s

|

M 2

RTI

2

RTM dt

(13)

RTI dM

2

RTM dt

RTM RTM

3 σ-

0.5 1.0 Size (/im )

0.5 1.0 Size (/x.m ) 3

3

ο c 3 σ 0)

0.5

1.0

Size ( f t m ) 3

1.5

0.5

1.0

Size l/xm ) 3

Figure 10. Computer simulation of a population using 200 unstructured cell models. There were 20 size classes with 10 cells per class in the simulation. Even at steady state the size distribution shows significant instabilities in shape.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

128

BIOCHEMICAL ENGINEERING

>% ο c 0) 3 σ­ α)

>* ο c α> 3 σ­ α)

0.5

1.0

Size (/im )

1.5

0.5 Size

1.0

1.5

(ftm ) 3

Figure 11. Computer simulation of a population using 2000 unstructured cell models. There were 20 size classes with 100 cells per class in the simulation. The steady state size distributions are considerably more stable than the simulation with 200 cells (See Figure 10).

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

5.

SHULER A N DDOMACH

Models

of Cell

129

Growth

unequal f i s s i o n was allowed. The p r e c i s i o n of f i s s i o n i s h i g h (70), so i t s i n c l u s i o n with r e a l i s t i c p r o b a b i l i t y values was not expected t o g r e a t l y a l t e r the r e s u l t s . The bulk of v a r i a t i o n i n b i r t h s i z e (> 75%) i s l i n k e d t o the v a r i a t i o n i n o v e r a l l f i s s i o n s i z e and not the l o c a t i o n of the c r o s s - w a l l plane. Since the assumption of equal f i s s i o n g r e a t l y s i m p l i f i e s programming and reduces demands on computer memory, i t i s prudent t o assume equal fission. F i g u r e 12 d i s p l a y s the s t e a d y - s t a t e s t a b i l i t y of s i z e d i s t r i b u t i o n s generated with the s t r u c t u r e d s i n g l e - c e l l model. Sixteen c e l l c l a s s e s with f i f t e e n c e l l s per c l a s s were used. Random processes allowed were v a r i a t i o n i n " b u r s t " s i z e of RP (20%) and i n r e p l i c a t i o n v e l o c i t y (10%). V a r i a t i o n with respect to other c r i t e r i a are c u r r e n t l y being i n v e s t i g a t e d . The s t a b i l i t y d i s p l a y e d by the d i s t r i b u t i o n w i l l b acceptabl i t potential applications (e.g. RNA, DNA, p r o t e i n , ) generate popu l a t i o n runs. Summary S i n g l e - c e l l models can be w r i t t e n that mimic very c l o s e l y the responses of l i v i n g c e l l s . Such models are convenient t o o l s f o r t e s t i n g the p l a u s i b i l i t y of b a s i c biochemical mechanisms. They may be p a r t i c u l a r l y a t t r a c t i v e i n t e s t i n g the p o t e n t i a l i n v i v o c o m p a t i b i l i t y of mechanisms p o s t u l a t e d on the b a s i s of i n v i t r o enzymology. The s i n g l e - c e l l models make reasonable p r e d i c t i o n s during t r a n s i e n t c o n d i t i o n s and are n u m e r i c a l l y s t a b l e . Since s t a b l e d i s t r i b u t i o n s of a p o p u l a t i o n can be constructed by using an ensemble of s i n g l e - c e l l models, i t should be p o s s i b l e to develop p o p u l a t i o n models with both high l e v e l s of segregation and s t r u c t u r e d . Such models need t o be f u r t h e r developed and t e s t e d f o r t h e i r a b i l i t y t o p r e d i c t the t r a n s i e n t behavior o f c e l l populations to p e r t u r b a t i o n s i n the a b i o t i c environment. Acknowledgment T h i s work was supported, i n p a r t , by NSF Grant

CPE-7921259.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

130

BIOCHEMICAL ENGINEERING

Τ

φ 3

σ­ α)

0.5 1.0 Size (/Ltm) 3

0.5 Size

1.03

(/im )

1.5

0.5 1.0 Size (/xm )

1.5

3

0.5 Size

1.0 ζ

(μπ\ )

Figure 12. Computer simulation of a population using 240 structured cells (the Cornell single-cell model). There were 16 size classes and 15 cells per class in the simulation. The steady-state size distributions display a level of stability acceptable for most applications.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

5.

SHULER AND DOMACH

Models

of Cell

Growth

131

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

Tsuchiya, Η.Μ.; Fredrickson, A.G.; Aris, R. Adv. Chem. Eng. 1966, 6, 125-205. Painter, P.R.; Marr, A.G. Ann. Rev. Microbiol. 1968, 22, 519-548. Van Uden, N. Ann. Rev. Microbiol. 1969, 23, 473-486. Garfinkel, D.; Garfinkel, L.; Pring, M.; Green, S.B.; Chance, B. Ann. Rev. Biochem. 1970, 39, 473-498. Fredrickson, A.G.; Megee, R.D., III; Tsuchiya, Η.Μ. Adv. Appl. Microbiol. 1970, 13, 419-465. Nyiri, L.K. Adv. Biochemical Eng. 1972, 2, 49-95. Boyle, W.C.; Berthouex, P.M. Biotechnol. Bioeng. 1974, 16 1139-1159. Fredrickson, A.G Bailey, J . E . Chem Fredrickson, A.G.; Ramkrisha, D.; Tsuchiya, Η.Μ. Chem. Eng. Symp. Series 1971, 67(108), 53-59. Campbell, A. Bacteriol. Rev. 1957, 21, 263-272. Williams, F.M. J . Theo. Biol. 1967, 15, 190-207. Williams, F.M. "Systems Analysis and Simulation in Ecology"; Patten, B.C., Ed.; Academic Press: New York, 1971, Vol. 1. Ramkrishna, D.; Fredrickson, A.G.; Tsuchiya, Η.Μ. Biotechnol. Bioeng. 1967, 9, 129-170. Van Foerster, Η. "The Kinetics of Cellular Proliferation"; Stohlman, F . , Ed.; Grune & Stratton: New York, 1959, p. 382. Trucco, E. Bull. Math. Biophys. 1965, 27, 285-304, 449-471. Yakovlev, A.Y.; Zorin, A.V.; Isanin, N.A. J . Theor. Biol. 1977, 64, 1-25. Fredrickson, A.G.; Tsuchiya, Η.Μ. AIChE J. 1963, 9, 459-468. Kozesnik, J . "Continuous Cultivation of Microorganisms"; Malek, I.; Beran, K.; Hospodka, J., Eds.; Academic Press: New York, 1964, p. 59. Lebowitz, J . L . ; Rubinow, S.I. J . Math. Biology 1974, 1, 17-36. Koch, A.L.; Schaechter, M. J . Gen. Microbiol. 1962, 29, 435-454. Eakman, J.M.; Fredrickson, A.G.; Tsuchiya, Η.Μ. Chem. Eng. Prog. Symp. Series 1966, 62(69), 37-49. Bailey, J . E . ; Fazel-Madjlessi, J.; McQuitty, D.N.; Lee, L . Y . ; Oro, J.A. AIChE J. 1978, 24, 570-576. Nishimura, Y . ; Bailey, J . E . Math. Biosciences 1980, 51, 305-328. Nishimura, Y . ; Bailey, J . E . AIChE J. 1981, 27, 73-81. Pickett, A.M.; Bazin, M.J.; Topiwala, Η.Η. Biotechnol. Bioeng. 1980, 22, 1213-1224. Pickett, A.M.; Bazin, M.J.; Topiwala, Η.Η. Biotechnol. Bioeng. 1979, 21, 1043-1055. Tanner, R.D. Biotechnol. Bioeng. 1970, 12, 831-843. Bischoff, K.B. Can. J . Chem. Eng. 1966, 44, 281-284.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

132

BIOCHEMICAL ENGINEERING

30.

Blanch, H.W.; Rogers, P.L. Biotechnol. Bioeng. 1972, 14, 151-171. 31. Constantinides, Α.; Spencer, J . L . ; Gaden, E . L . , Jr. Biotechnol. Bioeng. 1970, 12, 803-830. 32. Ho, L.Y.; Humphrey, A.E. Biotechnol. Bioeng. 1970, 12 291-311. 33. Koga, S.; Burg, C.R.; Humphrey, A.E. Appl. Microbiol. 1967 15, 683-689. 34. Yamashita, S.; Hoshi, Η.; Inagaki, T. "Fermentation Advances"; Perlman, D.; Academic Press: New York, 1969, p. 441. 35. Heinmets, F. "Analysis of Normal and Abnormal Cell Growth"; Plenum Press: New York, 1966. 36. Davison, E . J . Bull. Math. Biol. 1975, 37, 427-458. 37. Simon, Z. J . Theor Biol 1973 38 39-49 38. Weinberg, R.; Zeigler 1971, 1, 34-48. 39. Zeigler, B.P.; Weinberg, R. J . Theor. Biol. 1970, 29, 35-56. 40. Dennis, P.P.; Bremer, H. J . Bacteriol. 1974, 119, 270-281. 41. Brunschede, Η.; Dove, T . L . , Bremer, H. J . Bacteriol. 1977, 129, 1020-1033. 42. Bremer, H . ; Chuang, L. J . Theor. Biol. 1981, 88, 47-81. 43. Cooper, S.; Helmstetter, C.E. J . Mol. Biol. 1968, 31, 519540. 44. Donachie, W.D. Nature, 1968, 219, 1077. 45. Ho, S.V.; Shuler, M.L. J . Theor. Biol. 1977, 68, 415-435. 46. Shuler, M.L.; Leung, S.; Dick, C.C. Ann. N.Y. Acad. Sci. 1979, 326, 35-55. 47. Domach, M.M.; Leung, S.K.; Cahn, R.E.; Cocks, G.G.; Shuler, M.L. J . Bacteriol. (Submitted for publication) 48. Leung, S.K. M.S. Thesis, Cornell University, Ithaca, New York, 1979. 49. Dick, C.C. M.S. Thesis, Cornell University, Ithaca, New York, 1978. 50. Domach, M.M. Ph.D. Thesis, Cornell University, Ithaca, New York, 1982. 51. Fralick, J.A. "DNA Synthesis - Present and Future"; Molineux, I.; Kohiyama, Μ., Eds.; Plenum Press: New York, 1978, 71-83. 52. Messer, W.; Dankwork, L.; Tippe-Schindler, R.; Womack, J . E . ; Zahn, G. "DNA Synthesis and Its Regulation"; Goulian, M.; Hanawalt, P., Eds.; W.A. Benjamin: Menlo Park, California, 1975, p. 602. 53. Fayet, O.; Louarn, J . "DNA Synthesis - Present and Future"; Molineux, I.; Kohiyama, Μ., Eds.; Plenum Press: New York, 1967, p. 27. 54. Grossman, N.; Ron, E.Z. J . Bacteriol. 1980, 143, 100-104. 55. Fantes, P.Α.; Grant, W.D.; Pritchard, R.H.; Sudbery, P.E.; Wheals, A.E. J . Theor. Biol. 1975, 50, 213-244.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

5.

SHULER AND DOMACH

Models of Cell Growth

56.

133

Pritchard, R.H.; Barth, P.T.; Collins, T. Symp. Soc. Gen. Microbiol. 1969, 19, 263-297. 57. Stevenson, R.; Silver, S. Biochem. Biophys. Res. Comm. 1977, 75, 1133-1138. 58. Kavanagh, B.M.; Cole, J.A. "Continuous Culture 6: Applica­ tions and New Fields"; Ellwood, D.C.; Evans, C.G.T.; Melling, J., Eds.; E l l i s Horwood Ltd.: Chichester, Great Britain, 1976, Chap. 14. 59. Dalton, H. "Microbial Biochemistry"; Quayle, J . R . , Ed.; University Park Press: Baltimore, 1979, Chap. 6. 60. Woolfolk, C.A.; Shapiro, B.; Stadtman, E.R. Arch. Biochem. Biophys. 1966, 116, 177-192. 61. Miller, R.E.; Stadtman, E.R. J . Biol. Chem. 1972, 247, 74077419. 62. Ginsburg, Α.; Stadtman Metabolism"; Prusiner Press: New York, 1973, p. 9. 63. Varricchio, F. Biochim. Biophy. Acta 1969, 177, 560-564. 64. Helmstetter, C. J . Mol. Biol. 1974, 84, 21-36. 65. Holme, T. Acta Chem. Scand. 1957, 11, 763-775. 66. Cashel, M. Ann. Rev. Microbiol. 1975, 29, 301-318. 67. Gallant, J . Ann. Rev. Genetics 1979, 13, 393-415. 68. Shuler, M.L.; Domach, M. 72nd Annual AIChE Meeting, San Francisco, California, November 25-29, 1979. 69. Koppes, L . J . H . ; Woldringh, C.L.; Nanninga, N. J . Bacteriol. 1978, 134, 423-433. 70. Marr, A.G.; Harvey, R . J . ; Tentini, W.C. J . Bacteriol. 1966, 91, 2388-2389. 71. Helmstetter, C.; Pierucci, O. J . Mol. Biol. 1978, 102, 477486. RECEIVED June 29, 1982

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

6

Single-Cell by

Metabolic

Analysis

of

Model

Microbial

Determination

Populations

JAMES E. BAILEY California Institute of Technology, Department of Chemical Engineering, Pasadena, CA 91125

The properties of microbial populations result from the characteristic the level of the tions of population behavior may therefore be constructed based on understanding of single-cell metabolism, and, conversely, studies of population properties may be employed to extract information about single-cell operation. Population balance equations provide the primary mathematical tool for these purposes, and flow cytometry allows experimental access to the distribution of cell states in the population. Application of these methods to bacteria and yeasts is illustrated using three example systems. The m i c r o b i a l populations propagated i n r e a c t o r s ranging from P e t r i dishes to fermentors to n a t u r a l ecosystems are t y p i c a l l y heterogeneous with respect to age, s i z e , and biochemical a c t i v i t y . The o v e r a l l r a t e s of substrate u t i l i z a t i o n , b i o s y n t h e s i s and product formation i n these r e a c t o r s a r e sums, taken over the c e l l popu l a t i o n , o f the r a t e s o f the corresponding processes i n the i n d i v i d u a l c e l l s present (1,2). Viewed from t h i s p e r s p e c t i v e , o p t i m i z ing the performance o f a m i c r o b i a l process r e q u i r e s determination of the c e l l s ' genotype and o f a r e a c t o r design such that the optima l d i s t r i b u t i o n o f s t a t e s i s achieved i n the process's m i c r o b i a l population. Adoption o f t h i s approach to m i c r o b i a l process development cannot occur u n t i l methods e x i s t f o r determining the i n f l u e n c e o f r e a c t o r design and o p e r a t i n g parameters on s i n g l e - c e l l metabolic c o n t r o l a c t i o n s and r e a c t i o n r a t e s . I f t h i s i n f o r m a t i o n i s a v a i l a b l e , p o p u l a t i o n balance equations and a s s o c i a t e d medium conservat i o n equations provide the r e q u i r e d bases f o r r e a c t o r a n a l y s i s (_1,2). For example, f o r a well-mixed, continuous-flow isothermal m i c r o b i a l r e a c t o r a t s t e a d y - s t a t e , the p o p u l a t i o n balance equation may be w r i t t e n : 0097-6156/83/0207-0135$07.50/0 © 1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

136

^

[ r ( p , s ) f ( p , s ) ] = D[4 0). Curves A , B , and C on the rear panel are the mass, DNA content, and cell numbers in the culture, each normalized by their respective values at t = 0. Reproduced, with permission, from Ref. 14. Copyright 1980, Elsevier North Holland, Inc.

w

144

BIOCHEMICAL ENGINEERING

c o o r d i n a t i o n of DNA synthesis and c e l l d i v i s i o n i n the f i s s i o n yeast S. pombe. To put the experimental r e s u l t s i n t o p e r s p e c t i v e , consider the composite diagram showing the i n t e r r e l a t e d c y c l e s of DNA s y n t h e s i s and s e p a r a t i o n , c e l l shape, and c e l l volume i n d i cated s c h e m a t i c a l l y i n Figure 6 (20-24). Here the events which occur during the c e l l c y c l e are d i s p l a y e d i n r e l a t i v e p o s i t i o n and d u r a t i o n along arcs of a c i r c l e , the top of which i s taken a r b i t r a r i l y to be c o i n c i d e n t with the c e l l s e p a r a t i o n event. In t h i s d i s c u s s i o n , the r e l a t i o n s h i p of the i n t e r v a l of DNA s y n t h e s i s , which i n t h i s eucaryote provides d u p l i c a t i o n of a l l of the chromosomes i n the mother c e l l , r e l a t i v e to the time of p h y s i c a l separa t i o n of daughter c e l l s i s of s p e c i a l i n t e r e s t . For t h i s organism, as i t i other eucaryotes, the DNA content of the c e l l e x h i b i t s l e s s v a r i a t i o n than i n the b a c t e r i a l case, with the content f o r an i n d i v i d u a l c e l l ranging between one com p l e t e set of genetic information e q u i v a l e n t (1C), and two organism a r a t h e r unusual f e a t u r e occurs i n which p h y s i o l o g i c a l s e p a r a t i o n of the daughter c e l l s takes place before p h y s i c a l sepa r a t i o n , so that DNA s y n t h e s i s may begin i n the p h y s i o l o g i c a l l y p a r t i t i o n e d daughter c e l l s before those c e l l s a c t u a l l y p h y s i c a l l y separate. Thus, depending upon the d i s p o s i t i o n of the i n t e r v a l of DNA synthesis r e l a t i v e to c e l l s e p a r a t i o n , c e l l s w i l l e x i s t i n the p o p u l a t i o n c o n t a i n i n g up to 4C DNA content i f DNA s y n t h e s i s i s complete before the c e l l s separate and as l i t t l e as 1C DNA i f the c e l l s separate before DNA s y n t h e s i s begins (here and below, the term " c e l l " r e f e r s to the p h y s i c a l l y separated u n i t s which are observed i n a flow cytometry measurement) . Previous experiments on the c o o r d i n a t i o n between DNA s y n t h e s i s and c e l l s e p a r a t i o n i n t h i s organism are somewhat ambiguous (20-24), so that the S-phase has been shown i n the above diagram as s t r a d d l i n g the p o i n t of c e l l separation. Notice that, independent of the d i s p o s i t i o n of t h i s r e l a t i v e l y b r i e f i n t e r v a l of the c e l l c y c l e , the m a j o r i t y of c e l l s i n a f i s s i o n yeast p o p u l a t i o n w i l l possess a DNA content of 2C. The upper four frames of Figure 7 show flow cytometer measurements of the frequency functions of i n d i v i d u a l c e l l DNA content i n S. pombe (972 h"") populations grown i n steady-state chemos t a t c u l t u r e . The parameters i n d i c a t e d i n the f i g u r e frames are the s p e c i f i c growth r a t e s i n u n i t s of h r " . The dominant peak i n each of these measurements corresponds, as explained p r e v i o u s l y , to a DNA content of two genome e q u i v a l e n t s (2C). An i n t e r e s t i n g f e a t u r e i s observed i n the data obtained at lower growth r a t e s . The frequency f u n c t i o n f o r an o v e r a l l p o p u l a t i o n s p e c i f i c growth r a t e of 0.088 hr"" e x h i b i t s three modes, the f i r s t corresponding to a DNA content of 1C, the second to the most prevalent 2C popul a t i o n , and the f i n a l one to a p o p u l a t i o n of c e l l s c o n t a i n i n g a DNA content of 4C. The l a s t mode i s not b e l i e v e d to be the r e s u l t of c e l l clumping, as a l l samples i n these analyses were t r e a t e d by s o n i c a t i o n immediately p r i o r to flow cytometric a n a l y s i s . (The s u i t a b i l i t y of t h i s procedure f o r p r o v i d i n g accurate c e l l counts, 1

1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

6.

BAILEY

Cell Cell

Single-Cell

Metabolic

145

Model

diameter 3.5pm length ^ 14pm

Cell Cell

diameter length

3.5pm ^ 8pm

1 i near mass i n crease , constant volume

1 i n e a r mass increase , exponential volume increase Cell

®

Nucleus

with

2 C DNA

®

Nucleus

with

DNA

®

Nucleus

with

1 C DNA

CS - c e l l

separation CP - c e l l

Figure 6.

size

content

content

1C& 2 C

content

; ND - n u c l e a r plate

between

division ;

formation

Schematic diagram of the nuclear and cell division cycles of fission yeast S. pombe.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

146

BIOCHEMICAL ENGINEERING

and thereby minimum clumping, was v e r i f i e d i n separate c o n t r o l experiments.) Consequently, these data i n d i c a t e that the c o o r d i n a t i o n between DNA s y n t h e s i s and c e l l s e p a r a t i o n becomes imprecise i n t h i s organism at low growth r a t e s , with some c e l l s d i v i d i n g before i n i t i a t i n g DNA s y n t h e s i s and others completing DNA s y n t h e s i s before dividing. This interesting imprecision i n c e l l cycle operation would not have been evident by any population-average measurements upon t h i s system. Only measurement of the frequency f u n c t i o n prov i d e s the s e n s i t i v i t y and d e t a i l of i n f o r m a t i o n r e q u i r e d to observe t h i s f e a t u r e . The two frequency f u n c t i o n s shown i n the bottom two frames of Figure 7 correspond to d i f f e r e n t s t e a d y - s t a t e populations growing at approximately the same o v e r a l l p o p u l a t i o n growth r a t e s as those shown i n the two middl frames Thes d i f f e r e n t stead state were achieved by d i f f e r e n seem to be connected w i t clumping phenomeno when r e a c t o r s t a r t - u p i n i t i a t e s with a s i g n i f i c a n t glucose l i m i t a t i o n of growth. A d d i t i o n a l i n f o r m a t i o n on t h i s m u l t i p l e steadys t a t e phenomenon and on i t s m a n i f e s t a t i o n i n other types o f measurements i s a v a i l a b l e elsewhere ( 9 ) . Figure 8 shows the frequency f u n c t i o n s f o r s i n g l e c e l l prot e i n content obtained by the same c u l t i v a t i o n methods as j u s t outl i n e d . Considering the s e t of steady-state r e s u l t s obtained by the same s t a r t - u p procedure (the top f o u r frames i n F i g u r e 8), i t i s apparent that there i s a s i g n i f i c a n t s h i f t o f the frequency f u n c t i o n towards higher p r o t e i n contents and a l s o i n c r e a s e d skewing to the r i g h t as the o v e r a l l p o p u l a t i o n s p e c i f i c growth r a t e increases. Q u a n t i t a t i v e a n a l y s i s of these measurements has been undertaken by two d i f f e r e n t s t r a t e g i e s based upon the governing popul a t i o n balance equations which d e s c r i b e the system (25). One method employed the Collins-Richmond equation (26), the i n t e g r a t e d form o f the p o p u l a t i o n balance equation, with r e s u l t s which are summarized i n d e t a i l elsewhere (25). In the second approach, a simple f u n c t i o n a l form was chosen f o r the f i s s i o n frequency funct i o n b_

where φ ^ ) i s the feeding r a t e per protozoan c e l l when the bac­ t e r i a l d e n s i t y i s b, b i s the threshold density of b a c t e r i a , and φ and L are model parameters, the former being the maximum, or s a t u r a t i o n v a l u e , of φ ^ ) . Models l i k e t h i s are inconvenient from the mathematical and computational point of view, however. The m u l t i p l e s a t u r a t i o n model of J o s t et a l . (17) i s t

π1

*

( b )

"

(L,

Λ(L

2

+ b)

( 2 )

and i t avoids the mathematical and computational d i f f i c u l t i e s inherent i n use of an e x p l i c i t threshold model, l i k e Equation (1). Equation (2) does not have a threshold value of b, of course, but i t does p r e d i c t that (3)

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

220

BIOCHEMICAL ENGINEERING

which i s c h a r a c t e r i s t i c of a t r u e threshold model but not of Monod's model. I t has been shown that the m u l t i p l e s a t u r a t i o n model does a much b e t t e r job of c o r r e l a t i n g data f o r feeding of Tetrahymena on b a c t e r i a than does Monod's model (17 ,70 ,71 ,72) . As pointed out above, Tetrahymena p y r i f o r m i s c o n s i s t e n t l y f a i l s to c l e a r batches of water of b a c t e r i a , and the explanation f o r t h i s may be that some of the b a c t e r i a are too small or too l a r g e to be captured by the protozoans. I f t h i s i s the case, then there i s no t h r e s h o l d d e n s i t y of the b a c t e r i a , of course, so there would be l i t t l e j u s t i f i c a t i o n f o r using models l i k e Equations (1) or ( 2 ) . In t h i s circumstance, what one needs to do i s to d i v i d e the b a c t e r i a i n t o sub-populations, one which i s eaten by the p r o t o zoans and one or more which i s (are) not eaten by them. Monod's model might be assumed f o r feeding of the protozoans on the subpopulation of b a c t e r i a that they can eat and models f o r t r a n s f e r of b a c t e r i a from one sub-populatio also. A c t u a l l y use of models l i k e those that we have been d i s c u s s i n g can probably never y i e l d b e t t e r than order-of-magnitude p r e d i c t i o n s of p o p u l a t i o n d e n s i t i e s i n dynamic, t r a n s i e n t s i t u a t i o n s . Recent s t u d i e s of the responses of Tetrahymena p y r i f o r m i s to sudden changes i n the b a c t e r i a l d e n s i t y of i t s surroundings r e v e a l phenomena (57 ,65) which seem to r e q u i r e p a r t i a l d i f f e r e n t i a l equations r a t h e r than o r d i n a r y d i f f e r e n t i a l equations f o r t h e i r accurate description. F i n a l l y , i t should be mentioned that feeding by protozoans would be expected to exert strong r e g u l a t o r y e f f e c t s on the bact e r i a l populations on which they feed, e s p e c i a l l y i f these l a t t e r populations compete with one another f o r n u t r i e n t s . J o s t et a l . (17), f o r example, found that f e e d i n g of Tetrahymena p y r i f o r m i s on E s c h e r i c h i a c o l i and Azotobacter v i n e l a n d i i i n a chemostat seemed to lead to coexistence of the three populations i n a p e r p e t u a l l y t r a n s i e n t s t a t e ; i n the absence of the protozoans, however, Azotob a c t e r was excluded by E. c o l i . C l e a r l y , an important f a c t o r to be considered i n s i t u a t i o n s l i k e the foregoing i s the p o s s i b i l i t y that the protozoans may e x h i b i t preference f o r one b a c t e r i a l species over the other. As mentioned p r e v i o u s l y , i t seems l i k e l y that food preference by suspension-feeding microorganisms must be based e n t i r e l y , or almost e n t i r e l y , on d i f f e r e n c e s i n hydromechanically s i g n i f i c a n t propert i e s l i k e s i z e , shape, and d e n s i t y , of the food organisms. Experiments i n which protozoans are presented which choice of food, the food organisms d i f f e r i n g i n the p r o p e r t i e s noted, need to be done. We are c u r r e n t l y p r e s e n t i n g Tetrahymena p y r i f o r m i s with E. c o l i and A. v i n e l a n d i i , these being b a c t e r i a whose s i z e s are q u i t e d i f f e r e n t . But experiments i n which a suspension-feeder i s presented with b a c t e r i a having the same s i z e and shape, but d i f f e r i n g i n some p r o p e r t i e s that are not hydromechanically s i g n i f i c a n t , need to be done, too. One expects no preference i n such cases, and the one experiment of the kind that I know of showed no preference

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

9.

FREDRiCKSON

Interactions

of

Microbial

221

Populations

(73), but more data of the same kind are needed before one can conclude that food preference by suspension-feeders i s based s o l e l y on d i f f e r e n c e s of hydromechanically s i g n i f i c a n t p r o p e r t i e s of food organisms. P a r a s i t i s m . In t h i s d i r e c t i n t e r a c t i o n a p a r a s i t e c e l l or p a r t i c l e attaches i t s e l f to a host c e l l and makes a p a r t i a l or t o t a l p e n e t r a t i o n i n t o i t , where i t then uses the host's biomass or metabolic a c t i v i t i e s to grow and reproduce i t s e l f . Examples are provided by the p a r a s i t i s m of v i r u s e s on b a c t e r i a and other microorganisms, by the p a r a s i t i s m of the very small bacterium B d e l l o v i b r i o on other b a c t e r i a , and by the p a r a s i t i s m of b a c t e r i a on protozoa (30,74_,75) . P a r a s i t i s m i s c h a r a c t e r i z e d by a v a r i a b l e but always high degree of host s p e c i f i c i t y . That i s , a given p a r a s i t e i s able to i n f e c t onl l i m i t e d numbe f hosts d i some cases, the number ma A number of mathematica host-parasit have been published. For references to l i t e r a t u r e appearing before 1977, see F r e d r i c k s o n (2). A more recent model has been given by L e v i n ^ t a l . (76). P a r a s i t i s m can serve to r e g u l a t e competition between d i f f e r e n t host populations. An example i s provided by the work of L e v i n et a l . (76). They found that p a r a s i t i s m by the v i r u l e n t b a c t e r i o ­ phage T2 on two s t r a i n s of E s c h e r i c h i a c o l i s t a b i l i z e d the compe­ t i t i o n of the s t r a i n s f o r sugar, and allowed the competitors to c o e x i s t i n a chemostat. One of the s t r a i n s was s u s c e p t i b l e to i n f e c t i o n by T2 but the other was not. A most i n t e r e s t i n g aspect of the v i r u s - b a c t e r i a h o s t - p a r a s i t e i n t e r a c t i o n i s the tendency f o r genetic changes of the populations to keep a l t e r i n g the dynamics of the i n t e r a c t i o n . T h i s i s w e l l i l l u s t r a t e d by some a d d i t i o n a l work of Chao et a l . (77). A host bacterium B (a s t r a i n of E. c o l i ) and a bacteriophage T were introduced i n t o a chemostat; B was s u s c e p t i b l e to i n f e c t i o n by T . Mutation of B produced a new s t r a i n of b a c t e r i a , B^, which was not s u s c e p t i b l e to i n f e c t i o n by T . However, mutation of the phage produced a new v i r u s , T^, which was capable of i n f e c t i n g both B and B^. A second mutuation of the b a c t e r i a produced a t h i r d s t r a i n , Β£, which was immune to i n f e c t i o n by T and T-^. In these experiments, the v a r i o u s s t r a i n s of b a c t e r i a competed with one another f o r sugar, but the presence of the p a r a s i t e s prevented competitive e x c l u s i o n s from o c c u r r i n g . When a s t r a i n of b a c t e r i a that was not s u s c e p t i b l e to i n f e c t i o n by any of the p a r a s i t e s was present, sugar c o n c e n t r a t i o n was low and b a c t e r i a l and phage den­ s i t i e s were high. However, when a l l s t r a i n s of b a c t e r i a present were s u s c e p t i b l e to i n f e c t i o n by the phages, sugar c o n c e n t r a t i o n was high and b a c t e r i a l and phage d e n s i t i e s were low. These obser­ v a t i o n s of Chao et a l . (77) suggest that the h o s t - p a r a s i t e r e l a t i o n i s a kind of genetic race between the two groups of organisms. Undoubtedly, analagous s i t u a t i o n s occur with other i n t e r m i c r o b i a l i n t e r a c t i o n s , and e f f o r t s to detect and analyze such s i t u a t i o n s would very l i k e l y prove to be most f r u i t f u l . Q

Q

Q

0

Q

Q

Q

q

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

222

BIOCHEMICAL ENGINEERING

Symbiosis. T h i s i s a d i r e c t i n t e r a c t i o n between two microb i a l populations which i s c h a r a c t e r i z e d not only by the mutual (even i f i m p e r f e c t l y understood) b e n e f i t s which i t confers upon the partners i n the a s s o c i a t i o n but a l s o , l i k e p a r a s i t i s m , by i t s high degree of s p e c i f i c i t y . That i s , the two partners are more or l e s s uniquely adapted to l i v e together, and i t i s impossible or very d i f f i c u l t to r e p l a c e one of the partners i n the a s s o c i a t i o n by another organism of s i m i l a r k i n d . Undoubtedly, syntrophism i s involved i n many m i c r o b i a l symbioses, and perhaps models l i k e those f o r t h i s m u t u a l i s t i c i n t e r a c t i o n would be a p p l i c a b l e to symbiosis. Q u a n t i t a t i v e models f o r symbiosis seem to be none x i s t e n t at the present time, however. Crowding. T h i s i n t e r a c t i o n i s important when population d e n s i t i e s become so l a r g that th a v a i l a b i l i t f become a l i m i t i n g f a c t o r i n th s p e c i f i c i n t e r a c t i o n of g probably importanc i n s i t u a t i o n s where the i n t e r a c t i n g populations are suspended i n a l i q u i d medium, because d e n s i t i e s t h e r e i n are not l i k e l y to become so high that a v a i l a b i l i t y of space becomes a r a t e - l i m i t i n g f a c t o r f o r both populations. I n t r a s p e c i f i c crowding can become important i n l i q u i d c u l t u r e s , i t appears; the existence of the v e r t i c a l asymptote i n the graph of F i g u r e 3 i s an example of an e f f e c t due to i n t r a s p e c i f i c crowding. I n t e r s p e c i f i c crowding may be of great importance when we are d e a l i n g with systems i n which much s u r f a c e area, upon which the organisms attach themselves, i s present. A good d e a l of e f f o r t has been expended i n recent years to understand the mechanisms involved i n attachment of organisms to s u r f a c e s . The mechanisms are complex, even when only a s i n g l e population i s i n v o l v e d , f o r the d e n s i t y of attached c e l l s i s found to depend on the i d e n t i t y and p h y s i o l o g i c a l s t a t e of the organism, the i d e n t i t y of the m a t e r i a l of which the surface i s made as w e l l as the p r i o r t r e a t ment of the s u r f a c e , the composition of the l i q u i d medium adjacent to the s o l i d s u r f a c e , the d e n s i t y of the organisms i n the l i q u i d medium, and the time of contact between the suspension of organisms and the s u r f a c e (78). F a m i l i a r concepts that apply to adsorption of molecules on s u r f a c e s , l i k e that of the a c t i v e s i t e , seem not to apply, and t h i s means that the Langmuir-Hinshelwood model of adsorption, or one of i t s g e n e r a l i z a t i o n s , i s not l i k e l y to apply, either. Instead, i t seems that we need to construct dynamic s t o c h a s t i c models which w i l l make the p r o b a b i l i t y of attachment of one c e l l to a given area of s u r f a c e i n a short i n t e r v a l of time dependent upon the number of c e l l s already attached to that s u r face as w e l l as to the d e n s i t y of c e l l s present i n the bulk l i q u i d , e t c . Since I am not aware that models l i k e t h i s have been worked out even f o r s i n g l e populations, I cannot say anything meaningful about models f o r competition of two populations f o r

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

9.

FREDRiCKSON

Interactions

of Microbial

Populations

223

space on a s o l i d substratum. We are t r y i n g to study t h i s i n t e r a c t i o n i n our l a b o r a t o r y a t the present time, but i t i s not an easy t h i n g to do. I t was pointed out above that "crowding" as I have used the term r e f e r s t o an i n t e r s p e c i f i c i n t e r a c t i o n but that b i o l o g i s t s o f t e n use the term f o r an i n t r a s p e c i f i c i n t e r a c t i o n . The context w i l l make i t c l e a r i n most cases which kind of i n t e r a c t i o n i s being r e f e r r e d to, so there should be no d i f f i c u l t y i n using the same word f o r two d i f f e r e n t kinds of s i t u a t i o n s . Summary and d i s c u s s i o n The foregoing d i s c u s s i o n shows that improved understanding of i n t e r a c t i o n s between m i c r o b i a l populations w i l l r e q u i r e research i n a number of r e l a t e d A partial list i follows. Much work remains autecology populations; that i s , on the responses of i n d i v i d u a l populations to changes i n t h e i r environment and on the changes produced i n the a b i o t i c environment by the a c t i v i t i e s of such p o p u l a t i o n s . Of p a r t i c u l a r importance i n s o f a r as osmotrophic microorganisms a r e concerned i s research aimed at p r o v i d i n g good models f o r the e f f e c t s of m u l t i p l e n u t r i e n t l i m i t a t i o n on growth r a t e s , f o r the k i n e t i c s of s u b c e l l u l a r processes i n general, f o r the k i n e t i c s of formation of e x t r a c e l l u l a r chemicals and enzymes, f o r the k i n e t i c s of a c t i o n of i n h i b i t o r s , t o x i n s , and l y t i c enzymes, e t c . More work i s needed on the autecology of phagotrophic microorganisms, a l s o . The mechanisms that make such organisms "prudent" feeders need t o be e s t a b l i s h e d and compared and the question of the extent to which they s e l e c t t h e i r food needs to be examined f u r t h e r . Almost a l l attempts t o c o n s t r u c t mathematical models of popul a t i o n i n t e r a c t i o n s assume that the populations present are e n t i t i e s of f i x e d genetic c o n s t i t u t i o n . I f they allow f o r the occurrence of mutuation, i t i s almost always i n the sense of assuming that a mutant of given p r o p e r t i e s has formed, and then t r y i n g to see how the system of mutant, w i l d organism, and any other organisms present, w i l l evolve i n time. Models which are b u i l t on some of the e x c i t i n g new information that m i c r o b i a l g e n e t i c i s t s have provided need t o be developed and a p p l i e d to systems of i n t e r a c t i n g populations. High p r i o r i t y should be given to producing models which take i n t o account mechanisms of mutation and genetic recombination. Several b i n a r y i n t e r a c t i o n s have been neglected by people who take a q u a n t i t a t i v e , mathematical approach t o such processes. Amensalism, antagonism, and e c c r i n o l y s i s are i n d i r e c t i n t e r a c t i o n s which f a l l i n t o t h i s category, and there i s room and motivation for much work on them. In a d d i t i o n , there are many elementary mechanisms of commensalism, mutualism, and protocooperation that have been neglected. Among the d i r e c t i n t e r a c t i o n s , nothing q u a n t i t a t i v e i s known about crowding and symbiosis, and the former i n t e r a c t i o n , at l e a s t , should be made the object o f study q u i t e soon.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

224

BIOCHEMICAL ENGINEERING

New experimental techniques and apparatus f o r studying popul a t i o n i n t e r a c t i o n s need to be developed. A l t e r n a t e and improved methods of o b t a i n i n g census data on systems c o n t a i n i n g two or more populations are c r i t i c a l needs, and improved, automated means of making chemical analyses of a b i o t i c media would be most h e l p f u l , too. New mathematical techniques f o r d e a l i n g with the systems of n o n l i n e a r d i f f e r e n t i a l equations that r e s u l t from models of popul a t i o n i n t e r a c t i o n s need to be found. D i s c u s s i o n s with mathemat i c i a n s make i t c l e a r that techniques which would seem to be u s e f u l have not been much developed, so r a p i d progress i s not to be expected i n t h i s d i f f i c u l t l i n e of endeavor. However, some progress has been made. For example, Stephanopoulos (79,80) has shown how the theory of the Poincaré index can be a p p l i e d to the equations of b i n a r y p o p u l a t i o i n t e r a c t i o n s Th proble with t h i s technique i s that i reduced to two o r d i n a r y equations y of b i n a r y i n t e r a c t i o n f a l l i n t o t h i s category (79), but many do not and of course ternary, quaternary, e t c . i n t e r a c t i o n s do not, either. Another l i n e of research, e n t i r e l y d i f f e r e n t from what has j u s t been mentioned, concerns the a p p l i c a t i o n s of mixed c u l t u r e s and of knowledge about i n t e r a c t i o n s i n mixed c u l t u r e s . I t seems to me that i t would now be worthwhile to t r y to think of i n d u s t r i a l operations where mixed c u l t u r e s could be used to advantage. Development of g e n e t i c engineering techniques f o r making microorganisms capable of doing s p e c i f i c , assigned tasks would seem to have increased the l i k e l i h o o d that s u c c e s s f u l mixed c u l t u r e processes can be developed, and work on developing them might now prove to be rewarding. There i s a l s o the a d d i t i o n a l f i e l d of a p p l i c a t i o n of models and t h e o r i e s of p o p u l a t i o n i n t e r a c t i o n s to problems of understanding the dynamics of n a t u r a l ecosystems. M i t i g a t i o n of p o l l u t i o n of lakes and streams, cleanup of o i l and chemical s p i l l s , prevention of acid mine drainage, and so on, are a l l r e a l and l a r g e problems, and i t i s reasonable to expect that a p p l i c a t i o n of the models and t h e o r i e s noted can be of help i n s o l v i n g such problems. Acknowledgement The support of the N a t i o n a l Science Foundation, through grants ENG77-21632 and CPE-8020783, i s acknowledged with thanks.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

9. FREDRiCKSON

Interactions of Microbial Populations

225

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

Odum, P. "Fundamentals of Ecology", 3rd. ed., Saunders: Philadelphia, 1971, pp. 211-213. Fredrickson, A. G. Annu. Rev. Microbiol. 1977, 31, 63. Kaiser, D.; Manoil, C . ; Dworkin, M. Annu. Rev. Microbiol. 1979, 33, 595. Fredrickson, A. G.; Stephanopoulos, G. N. Science 1981, 213, 972. Stephanopoulos, G. N.; Fredrickson, A. G. Biotechnol. Bioeng. 1979, 21, 1491. Stewart, F. M.; Levin, B. R. Am. Nat. 1973, 107, 171. Grenney, W. J.; Bella, D. Α.; Curl, H. C., Jr. Am. Nat. 1973, 107, 405. Chisholm, S. W.; Nobbs P A "Modeling Biochemical Processes in Aquatic Ecosystems" Ann Arbor, Michigan, , pp Stephanopoulos, G. N.; Fredrickson, A. G.; Aris, R. AIChE J. 1979, 25, 863. Hsu, S. B. J. Math. Biol. 1980, 9, 115. Smith, H. L. SIAM J. Appl. Math. 1981, 40, 498. Hsu, S. B.; Hubbell, S.; Waltman, P. SIAM J. Appl. Math. 1977, 32, 366. Hsu, S. B. SIAM J. Appl. Math. 1978, 34, 760. Koch, A. L. J. Theor. Biol. 1974, 44, 387. Hsu, S. B.; Hubbell, S. P.; Waltman, P. SIAM J. Appl. Math. 1978, 35, 617. Hus, S. B.; Hubbell, S. P.; Waltman, P. Ecol. Monogr. 1978, 48, 337. Jost, J . L.; Drake, J . F . ; Fredrickson, A. G.; Tsuchiya, H. M. J . Bacteriol. 1973, 113, 834. León, J . Α.; Tumpson, D. B. J. Theor. Biol. 1975, 50, 185. Peterson, R. Am. Nat. 1975, 109, 35. Taylor, P. Α.; Williams, P. J . LeB. Can. J. Microbiol. 1975 21, 90. Yoon, H.; Blanch, H. W. J. Appl. Chem. Biotechnol. 1977, 27, 260. Yoon, H.; Klingzing, G.; Blanch, H. W. Biotechnol. Bioeng. 1977, 19, 1193. Stephanopoulos. G. N.; Schuelke, L. M.; Stephanopoulos, G. Theor. Pop. Biol. 1979, 16, 126. Smouse, P. E. Theor. Pop. Biol. 1980, 17, 16. Hsu, S. B.; Cheng, K-S.; Hubbell, S. P. SIAM J. Appl. Math. 1981, 41, 422. Gottschal, J. C.; de Vries, S.; Kuenen, J . G. Arch. Micro­ biol. 1979, 121, 241. Laanbroek, H. J.; Smit, A. J.; Nulend, G. M.; Veldkamp, H. Arch. Microbiol. 1979, 120, 61. DeFreitas, M.; Fredrickson, A. G. J . Gen. Microbiol. 1978, 106, 307.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

226 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59.

BIOCHEMICAL ENGINEERING Miura, Y.; Tanaka, H.; Okazaki, M. Biotechnol. Bioeng. 1980, 22, 929. Alexander, M. "Microbial Ecology", Wiley: New York, 1971, pp. 290; 327-368. van Gemerden, H. Microbial Ecol. 1974, 1, 104. Wilder, C. T.; Cadman, T. W.; Hatch, R. R. Biotechnol. Bioeng. 1980, 22, 89. Adams, J.; Kinney, T.; Thompson, S.; Rubin, L . ; Hellin, R. B. Genetics 1979, 91, 627. Meers, J . L. CRC Critical Rev. Microbiol. 1973, 2, 139. Megee, R. D., III; Drake, J . F . ; Fredrickson, A. G.; Tsuchiya, H. M. Can. J. Microbiol. 1972, 18, 1733. Miura, Y.; Sugiura, K.; Yoh, M.; Tanaka, H.; Okazaki, M.; Komenmushi, S. J . Ferment. Technol. 1978, 56, 339. Reilly, P. J . Biotechnol Bioeng 1974 16 1373 Chao, C . - C ; Reilly Sheintuch, M. Biotechnol Bioeng , , Lee, I. H.; Fredrickson, A. G.; Tsuchiya, H. M. Biotechnol. Bioeng. 1976, 18, 513. Lee, I. H.; Fredrickson, A. G.; Tsuchiya, H. M. Appl. Microbiol. 1974, 28, 831. Nurmikko, V. Experientia 1956, 12, 245. Wolfe, R. S.; Pfennig, N. Appl. Env. Microbiol. 1977, 33, 427. Slater, J . H. "The Oil Industry and Microbial Ecosystems", Chater, K. W. Α.; Somerville, H. S. Eds., Heyden and Son, London, pp. 137-154. Lamb, S. C.; Garver, J . C. Biotechnol. Bioeng. 1980, 22, 2119. Meyer, J . S.; Tsuchiya, Η. M.; Fredrickson, A. G. Biotechnol. Bioeng. 1975, 17, 1065. Wilkinson, T. G.; Topiwala, H. H.; Hamer, G. Biotechnol. Bioeng. 1974, 16, 41. Van Dedem, G.; Moo-Young, M. Biotechnol. Bioeng. 1973, 15, 419. Gause, G. F. "The Struggle For Existence", Williams & Wilkins, Baltimore, 1934, pp. 114-140. Berger, J . Trans. Am. Micros. Soc. 1979, 98, 487. Seravin, L. N.; Orlovskaja, Ε. E. Acta Protozool. 1977, 16, 309. Berger, J . J . Gen. Microbiol. 1980, 118, 397. Slobodkin, L. B. Am. Zool. 1968, 8, 43. Luckinbill, L. S. Ecology 1973, 54, 1320. Luckinbill, L. S. Ecology 1974, 55, 1142. Tsuchiya, H. M.; Drake, J . F . ; Jost, J . L.; Fredrickson, A. G. J. Bacteriol. 1972, 110, 1147. Swift, S. T.; Najita, I. Y.; Ohtaguchi, K.; Fredrickson, A. G. paper in preparation, 1982. Jørgensen, C. B. "Biology of Suspension Feeding", Pergamon: Oxford, 1966. Bader, F. G.; Tsuchiya, H. M.; Fredrickson, A. G. Biotechnol. Bioeng. 1976, 18, 311.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

9. 60. 61. 62. Ill., 63. 64. 65. 66. 67. 68. 69. 70.

71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

FREDRICKSON

Interactions of Microbial Populations

227

Fenchel, T. Microbial Ecol. 1980, 6, 13. Drake, J . F . ; Tsuchiya, H. M. Appl. Env. Microbiol. 1977, 34, 18. Kudo, R. "Protozoology", 5th. ed., Thomas: Springfield, 1966, p. 870. Corliss, J . O. J . Protozool. 1970, 17, 198. Habte, M.; Alexander, M. Ecology 1978, 59, 140. Watson, P. J.; Ohtaguchi, K.; Fredrickson, A. G. J. Gen. Microbiol. 1981, 122, 323. Fenchel, T. Microbial Ecol. 1980, 6, 1. Alexander, M. Annu. Rev. Microbiol. 1981, 35, 113. Salt, G. W. Ecol. Monogr. 1967, 37, 113. Monod, J . "Recherches sur la croissance des cultures bactériennes", Hermann: Paris, 1942. Bader, F. G.; Fredrickson A G. Tsuchiya H M "Modelin Biochemical Processe Ed., Ann Arbor Science: Ann Arbor, Michigan, 1976, pp. 257 279. Stephanopoulos, G. N.; Fredrickson, A. G. Bull. Math. Biol. 1981, 43, 165. Ratnam, D. Α.; Pavlou, S.; Fredrickson, A. G. paper in preparation, 1982. Coleman, G. S. J . Gen. Microbiol. 1964, 37, 209. Stainer, R. Y.; Adelberg, Ε. Α.; Ingraham, J . "The Microbial World", 4th ed., Prentice-Hall: Englewood Cliffs, New Jersey, 1976, pp. 766-773. Atlas, R. M.; Bartha, R. "Microbial Ecology", Addison-Wesley: Reading, Mass., 1981, pp. 273-276. Levin, B. R.; Stewart, F. M.; Chao, L. Am. Nat. 1977, 111, 3. Chao, L.; Levin, B. R.; Stewart, F. M. Ecology 1977, 58, 369. Ellwood, D. C.; Melling, J.; Rutter, P., Eds., "Adhesion of Microorganisms to Surfaces", Society for General Microbiology: London, 1979. Stephanopoulos, G. N. AIChE J . 1980, 26, 802. Stephanopoulos, G. N. Biotechnol. Bioeng. 1981, 23, 2243.

RECEIVED

June 1, 1982

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10

The

Role

of S p e c i a l i s t s a n d G e n e r a l i s t s

in

Microbial

Population

Interactions

J. G. KUENEN Delft University of Technology, Laboratory of Microbiology, Julianalaan 67a, 2628 BC Delft, The Netherlands In many environments highly specialized bacteria coexist with generalists bolize a large diversit understand the mechanisms of interaction between these types of bacteria, model experiments in continuous culture have been carried out with two typical specialists and one generalist. It could be shown that the generalist can compete successfully with specialists for growth limiting substrates when mixtures of substrates are available. Under these conditions the generalist can utilize these mixtures simultaneously. Another advantage of generalists might lie in their capability to continue to grow when the supply of different substrates a l ternate. In that case specialists would alternatively grow and starve. Model-competition experiments indicate that, in general, the success of specialists was favoured by increased length of growth and starvation periods. The breakdown of organic and i n o r g a n i c compounds i n nature i s c a r r i e d out by an enormous d i v e r s i t y of b a c t e r i a which are adapted to a v a r i e t y of p h y s i c a l and chemical environmental parameters. In a given environment, many microorganisms may c o e x i s t which o f t e n have completely d i f f e r e n t metabolic c a p a b i l i t i e s , but sometimes a l s o have overlapping p r o p e r t i e s . T y p i c a l l y , one can f i n d h i g h l y s p e c i a l i z e d organisms, able to metabolize only one or a few compounds, c o e x i s t i n g with very v e r s a t i l e organisms, termed general i s t s . The l a t t e r are able to metabolize a great d i v e r s i t y of o r ganic compounds. From the e c o l o g i c a l p o i n t of view one may ask how to e x p l a i n t h i s coexistence of microorganisms and how t h e i r r e s p e c t i v e phys i o l o g i c a l p r o p e r t i e s may give them an advantage or disadvantage under a given growth c o n d i t i o n . S i m i l a r l y , from the p o i n t of view of management of sewage treatment p l a n t s , one may ask how the 0097-6156/83/0207-0229$06.75/0 © 1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

230

BIOCHEMICAL ENGINEERING

regime of a p l a n t may s e l e c t c e r t a i n metabolic types and how t h i s may have a bearing on p r o p e r t i e s of the p l a n t such as s u s c e p t i b i l i t y to pulse charges and loading c a p a c i t y . In order to understand the complicated r e a c t i o n s occuring between s p e c i a l i s t s and g e n e r a l i s t s w i t h i n a complex mixture of other organisms, a thorough i n s i g h t i n t o t h e i r b a s i c metabolic p r o p e r t i e s , that i s t h e i r p h y s i o l o g i c a l behaviour, i s needed. Unf o r t u n a t e l y the physiology of most microorganisms i s impossible to study i n the very complicated mixtures i n which they n a t u r a l l y occur. Therefore, as a i n i t i a l approach, i t has been necessary to study s p e c i a l i s t s and g e n e r a l i s t s i n pure c u l t u r e s , and i n a r t i f i c i a l composite-mixtures of organisms i n order to obtain i n s i g h t i n t o t h e i r e c o l o g i c a l niches. When grown on t h e i r s p e c i f i c substrate i n the laboratory, the s p e c i a l i s t s are c h a r a c t e r i z e d b high s p e c i f i growth rate (ymax), whereas the g e n e r a l i s t low maximum s p e c i f i c growt y l i z e . Even at very low concentrations of a s u b s t r a t e , as they g e n e r a l l y occur i n the environment, the v e r s a t i l e organisms grow r e l a t i v e l y slowly. F i g u r e 1 shows a g e n e r a l i z e d p i c t u r e of the r e l a t i o n s h i p between the growth l i m i t i n g substrate and the s p e c i f i c growth r a t e of a s p e c i a l i s t and a g e n e r a l i s t . I t may be asked whether the g e n e r a l i s t s might be able to grow f a s t e r than s p e c i a l i s t s i n mixtures of s u b s t r a t e s . However, under such c o n d i t i o n s the g e n e r a l i s t s o f t e n show s e q u e n t i a l substrate u t i l i z a t i o n , known as d i a u x i e . A w e l l known example i s the growth of the bacterium Escherichia coli on mixtures of glucose and l a c tose. F i r s t the glucose i s u t i l i z e d , and only when t h i s compound i s completely metabolized, the enzymes needed f o r l a c t o s e u t i l i z a t i o n w i l l be induced, allowing growth on l a c t o s e . Thus at high concentrations of mixtures of s u b s t r a t e s , simultaneous u t i l i z a t i o n i n t h i s case i s not p o s s i b l e . One should r e a l i z e that i n many n a t u r a l and seminatural e n v i ronments concentrations of substrates are g e n e r a l l y low, u s u a l l y below the mM and even o f t e n below the pM range. Under such condit i o n s , the growth r a t e of microorganisms w i l l be l i m i t e d by the concentration of t h e i r s u b s t r a t e s , and mixed substrate u t i l i z a t i o n might be p o s s i b l e . In the l a b o r a t o r y , growth under dual subs t r a t e l i m i t a t i o n can be conveniently created i n a f l o w - c o n t r o l l e d chemostat, or continuous c u l t u r e . In the growth medium supplied to the c u l t u r e , a l l i n g r e d i e n t s necessary f o r growth are i n excess except f o r the two substrates i n question. I t has been shown for E. coli by S i l v e r and Mateles (1) that under such c o n d i t i o n s simultaneous u t i l i z a t i o n of glucose and l a c t o s e was p o s s i b l e . Analogous r e s u l t s have been obtained f o r other b a c t e r i a , such as Pseudomonas oxalaticus growing on mixtures of formate and acetate (2) and Thiobacillus s t r a i n A2 growing on t h i o s u l f a t e and acetate (J3). Our own work on the g e n e r a l i s t Thiobacillus A2 may serve as

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Microbial

Specialists and

Generalists

Specialist

Generalist

-> s

Figure 1. The relationship between the concentration (s) of the growth-limiting substrate and the specific growth rate (μ) of a typical specialist and a typical gen­ eralist bacterium growing on the same substrate.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

232

BIOCHEMICAL ENGINEERING

an example, T. A2 i s a very v e r s a t i l e organism able to grow on at l e a s t 25-30 d i f f e r e n t organic s u b s t r a t e s , and, i n a d d i t i o n , a l s o capable of a u t o t r o p h i c growth on i n o r g a n i c reduced s u l f u r com­ pounds. (See Table I)· Under the l a t t e r c o n d i t i o n s i t o x i d i z e s , f o r example, t h i o s u l f a t e or s u l f i d e as a source of energy while using carbon d i o x i d e as the only carbon source f o r growth. When grown i n batch c u l t u r e i n the presence of high concentrations of acetate and t h i o s u l f a t e Τ. A2 c l e a r l y shows a b i p h a s i c u t i l i z a t i o n of the two compounds (Figure 2). However when grown i n the chemos­ tat under growth l i m i t a t i o n by t h i s mixture, simultaneous u t i l i ­ z a t i o n of acetate and t h i o s u l f a t e i s p o s s i b l e i r r e s p e c t i v e of the a v a i l a b l e r a t i o of t h i o s u l f a t e and acetate (Figure 3). Under such c o n d i t i o n s , acetate and t h i o s u l f a t e concentrations i n the c u l t u r e are below the d e t e c t i o n l e v e l . The metabolic machinery of T. A2 adapts to the r e q u i r e d turnover rates of the r e s p e c t i v e sub s t r a t e s . For example, th sent at maximum c a p a c i t c u l t u r e , whereas no t h i o s u l f a t e r e s p i r a t i o n c a p a c i t y i s present when only acetate i s a v a i l a b l e . I n t e r e s t i n g l y , the a b i l i t y of the c e l l s to a s s i m i l a t e C O 2 f o r c e l l carbon i s e f f i c i e n t l y adapted to the a v a i l a b l e organic carbon i n the c u l t u r e . This implies that when the r a t i o of t h i o s u l f a t e to acetate i s r e l a t i v e l y h i g h , ace­ tate i s used p r i m a r i l y as a carbon source to "save" energy f o r C O 2 f i x a t i o n . F u r t h e r work i n our laboratory by others (Ji and j ) has shown that simultaneous u t i l i z a t i o n of mixtures of other substrates i s e q u a l l y p o s s i b l e . The aim of our research was then focussed on the question of whether t h i s g e n e r a l i s t would be able to compete s u c c e s s f u l l y f o r g r o w t h - l i m i t i n g substrates with s p e c i a l i s t s during mixotrophic growth under n u t r i e n t l i m i t a t i o n . For our purpose we used the three model organisms shown i n Table I I . These included a t y p i c a l g e n e r a l i s t , namely the v e r s a t i l e Thiobacillus A2, and two s p e c i a ­ l i s t s . The f i r s t s p e c i a l i s t was the chemolithoautotroph, Thioba­ cillus neap olitonus which can grow very f a s t i n m i n e r a l s - t h i o ­ s u l f a t e medium using C O 2 as i t s carbon source, and the second was a chemoorganoheterotroph Spirillum G7, which can grow very r a p i d l y on m i n e r a l s - a c e t a t e medium using acetate as carbon and energy source. (See a l s o Table I ) . A s e r i e s of experiments was c a r r i e d out i n continuous c u l t u r e to study the competition between sets of two and three organisms. 9

In

the

first

experiment, Thiobacillus

A2

and

Thiobacillus

neapoli-

tanus were each grown s e p a r a t e l y i n a t h i o s u l f a t e - l i m i t e d chemos­ t a t . Once steady s t a t e s had been e s t a b l i s h e d at a f i x e d d i l u t i o n r a t e , the c u l t u r e s were mixed one to one (v/v) and the change i n the percentages of the two organisms was followed u n t i l no f u r t h e r change could be observed f o r one or two volume changes. F i g u r e 4 shows that i n m i n e r a l s - t h i o s u l f a t e medium, Thiobacillus A2 was out-competed by the s p e c i a l i s t . T. A2 was not completely e l i m i n a ­ ted s i n c e i t has been shown that the s p e c i a l i s t excretes g l y c o l l a t e (6) which can be consumed by T. A2.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10.

KUENEN

Microbial

Specialists

and

233

Generalists

Table I 11

Types of metabolism of "model b a c t e r i a used f o r the study of competition between " s p e c i a l i s t s " and " g e n e r a l i s t s " .

GENERALIST: Facultative

chemolitho(auto)troph ("mixotroph") (Thiobacillus

S 0 2

Energy source:

3

= (or S )

°2

> S0

4

and/or

Λ U

(many) organic compound(s) CO2 — * Carbon source:

A2)

2

> CO^

cellmaterial

and/or (many) organic compound(s) — ^ c e l l m a t e r i a l

SPECIALIST I O b l i g a t e chemolitho(auto)troph (Thiobacillus 0

2 =-> SO,

S20 3 «

Carbon source:

CO^—^ c e l l m a t e r i a l

u

?

(or S )

o

Energy source:

5

neapolitanus)

SPECIALIST I I Chemo(organo)heterotroph (Spirillum

G7)

°

2

Energy source:

(few) organic compounds

> CO^

Carbon source:

(few) organic compounds—^ c e l l m a t e r i a l

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

234

BIOCHEMICAL ENGINEERING

0

2

4

6

8 time (h)

10

12

%

16

Figure 2. Maximum substrate oxidation capacities ( Q o ^ ' j and substrate concen­ tration during growth of T. A2 on a mixture of acetate and thiosulfate in batch culture. The inoculum consisted of cells from an acetate-grown culture. Key: · , q ™*-thiosulfate; A , Qog^'-acetate; O , thiosulfate concentration; Δ , acetate concentration. Reproduced, with permission, from Ref. 3. Copyright 1980, SpringerVerlag. 0

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10.

KUENEN

Microbial

Specialists and

0

2

4

40

36

32

6

235

Generalists

8 10 12 14 acetate (mM) 28 24 20 16 12 thiosulfate (mM)

16

18 20

8

4

0

Figure 3. Maximum substrate oxidation potentials and carbon dioxide fixation potential of whole cells of T . A2 as a function of different acetate and thiosulfate concentrations in the reservoir medium of the chemostat cultures. Key: · , Qo™*thiosulfate; A , QoJ™ *-acetate; M, C0 -fixation potential. Reproduced, with permission, from Ref. 3. Copyright 1980, Springer-Verlag. 1

2

Data were obtained with cells from thiosulfate- and/or acetate-limited chemostat cultures in steady state at a dilution rate of 0.05 h~ . Acetate and thiosulfate concentrations in the cultures were below the detection level. Cellular carbon in the cultures ranged from 110 mg C/L (40 mM thiosulfate) to 200 mg C/L (20 mM acetate). 1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

236

BIOCHEMICAL ENGINEERING

When acetate was s u p p l i e d to the i n f l o w i n g medium, the number of T. A 2 c e l l s increased s i n c e T. neapolitanus cannot u t i l i z e acetate. F i g u r e 5 shows that with i n c r e a s i n g acetate c o n c e n t r a t i o n the percentage of T. A 2 g r a d u a l l y increased and coexistence of the two organisms became p o s s i b l e . Above a c o n c e n t r a t i o n of about 10 mM acetate, the s p e c i a l i s t was e l i m i n a t e d from the c u l t u r e . The explanation f o r t h i s l i e s i n the a b i l i t y of T. A 2 to u t i l i z e acetate and t h i o s u l f a t e simultaneously under these growth c o n d i t i o n s . With i n c r e a s i n g acetate c o n c e n t r a t i o n , the absolute concent r a t i o n of the T. A 2 c e l l s increased and allowed these organisms to c l a i m an i n c r e a s i n g l y l a r g e r share of t h i o s u l f a t e . E v e n t u a l l y , the r a t i o of acetate to t h i o s u l f a t e became such that T. A 2 was able to reduce the t h i o s u l f a t e c o n c e n t r a t i o n to below the l e v e l at which T. neapolitanus could maintain the r e q u i r e d growth r a t e , r e s u l t i n g i n the wash out of the s p e c i a l i s t Very s i m i l a r r e s u l t s were obtained with mixture t h i o s u l f a t e and glucose Competition experiments between the s p e c i a l i s t Spirillum G7 and T. A 2 gave analogous r e s u l t s . In acetate medium Spirillum G7 out-competed T. A 2 completely. Thiobacillus A 2 out-competed the s p e c i a l i s t when more than 10 mM t h i o s u l f a t e was present i n the acetate-minerals medium. Obviously, under " n a t u r a l " conditions i n the environment, or i n sewage treatment p l a n t s , the g e n e r a l i s t would have to compete with both s p e c i a l i s t s at the same time. Therefore, three-membered c u l t u r e s were a l s o s t u d i e d . The r e s u l t s , as summarized i n F i g u r e 6, show that coexistence of the three organisms was p o s s i b l e over a large range of c o n c e n t r a t i o n r a t i o ' s with T. A 2 dominating the c u l t u r e . The coexistence of three organisms does not agree with t h e o r e t i c a l p r e d i c t i o n s which w i l l be discussed below. In any case the outcome of these experiments c l e a r l y i n d i c a t e d that when mixed substrates are s u p p l i e d , general i s t s have metabolic advantages which allow them to c l a i m a "niche", that i s , a r i g h t of existence i n the n a t u r a l environment. The v a l i d i t y of t h i s g e n e r a l i s a t i o n was confirmed by the r e s u l t s of enrichment c u l t u r e s c a r r i e d out i n the chemostat i n o c u l a t e d with n a t u r a l samples. Table I I I shows the outcome of such e n r i c h ment c u l t u r e s performed with d i f f e r e n t mixtures of t h i o s u l f a t e and a c e t a t e . In a l l cases when f r e s h water i n o c u l a were used, a dominant c u l t u r e of a g e n e r a l i s t Thiobacillus was obtained. I n t e r e s t i n g l y , i n 4 out of 5 cases the g e n e r a l i s t was a f a c u l t a t i v e chemolithotroph able to grow a u t o t r o p h i c a l l y . However, i n one case when r e l a t i v e l y high amounts of acetate were presented to the c u l t u r e , a bacterium able to o b t a i n energy from t h i o s u l f a t e but not able to f i x C O 2 came to the f o r e . This i s not s u r p r i s i n g , s i n c e at t h i s r a t i o C O 2 f i x a t i o n i s not r e q u i r e d (compare F i g u r e 3 f o r T. A2). As mentioned b e f o r e , a somewhat p u z z l i n g r e s u l t of the compet i t i o n experiments with the three-membered c u l t u r e was that coexistence of three organisms seemed p o s s i b l e . In s e v e r a l theore-

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10.

Microbial

KUENEN

Specialists

and

237

Generalists

Table I I Maximum s p e c i f i c growth rates ν^οχ (h ^) of the o b l i g a t e l y c h e m o l i t h o ( a u t o ) t r o p h i c Thvobacillus

specialized, neapolitanus,

the v e r s a t i l e , f a c u l t a t i v e l y chemolithοtrophic Thiobacillus A2 (a g e n e r a l i s t ) , and a s p e c i a l i z e d h e t e r o t r o p h i c Spirillum G7, during growth i n minerals medium supplemented with t h i o s u l f a t e ( t ) , acetate (a) or mixtures of both substrates ( t + a ) . T. neapolitanus

and Spirillum

sulfate respectively

G7 cannot grow on acetate or t h i o ­

(10). Maximum s p e c i f i c growth r a t e P t

T.

neapolitanus

Thiobacillus Spirillum

a

m a x

(h ^)

t +a

0.3 A2

0.10

G7

-

3

A

5

0.22

0.22

0.43

0.43

6

7

8

Volume changes Figure 4. Competition in continuous culture between T. neapolitanus (the special­ ist) and T. A2 (the generalist) for thiosulfate as the only growth-limiting substrate. Key: Φ, relative cell number of Τ. A2; Ο , T. neapolitanus. Reproduced, with per­ mission, from Ref. 4. Copyright 1979, Springer-Verlag. 1

The chemostat was run at a dilution rate of 0.05 h' with a 40 mM thiosulfate concentration in the reservoir medium. Organisms had been pregrown separately in continuous culture at Ό = 0.05 h' and at zero time mixed in a 1:1 rate. 1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

238

BIOCHEMICAL ENGINEERING

Figure 5A. Effect of different concentrations of organic substrate on the outcome of the competition between T . A 2 and T. neapolitanus for thiosulfate. Protein concentration and organic content in the cultures are shown, limited by thiosulfate plus acetate or glycollate. Reproduced, with permission, from Ref. 4. Copyright 1979, Springer-Verlag. 1

The chemostat was run at a dilution rate of 0.07 h' . The inflowing medium contained thiosulfate (40 mM) together with either acetate or glycollate at concentrations ranging from 0-7 mM. Relative cell numbers, protein content, and organic cell carbon in the culture were determined after steady states had been established.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10.

KUENEN

Microbial

Specialists

and

Generalists

239

(• glycollate)

J. neapolitanus (•glycollate)

Oh

-L

-L

JL

3 4 5 6 7 8 9 GLYCOLLATE OR ACETATE (mM)

10

Figure 5B. Effect of different concentrations of organic substrate on the outcome of the competition between T . A2 and T. neapolitanus for thiosulfate. Conditions as in Figure 2A. The percentage of T . A2 cells and of T . neapolitanus cells in cultures are shown, with thiosulfate plus acetate or glycollate in the reservoir medium. Reproduced, with permission, from Ref. 4. Copyright 1979, SpringerVerlag.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

240

BIOCHEMICAL ENGINEERING

mM

THIOSULFATE

Figure 6. Results of competition between the generalist T . A2, and two specialists, T. neapolitanus and Spirillum G7 for thiosulfate and acetate as growth-limiting substrates in the chemostat at a dilution rate of 0.07 h' . Concentrations in the inflowing medium ranged from 0-20 mM for acetate and from 0-40 mM for thiosulfate. After a steady state had been established relative cell numbers were determined. Solid line, experimental data; dashed line, outcome of the competition as predicted from mathematical modeling. 1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983. 1

sample

canal canal canal ditch ditch

Number

I II III IV V

30 10 30 20 10

t t t t t

+ 5a + 15 a + 5a + 10 a + 15 a

substrate concentration i n medium (mM) 82 75 85 50 86

% of t o t a l

chemolithotroph It ft II

type

chemolithoheterotroph

facultative tt tt It

metabolic

Dominant population

Results of enrichment c u l t u r e s (I - V) from f r e s h water samples a f t e r 15-20 volume changes i n the chemostat under dual substrate l i m i t a t i o n of t h i o s u l f a t e ( t ) and a c t e t a t e (a) at a d i l u t i o n r a t e of 0.05 h " , using d i f f e r e n t mixtures of t + a. Adapted from G o t t s c h a l and Kuenen, ( Π ) .

Table I I I

242

BIOCHEMICAL ENGINEERING

t i c a l treatments of the growth of m i c r o b i a l populations on mix­ tures of substrates i t has been p r e d i c t e d that the maximum number of organisms which can c o e x i s t can never be more than the number of g r o w t h - l i m i t i n g substrates supplied to the c u l t u r e . This holds i f no i n t e r a c t i o n other than mere competition takes place i n the c u l t u r e . Based on previous p u b l i c a t i o n s of other workers G o t t s c h a l and Things tad (_7) have developed a mathematical model f o r growth of the three organisms i n the p a r t i c u l a r case. The model i s based on simple Monod k i n e t i c s f o r growth. The s p e c i f i c growth r a t e of the s p e c i a l i s t autotroph (A) on t h i o s u l ­ fate (t) i s

U

max (8 ) = t A · t y

tA

S

i n which s i s the c o n c e n t r a t i o n of the t h i o s u l f a t e and K ^ the substrate s a t u r a t i o n constant of the autotroph f o r t h i o s u l f a t e . S i m i l a r l y , f o r growth of the heterotroph (H) on acetate (a) one obtains t

t

max M

aH

I •I ' I ' I

0

ε C02-f'xotion

Ô ^

CM

ο

4-+ * -1000k

pH extremes a l i p h a t i c alcohols

Pseudomonas

sugars amino acids nucleotides

inorganic ions pH extremes amino acids

Bacillus

sugars amino acids

inorganic ions pH extremes metabolic poisons

Salmonella

°2 sugars amino acids

a l i p h a t i c alcohols

0„ Vibrio

amino acids

Spirillum

sugars amino acids

inorganic ions pH extremes

Rhodospirilium

nucleotides s u l f h y d r y l compounds

pH extremes poisons

Clostridium Bdellovibrio

amino acids

Proteus

sugars amino acids °2 sugars

Erwinia

inorganic acids pH extremes inorganic ions pH extremes inorganic ions pH extremes

Sarcina Serratia

sugars amino acids

inorganic ions pH extremes

0„ Bordetella Pasteurella Marine b a c t e r i a

algal culture f i l t r a t e s

heavy metals t o x i c hydrocarbons

Source: Refs. 36-38.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

270

BIOCHEMICAL ENGINEERING

s t i m u l i , p r o b a b l y b o t h a t t r a c t a n t s and r e p e l l e n t s , a r e present. M u l t i p l e s i g n a l s a r e a d d i t i v e i n some s e n s e ( 1 6 ) , and p r e s u m a b l y t h e b a c t e r i a a t t e m p t t o o p t i m i z e t h e i r growth through p r e f e r e n t i a l m i g r a t i o n . F r o m an e n g i n e e r i n g p e r s p e c t i v e , t h e r e i s no q u a n t i t a t i v e b a s i s f o r p r e d i c t i o n o f the e f f e c t s o f c e l l m o t i l i t y and c h e m o t a x i s o n m i c r o b i a l p o p u l a t i o n d y n a m i c s i n a n y given s i t u a t i o n at present. T h i s paper i s devoted to r e v i e w o f the s m a l l body o f i n f o r m a t i o n a v a i l a b l e i n t h i s area at t h i s time. Experimental

Observations

T h e r e e x i s t s o n l y a s m a l l number o f p u b l i s h e d experiments p e r t a i n i n t th effect f cell motilit on p o p u l a t i o n g r o w t h g i v e s one example w i t h o u c o m p e t i t i o n b e t w e e n an a e r o t a c t i c ( i . e . , c h e m o t a c t i c a l l y a t t r a c t e d by o x y g e n ) P s e u d o m o n a s s p e c i e s a n d an i m m o t i l e A c i n e t o b a c t e r s p e c i e s , f o r o x y g e n ( 1 7 ) . When t h e g r o w t h medium i s w e l l - a e r a t e d t h e A c i n e t o b a c t e r predominate, thus showing s u p e r i o r g r o w t h k i n e t i c s on t h e r a t e - l i m i t i n g s u b s t r a t e (presumably oxygen) s i n c e c e l l m o t i l i t y i s a p p a r e n t l y irrelevant. But i n a non-mixed c u l t u r e the Pseudomonas p r e d o m i n a t e . The c h e m o t a c t i c a b i l i t y of the Pseudomonas s p e c i e s p r o v i d e s , i n t h i s s i t u a t i o n , enough o f a b e n e f i t t o overcome i t s growth k i n e t i c inferiority. The f i r s t l i t e r a t u r e r e p o r t i n t h i s a r e a was by S m i t h a n d D o e t s c h (]J*) , who s t u d i e d c o m p e t i t i o n b e t w e e n a e r o t a c t i c P s e u d o m o n a s f l u o r e s c e n s and an i m m o t i l e m u t a n t s t r a i n o f t h e same s p e c i e s , f o r o x y g e n (see Figure 2 ). In a e r a t e d mixed c u l t u r e b o t h s t r a i n s g r e w t o a r o u g h l y 1:1 r a t i o o v e r a 2 4 - h o u r p e r i o d i n d i c a t i n g t h a t t h e i r g r o w t h k i n e t i c p r o p e r t i e s were i d e n t i c a l as e x p e c t e d . In n o n - a e r a t e d media, the a e r o t a c t i c s t r a i n outgrew the mutant t o a f i n a l ratio o f o v e r 10:1 a f t e r 24 h o u r s . U n f o r t u n a t e l y , the a u t h o r s c r e d i t e d m o t i l i t y per se f o r t h i s a d v a n t a g e , e v e n t h o u g h i t i s not c l e a r whether random m o t i l i t y without chemotaxis i s n e c e s s a r i l y always b e n e f i c i a l . In the c o u r s e o f s t u d y i n g t h e r o l e o f f i m b r i a e i n b a c t e r i a l g r o w t h , O l d and D u g u i d l o o k e d a t c o m p e t i t i o n f o r o x y g e n b e t w e e n two n o n f i m b r i a t e s t r a i n s o f Salmonella typhimurium: one a e r o t a c t i c and one immotile (_19) (see Table 2 ) . In a e r o b i c shaken b r o t h , t h e a e r o t a c t i c s t r a i n m u l t i p l i e d by a f a c t o r o f 46 w i t h i n 48 h o u r s , w h i l e t h e i m m o t i l e s t r a i n m u l t i p l i e d by a f a c t o r o f 52. Again the growth k i n e t i c

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

12.

LAUFFENBURGER

Cell

Time (hr)

211

Motility

Time (hr)

Figure 2. Multiplication of aerotactic (O) and immotile (Φ) strains of Pseudo­ monas fluorescens in two different experiments, each in aerated mixed culture (left) and nonaerated mixed culture (right). Reproduced, with permission, from Ref. 18. Copyright 1969, Society for General Microbiology.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2.

0.15 2.91 3.00 2.94

0.15 0.38 0.55 0.69

0.19 0.35 0.46 0.48 0.66 1.41

0.16 3.27 3.48 3.61

0.16 0.37 0.71 1.84

typhimurium

Society

94 6,900 3,800 4,900

94 380 500 540

65 270 195 86 105 190

130 4,200 4,600 4,700

130 530 380 1,030

Challenged bacteria

f o r Microbiology.

0.00024 0.016 0.011 0.011

0.00024 0.00080 0.0016 4.5

0.00017 0.00080 4.8 74 185 450

0.00033 0.0012 0.0029 0.0093

0.00033 0.0053 165 880

Challenging bacteria

Viable Count (10 bacteria)/ml o f

1970, A m e r i c a n

0 6 24 48

Aerobic shaken broth

Copyright

0 6 24 48

0 6 24 48 72 96

0 6 24 48

Aerobic s t a t i c broth

Aerobic s t a t i c broth

Aeiobic shaken broth

Aerobic s t a t i c broth

Conditions o f Growth

Amt of Growth

Strains of Salmonella

Time o f Incubation hr 0 6 24 48

of P a i r s of Variant

f r o m R e f e r e n c e 19.

S6353, fim f l a

S6351, fim f l a

Reproduced w i t h p e r m i s s i o n

S6355, fim f l a

+

S6351, fim f l a

+

S6358, f i m f l a

S6352, fim f l a

Challenged (rha-)

i n Mixed C u l t u r e s

Challenging (rha+)

Growth

COMPETING STRAINS

Table

W

9

-J to

12.

LAUFFENBURGER

Cell

Motility

273

p r o p e r t i e s appeared n e a r l y the same. In a e r o b i c s t a t i c b r o t h , however, the a e r o t a c t i c s t r a i n m u l t i p l i e d by a f a c t o r o f 18,000 i n 48 hours w h i l e the immotile s t r a i n m u l t i p l i e d by a f a c t o r o f 6. Interp r e t a t i o n o f t h i s c a s e i s not s t r a i g h t f o r w a r d , t h o u g h , because p e l l i c l e f o r m a t i o n was noted a f t e r 24 h o u r s , c o m p l i c a t i n g the s i t u a t i o n . More r e c e n t l y , P i l g r a m and W i l l i a m s s t u d i e d a s l i g h t l y d i f f e r e n t c a s e — c o m p e t i t i o n between c h e m o t a c t i c P r o t e u s m i r a b i l i s and a nonchemotactic but randomly m o t i l e mutant o f the s p e c i e s (20) (see F i g u r e s 3 and 4 ) . In both pure and mixed c u l t u r e s o f p e r i o d i c a l l y a g i t a t e d amino a c i d b r o t h , the two s t r a i n s grew t o a 1:1 r a t i o a f t e r 14 h o u r s . On the o t h e r hand, i n both s o l i d agar the r a t i s t r a i n s was g r e a t e r than 5:1 a f t e r 14 h o u r s . The f i n a l e x p e r i m e n t a l r e p o r t s were by F r é t e r et_ al. (21, 22, 2 3 ) , who s t u d i e d growth o f V i b r i o c h o l e r a e i n mouse and r a b b i t l a r g e i n t e s t i n e (see Figure 5 and Table 3. Here t h r e e s t r a i n s were compared: the c h e m o t a c t i c w i l d t y p e , an immotile mutant s t r a i n , and a nonchemotactic but randomly m o t i l e mutant strain. In w e l l - s t i r r e d c o n t i n u o u s flow c u l t u r e , a l l t h r e e s t r a i n s grew i n p r o p o r t i o n . In the i n t e s t i n a l l o o p s , the nonchemotactic s t r a i n was r a p i d l y d i s p l a c e d by the c h e m o t a c t i c w i l d t y p e . Most i n t e r e s t i n g l y , i n another experiment the randomly m o t i l e s t r a i n was a l s o r a p i d l y d i s p l a c e d by the immotile s t r a i n . A p p a r e n t l y , i n t h i s s i t u a t i o n at l e a s t , m o t i l i t y w i t h o u t chemot a x i s was a l i a b i l i t y f o r the c e l l s . It i s e v i d e n t t h a t t h e o r e t i c a l a n a l y s i s o f m o t i l i t y and chemotaxis i s n e c e s s a r y i n o r d e r t o p r o v i d e q u a n t i t a t i v e i n t e r p r e t a t i o n o f these r e s u l t s , and even q u a l i t a t i v e e x p l a n a t i o n o f the l a s t , perhaps c o u n t e r - i n t u i t i v e , o b s e r v a t i o n by F r é t e r et al_. This w i l l be the c o n c e r n o f the next s e c t i o n o f t h i s p a p e r . But i s i m p o r t a n t to emphasize at t h i s p o i n t t h a t the e x p e r i m e n t a l r e s u l t s c i t e d here demonstrate t h a t the e f f e c t s o f c e l l movement p r o p e r t i e s can c l e a r l y be s i g n i f i c a n t , and even dominant, i n d e t e r m i n i n g the c o m p e t i t i v e a b i l i t i e s o f b a c t e r i a l p o p u l a t i o n s i n nonmixed e n v i r o n m e n t s . Theoretical

Analyses

E a r l y attempts at t h e o r e t i c a l a n a l y s i s o f the e f f e c t s o f c e l l m o t i l i t y on p o p u l a t i o n growth c e n t e r e d on uptake o f n u t r i e n t by a s i n g l e c e l l i n a medium o f i n f i n i t e e x t e n t (12, 24, 25, 2 6 ) . These a n a l y s e s have

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

274

BIOCHEMICAL ENGINEERING

6

J8

10

12

J H

Hours

6

8 10

12

H 2L

Hours Figure 3. Growth of pure cultures of chemotactic (O) and nonchemotactic ( O strains of Proteus mirabilis in periodically shaken amino acid broth (top) and soft-agar amino acid medium (bottom). Reproduced, with permission, from Ref. 20. Copyright 1976, National Research Council of Canada.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

12.

LAUFFENBURGER

Cell

Motility

ο

I

1

ι

ι

ι

ι

ι

0

2

4

6

8

10

12

IK

ι

Η 24

Hours Figure 4. Growth of mixed cultures of chemotactic (O) and nonchemotactic ( Q ) strains of Proteus mirabilis in periodically shaken amino acid broth (top) and soft-agar amino acid medium (bottom). Reproduced, with permission, from Ref. 20. Copyright 1976, National Research Council of Canada.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

276

c

ENGINEERING

100 η

I 90 5 80 Ο

^ 70 ° ~ 60 5 2 50 6 30ζ
6* w i l l t h e c h e m o t a c t i c s t r a i n o u t g r o w t h e immotile s t r a i n . Thus, s p e c u l a t i o n t h a t a m o t i l e c h e m o t a c t i c s t r a i n s h o u l d a l w a y s be s u p e r i o r t o an immotile s t r a i n i s not n e c e s s a r i l y t r u e . T h e s e s i n g l e p o p u l a t i o n r e s u l t s s u g g e s t some i m p o r t a n t i m p l i c a t i o n s f o r c o m p e t i t i o n b e t w e e n two o r more p o p u l a t i o n s g r o w i n g t o g e t h e r o n a s i n g l e r a t e limiting nutrient. I f one s p e c i e s h a s s u p e r i o r g r o w t h k i n e t i c p r o p e r t i e s but t h e o t h e r has s u p e r i o r m o t i l i t y p r o p e r t i e s , we m i g h A n a l y s i s o f the t h i r r a n d o m l y m o t i l e p o p u l a t i o n s , shows t h a t t h i s i s i n d e e d possible. T h e r e a r e now a c t u a l l y t h r e e p e r m i s s i b l e steady s t a t e s : 1) c o e x i s t e n c e , 2) s p e c i e s 1 o n l y , a n d 3) s p e c i e s 2 o n l y . For sake o f c l a r i t y , l e t the two s p e c i e s have i d e n t i c a l p r o p e r t i e s e x c e p t t h a t ki > k2« Then s p e c i e s 1 w i l l have a g r e a t e r growth rate at a l l n u t r i e n t concentrations. In a d d i t i o n , the t h r e s h o l d c o n c e n t r a t i o n f o r net growth o f s p e c i e s 2 must be g r e a t e r t h a n t h a t o f s p e c i e s 1; i . e . , c i * We c a n i m m e d i a t e l y see t h a t a n e c e s s a r y c o n d i t i o n f o r coexistence i s that ω * · The v a l u e s o f ω f o r e a c h s p e c i e s a r e d e t e r m i n e d by t h e same e q u a t i o n a s i n t h e s i n g l e p o p u l a t i o n c a s e , u n a f f e c t e d by t h e p r e s e n c e o f the other s p e c i e s . We c a n , t h e r e f o r e , move d i r e c t l y to a g r a p h i c a l d e s c r i p t i o n o f the steadys t a t e behavior f o r our c o m p e t i t i o n model. F i g u r e 11 shows i s o c l i n e s o f ω i n t h e p l a n e o f (κ,λ) v a l u e s . If we s p e c i f y v a l u e s λ χ and κι f o r p o p u l a t i o n 1, t h i s y i e l d s a value for ωι. We c a n t h e n immediately d i s c o v e r t h e p e r m i s s i b l e s t e a d y - s t a t e s f o r any s p e c i e s 2 with parameter values λ and κ (see Figure 1 2 ) . If κ < K o n l y s p e c i e s 1 can s u r v i v e , u n l e s s λ2 i s such t h a t o)2 > ω — which would a l l o w c o e x i s t e n c e . If κ > Κ χ , o n l y s p e c i e s 2 can s u r v i v e , u n l e s s λ is s u c h t h a t α)2 < ω ι , w h i c h a g a i n a l l o w s c o e x i s t e n c e . S o , t h e c o m p e t i t i o n o u t c o m e c a n be p r e d i c t e d f r o m t h e s i n g l e p o p u l a t i o n r e s u l t s , w i t h one m i n o r modification. Remember t h a t t h e ω c r i t e r i o n i s o n l y a necessary condition for coexistence. I t turns out t h a t a s e c o n d , s l i g h t l y more r e s t r i c t i v e c o n d i t i o n i s a l s o r e q u i r e d , t o e n s u r e t h a t t h e c e l l d e n s i t i e s and n u t r i e n t c o n c e n t r a t i o n r e m a i n p o s i t i v e e v e r y w h e r e (3JL) . The d i f f e r e n c e b e t w e e n t h e two c o n d i t i o n s i s s m a l l 2

1 #

u

>

c

>

ω

2

2

2

l

2

r

χ

2

2

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

2

u

LAUFFENBURGER

Figure 11.

Cell

Motility

Sample plot of curves of constant ω in plane of (Χ, λ).

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

288

BIOCHEMICAL ENGINEERING

Ω

10

!

!

e

I

10*

ΙΟ

1

COEXISTENCE

j

2

SPECIES 1 ONLY ι

! !

ι

/

/

ι

8

•

32

!

λ, =10"' •*•

Χ

• /

ΙΟ" 2

II I Ι

/

,ο

4

SPECIES 2 ONLY

ι

/

s

/

ι

-/ / -ι

I ι Ι

! COEXISTENCE j ίο j

J

6

I

K

1 1 =

12

Figure 12. Illustration of predicted results for competition between two randomly motile populations with identical properties except for Κ and λ.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

12.

LAUFFENBURGER

Cell

Motility

289

for t y p i c a l parameter v a l u e s , however, so t h a t g i v e n the a p p r o x i m a t i o n i n v o l v e d i n the model i t s e l f , we n e e d n o t be t o o c o n c e r n e d w i t h i t . When t h e c e l l d e n s i t i e s a r e c o m p u t e d f o r a c o e x i s t e n c e s t a t e , t h e s p e c i e s w i t h s m a l l e r k c a n grow to a g r e a t e r p o p u l a t i o n s i z e than the s p e c i e s w i t h l a r g e r k, i f i t s m o t i l i t y p r o p e r t i e s a r e s u f f i c i e n t l y superior. T h i s g i v e s an e x p l a n a t i o n t o t h e r e s u l t c i t e d by S t a n i e r e t a l (1_7) . S i m i l a r r e s u l t s a r e e x p e c t e d when c h e m o t a x i s i s present i n competing p o p u l a t i o n s , although the a n a l y s i s has not y e t been c a r r i e d o u t . Chapman (5) f o r m u l a t e d a m o d e l f o r c o m p e t i t i o n o f two chemotactic s p e c i e s i n a t r a v e l i n g band which p r e d i c t e d that superior chemotaxi i n f e r i o r growth r a t species. T h i s r e s u l t i s c o n s i s t e n t w i t h our e x p e c t a t i o n s ; the model, however, i s r a t h e r e m p i r i c a l . Conclusions R e v i e w o f t h e l i t e r a t u r e r e v e a l s a s m a l l number o f e x p e r i m e n t s t h a t show t h a t c e l l m o t i l i t y p r o p e r t i e s c a n h a v e d r a m a t i c e f f e c t s o n p o p u l a t i o n g r o w t h and c o m p e t i t i o n i n non-mixed systems. Simple mathematical models have been d e v e l o p e d w h i c h p r o v i d e q u a l i t a t i v e e x p l a n a t i o n f o r a l l t h e o b s e r v e d p h e n o m e n a , and yield q u a n t i t a t i v e p r e d i c t i o n of the magnitude of e f f e c t s w h i c h m i g h t be e x p e c t e d i n a v a r i e t y o f s i t u a t i o n s . Ac k nowledgme n t s T h i s work h a s b e e n p a r t i a l l y s u p p o r t e d by NSF C h e m i c a l and B i o c h e m i c a l P r o c e s s e s Program G r a n t CPE80-06701. D.A.L. w o u l d a l s o l i k e t o t h a n k P a t Thompson f o r t y p i n g t h i s m a n u s c r i p t and R e n a t e S c h u l t z f o r many o f t h e f i g u r e s .

L i t e r a t u r e Cited 1.

Breed, R. S.; Murray, E . D. G . ; Smith, N. R. "Bergey's Manual of Determinative Bacteriology"; Williams and w i l k i n s : Baltimore, 7th e d i t i o n , 1957.

2.

Koshland, Jr., D. E. "Bacterial Chemotaxis as a Model Behavioral System"; Raven Press: New York, 1980.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

290

BIOCHEMICAL ENGINEERING

3.

Lauffenburger, D. A. "Effects of M o t i l i t y and Chemotaxis in C e l l Population Dynamical Systems"; PhD Thesis, University of Minnesota, 1979.

4·

Fraenkel, G. S.; Gunn, D. L . "The Orientation of Animals"; Dover: New York, 1961.

5.

Chapman, P. A. "Chemotaxis of Bacteria"; PhD Thesis, University of Minnesota, 1973.

6.

Berg, H. C.; Brown, D. A. Nature 1972, 239, 500-504.

7.

Macnab, R. M . ; Koshland, Jr., D. E . J. Mechanochem. C e l l M o t i l . 1973 2 141-148

8.

Macnab, R. M. In "Biological Regulation and Development", v o l . 2; R. Goldberger, e d . ; Plenum Press: New York, 1980, pp. 377-412.

9.

Dahlquist,

J.

F . W.; E l w e l l , R. Α . ; Lovely, P. S.

Supramol. S t r u c t .

1976, 4, 329-342.

10.

A d l e r , J. Science 1969, 166, 1588-1597.

11.

Macnab, R. M . ; Koshland, Jr., D. E . Proc. N a t l . Acad. S c i . USA 1972, 69, 2509-2512. Berg, H. C.; P u r c e l l , E . M. Biophys. J. 1977, 20, 193-219.

12. 13.

Hazelbauer, G. L.; Parkinson, J. S. In "Receptors and Recognition: Microbial Interactions"; J. R e i s s i g , e d . ; Chapman and Wall: London, 1977; pp. 60-80.

14.

A d l e r , J. Annu. Rev. Biochem. 1975, 44, 341-356.

15.

DeFranco, A. T.; Parkinson, J. S.; Koshland, D. E . J. B a c t e r i a l 1979, 139, 107-114.

16.

Tsang, N . ; Macnab, R. Μ., Koshland, Science 1973, 181, 60-63.

Jr.,

Jr.,

D. E .

17.

Stanier, R . ; Adelberg, E.; Ingraham, J. "The Microbial World"; P r e n t i c e - H a l l : Englewood Cliffs, New Jersey, 1976. 18.

Smith, J. L.; Doetsch, 1969, 55, 379-391.

R. N. J. Gen. M i c r o b i o l .

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

12.

LAUFFENBURGER

291

Cell Motility

19.

O l d , D. C., Duguid, J. P. J. B a c t e r i o l . 103, 447-456.

20.

Pilgram, W. R.; Williams, F. D. Can. J. M i c r o b i o l . 1976, 22, 1771-1773.

21.

F r e t e r , R.; A l l w e i s s , B . ; O'Brien, P. C. M . ; Halstead, S. A. In "Proceedings of the 13th Joint Conference on Cholera", U.S. - Japan Cooperative Medical Sciences Program; U.S. Govt. Printing O f f i c e , Washington, D . C . ; pp. 153-181.

22.

F r e t e r , R.; O'Brien, P. C. M . ; Halstead, S. A. Adv. Exp. Med

23.

F r e t e r , R.; O'Brien, P. C. M . ; Macsai, M. S. Am. J. C l i n . Nutr. 1979, 32, 128-132.

24.

Carlson, F . D. In "Spermatozoan M o t i l i t y " ; D. W. Bishop, ed.; AAAS Publication No. 72: Washington, D. C., 1962.

25.

Koch, A. L . Adv. Microb. P h y s i o l .

1971,

1970,

6,

147-217. 26.

Brunn, P. O. J. Biomech. Eng. 1981,

103,

27.

P u r c e l l , Ε. M. Am. J. Physics 1977,

45,

28.

Lauffenburger, D. Α . ; A r i s , R.; K e l l e r , Κ. H. Microb. E c o l . 1981, 7, 207-227. Lauffenburger, D. Α . ; A r i s , R.; K e l l e r , Κ. H. Biophys. J . (submitted for p u b l i c a t i o n ) .

29.

32-37. 3-11.

30.

Lauffenburger, D. Α . ; Calcagno, B. Biotech. Bioeng. (submitted for p u b l i c a t i o n ) .

31.

Calcagno, B. "Analysis of Steady-State Growth and Competition of Motile B a c t e r i a l Popula­ tions in Non-mixed Environments", M.S. Thesis, University of Pennsylvania, 1981.

32.

K e l l e r , E . F.; Segel, L . A. J. Theor. B i o l . 30, 225-234.

33.

Segel, L . Α . ; Chet, I . ; Henis, Y. J. Gen. M i c r o b i o l . 1977, 98, 329-337.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1971,

292 34.

BIOCHEMICAL ENGINEERING

Segel, L . A.; Jackson, J. L . J. Mechanochem. C e l l M o t i l . 1973, 2, 25-34.

35.

Holz, M . ; Chan, S. Biophys. J. 1979, 26, 243-262.

36.

Barrachini, O.; S h e r r i s , J. C. J. Path. Bact. 1959, 77, 565-574. Seymour, F . W. K . ; Doetsch, R. N. J. Gen. M i c r o b i o l . 1973, 78, 287-296.

37. 38.

Chet, I . ; M i t c h e l l , R. Annu. Rev. M i c r o b i o l . 1976, 30, 221-239.

RECEIVED

June 1, 1982

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13 Macroscopic Thermodynamics and the Description of Growth and Product Formation in Microorganisms J. A. ROELS Delft University of Technology, Netherlands Central Organization for Applied Scientific Research, T.N.O., P.O. Box 108, 3700 A C ZEIST, The Netherlands

From the point o living organisms are energy transducers c o n v e r t i n g a source of energy,e.g. chemical substances or photons, i n t o other forms o f energy. As such they are subject to the c o n s t r a i n t s posed by the first and second laws o f thermodynamics. As micro­ organisms are open systems and as such e x i s t i n a s t a t e o u t s i d e e q u i l i b r i u m , n o n - e q u i l i b r i u m thermo­ dynamics provide the p e r f e c t v e h i c l e f o r a first approach to the d e s c r i p t i o n of t h e i r behaviour. The concept o f the thermodynamic e f f i c i e n c y of growth i s developed and it is shown t h a t , as a r u l e of thumb, the maximum observed e f f i c i e n c i e s are about 0.65 i r r e s p e c t i v e the nature of the energy supplying process. A number of notable exceptions are shown to be most probably caused by l i m i t a t i o n s other than a v a i l a b l e energy. The nature o f growth and product formation i s discussed i n terms o f the c o u p l i n g o f the transformation of a given amount of substrate energy i n t o biomass energy to the energy obtained from a flow of e l e c t r o n s to a l e v e l of high to a l e v e l of low energy. The treatment i s shown to r e s u l t i n a r e l i a b l e r u l e of thumb f o r a first estimate o f the order of magnitude of the growth y i e l d o f an organism feeding on a given energy supplying t r a n s f o r m a t i o n process.

The b i o s p h e r e o n e a r t h i s , t h e r m o d y n a m i c a l l y s p e a k i n g , i n a c e r t a i n s e n s e an o p e n s y s t e m . I t r e c e i v e s e n e r g y f r o m t h e s u n i n t h e f o r m o f r a d i a t i o n . The e n e r g y o f t h e p h o t o n s r e a c h i n g e a r t h i s , i n p a r t , converted t o chemical energy i n a process c a l l e d 0097-6156/83/0207Ό295$08.00/0 © 1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

296

BIOCHEMICAL

ENGINEERING

p h o t o s y n t h e s i s . F o r the l a r g e r p a r t t h i s energy takes the form o f c a r b o h y d r a t e s , e.g. s u g a r s , s t a r c h e s and c e l l u l o s i c s . The components o f t h e b i o m a s s o f t h e p r i m a r y p r o d u c e r s a r e t h e s t a r t i n g p o i n t o f a wide v a r i e t y o f t r a n s f o r m a t i o n s , which takes p l a c e under c a t a l y t i c a c t i o n o f l i v i n g organisms. As a f i n a l r e s u l t t h e s o l a r e n e r g y i s c o n v e r t e d t o l e s s energy r i c h forms o f r a d i a t i o n w h i c h t r a n s p o r t energy t o o u t e r space o r i s used t o d e c r e a s e t h e e n t r o p y o f t h e b i o s p h e r e . The r e a s o n i n g d e v e l o p e d above shows t h a t t h e b i o s p h e r e i s a s y s t e m , w h i c h i s s u b j e c t t o a f l o w o f e n e r g y . The e n e r g y e n t e r s t h e s y s t e m a t a l o w e n t r o p y l e v e l and l e a v e s i t a t a s u b s t a n t i a l l y h i g h e r e n t r o p y l e v e l . As s u c h t h e b i o s p h e r e c a n m a i n t a i n a s t a t e w i t h a n e n t r o p y l o w e r t h a n t h e maximum c o r r e s ­ p o n d i n g t o t h e r m o d y n a m i c e q u i l i b r i u m and p r o c e s s e s known as " l i f e " r e s u l t (J_). A s i n g l e organism o supplying process e x i s t positio b i o s p h e r e as a w h o l e . I t i s an open s y s t e m t h r o u g h w h i c h e n e r g y f l o w s f r o m a low e n t r o p y s t a t e , e.g. c h e m i c a l e n e r g y s t o r e d i n compounds more r e d u c e d t h a n C 0 , t o a h i g h e n t r o p y s t a t e , e.g. h e a t a t a l o w t e m p e r a t u r e l e v e l . As a r e s u l t t h e o r g a n i s m s c a n m a i n t a i n a s t a t e o u t s i d e t h e r m o d y n a m i c e q u i l i b r i u m and c a n continue performing the processes c h a r a c t e r i s t i c f o r t h e i r " l i f e " . As o r g a n i s m s a r e s y s t e m s w h i c h e x i s t o u t s i d e t h e r m o d y n a m i c e q u i l i b r i u m and i r r e v e r s i b l e p r o c e s s e s a r e t a k i n g p l a c e , t h e f o r m a l i s m o f thermodynamics of i r r e v e r s i b l e p r o c e s s e s c o n s t i t u t e s the l o g i c a l v e h i c l e t o t r e a t t h e i r b e h a v i o u r . I n the p r e s e n t a r t i c l e t h e f o r m a l i s m w i l l be b r i e f l y s u m m a r i z e d f o r t h e p u r p o s e o f i t s a p p l i c a t i o n t o m i c r o o r g a n i s m s engaged i n g r o w t h and p r o d u c t f o r m a t i o n . F o r a more t h o r o u g h t r e a t m e n t o f t h e b a s i c f o r m a l i s m t h e r e a d e r i s r e f e r r e d t o t h e s t a n d a r d t e x t s ( 2 - 4 ) and e a r l i e r w o r k o f t h e p r e s e n t a u t h o r ( 5 , 6^). 2

Macroscopic

t h e r m o d y n a m i c s and p r o c e s s e s

i n open s y s t e m s .

05, 6)

For t h e purpose o f the present a n a l y s i s o f m i c r o b i a l metabolism, a g i v e n amount o f m i c r o o r g a n i s m s i s c o n s i d e r e d t o be an e n e r g y t r a n s d u c e r . I t i s s c h e m a t i c a l l y r e p r e s e n t e d i n f i g . 1. The s y s t e m e x c h a n g e s c h e m i c a l e n e r g y and h e a t w i t h t h e e n v i r o n m e n t . F o r s i m p l i c i t y ' s s a k e t h e c a s e o f p r o c e s s e s i n v o l v i n g radiâtional e n e r g y i s e x c l u d e d . The b a s i c f o r m a l i s m , h o w e v e r , c a n be e a s i l y extended t o i n c l u d e these s i t u a t i o n s . The s t a t e o f t h e s y s t e m c a n be c h a r a c t e r i z e d by a number o f e x t e n s i v e q u a n t i t i e s ; t h e s e s p e c i f y t h e amount o f t h e v a r i o u s c h e m i c a l s u b s t a n c e s and t h e amount o f e n e r g y p r e s e n t i n t h e s y s t e m . F o r e a c h e x t e n s i v e q u a n t i t y , w h i c h c a n be a t t r i b u t e d t o t h e s y s t e m , a b a l a n c e e q u a t i o n c a n be f o r m u l a t e d ; i t e x p r e s s e s t h e a c c u m u l a t i o n o f t h e q u a n t i t y i n s i d e t h e s y s t e m as t h e sum o f t h e c h a n g e s o f i t s amount due t o t r a n s f o r m a t i o n and t r a n s p o r t p r o c e s s e s r e s p e c t i v e l y . M a t h e m a t i c a l l y t h i s c a n be e x p r e s s e d a s :

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13.

ROELS

Macroscopic

Thermodynamics

and

Growth

\ HEAT

Figure 1. An open system for macroscopic analysis. It exchanges chemical sub­ stances and heat with the environment. The flow of chemical substances, Φι, is characterized by the elemental composition and the partial enthalpy of the chemical substances.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

297

298

BIOCHEMICAL

ENGINEERING

(1) V

V

s

I n t h e f o r m u l a t i o n o f eqn. (1) i t i s assumed t h a t t h e volume and t h e s u r f a c e a r e a o f t h e s y s t e m do n o t change. I n t h e p r e s e n t a r t i c l e t h e d i s c u s s i o n w i l l be r e s t r i c t e d t o s y s t e m s i n a s t a t i o n a r y s t a t e , i . e . systems f o r which the time d e r i v a t i v e a p p e a r i n g a t t h e l e f t hand s i d e o f eqn. (1) has become z e r o . I n s u c h a c a s e eqn. (1) c a n be s i m p l i f i e d t o : (2) V W i t h respect to th n o n - e q u i l i b r i u m system the e x t e n s i v e q u a n t i t i e s c h a r a c t e r i z i n g t h e s y s t e m can be d i s t i n g u i s h e d i n t o two g r o u p s : c o n s e r v e d and non-conserved q u a n t i t i e s . S o - c a l l e d conserved q u a n t i t i e s cannot be p r o d u c e d o r consumed i n t h e t r a n s f o r m a t i o n p r o c e s s e s o p e n t o a g i v e n s y s t e m . T h e r e f o r e , t h e f i r s t t e r m a t t h e r i g h t hand s i d e of eqn. (1) i s n e c e s s a r i l y z e r o and eqn. (2) c a n be s i m p l y w r i t t e n as : (3)

E q u a t i o n (2) e x p r e s s e s t h e f a c t t h a t f o r e a c h c o n s e r v e d q u a n t i t y t h e t r a n s p o r t t o a s y s t e m i n s t a t i o n a r y s t a t e must e x a c t l y match t r a n s p o r t from t h a t system. For a non-conserved q u a n t i t y such s i m p l i f i c a t i o n i s not p o s s i b l e . The a p p l i c a t i o n o f t h e f o r m a l m a c r o s c o p i c t h e o r y t o t r a n s ­ f o r m a t i o n p r o c e s s e s i n o p e n s y s t e m s i s b a s e d on t h e f o r m u l a t i o n o f b a l a n c e e q u a t i o n s f o r a number o f c o n s e r v e d q u a n t i t i e s and an a d d i t i o n a l t h e r m o d y n a m i c c o n s t r a i n t a l l o w i n g t h e f o r m u l a t i o n of a u s e f u l e f f i c i e n c y measure. The e l e m e n t a l b a l a n c e e q u a t i o n s . In m i c r o b i a l conversion p r o c e s s e s t h e amounts o f t h e v a r i o u s a t o m i c s p e c i e s a r e c o n s e r v e d . T h i s o b s e r v a t i o n r e s u l t s i n the f o r m u l a t i o n of e l e m e n t a l balance e q u a t i o n s . U s i n g eqn. (3) t h e e l e m e n t a l b a l a n c e e q u a t i o n f o r a t o m i c s p e c i e s j c a n , a g a i n a s s u m i n g a s t a t i o n a r y s t a t e , be e x p r e s s e d as ( 5 , 6 ) : η Σ Φ.«*. .= 0 i-i 1

(4)

1 J

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13.

Macroscopic

ROELS

Thermodynamics

and

Growth

299

I n e q n . ( 4 ) Φ. s t a n d s f o r t h e n e t m o l a r f l o w o f compound i t o t h e s y s t e m , e. . s t a n d s f o r t h e number o f m o l e s o f a t o m i c s p e c i e s j i n one m J l e o f compound i . E q u a t i o n s o f t h e t y p e o f eqn. ( 4 ) p r o v i d e one c o n s t r a i n t t o t h e n e t exchange f l o w s f o r e a c h atomic species considered. The thermodynamic c o n s t r a i n t s . The a p p l i c a t i o n o f n o n - e q u i ­ l i b r i u m thermodynamics t o t r a n s f o r m a t i o n p r o c e s s e s i s based on t h e f o r m u l a t i o n o f two b a s i c b a l a n c e e q u a t i o n s . The f i r s t o n e , a b a l a n c e e q u a t i o n f o r e n e r g y , c a n , by v i r t u e o f t h e f a c t t h a t the f i r s t l a w o f t h e r m o d y n a m i c s a s s u r e s e n e r g y t o be a c o n s e r v e d q u a n t i t y i n any s y s t e m , f o r a s y s t e m i n s t a t i o n a r y s t a t e be expressed as: Φ

Ε

= 0

(5

i n w h i c h Φ^ i s t h e n e t f l o w o f e n e r g y t o w a r d s t h e s y s t e m . Thermodynamics show t h a t , f o r a n open s y s t e m o n w h i c h no work i s p e r f o r m e d by e x t e r n a l f o r c e f i e l d s , t h e e n e r g y f l o w t o w a r d s t h a t s y s t e m c a n be e x p r e s s e d as f o l l o w s : Φ

Φ

Ε - Η

+

Σ

Φ

Α

(

6

)

1

I n t h i s e q u a t i o n Φ^ i s t h e s o - c a l l e d h e a t f l o w o f P r i g o g i n e ( 2 ) and t h e h. a r e t h e p a r t i a l m o l a r e n t h a l p i e s o f t h e compounds exchanged w i t h t h e environment. I f eqns. ( 5 ) and ( 6 ) a r e combined t h e f a m i l i a r b a l a n c e equation f o r enthalpy i s obtained. I t allows the c a l c u l a t i o n of the heat exchanged w i t h t h e environment from t h e f o l l o w i n g equation: Φ

Η

= - Σ Φ h.

(7)

1

Equation ( 7 ) i n t r o d u c e s one new unknown f l o w , t h e h e a t f l o w Φ^, and one a d d i t i o n a l c o n s t r a i n t , hence t h e t o t a l number o f unknown f l o w s does n o t change by t h e a p p l i c a t i o n o f t h e f i r s t l a w o f thermodynamics. A second r e s t r i c t i v e e q u a t i o n r e s u l t s from t h e b a l a n c e e q u a t i o n f o r e n t r o p y . F o r a system i n s t a t i o n a r y s t a t e the b a l a n c e equation f o r entropy r e s u l t s i n the f o l l o w i n g expression:

i n w h i c h Tig i s t h e t o t a l e n t r o p y p r o d u c t i o n i n t h e s y s t e m , Φ 0

δ

ENGINEERING

(9)

Furthermore, be w r i t t e n as :

t h e r m o d y n a m i c s show t h a t t h e e n t r o p y f l o w c a n

0 i

(12)

ί

The p a r t i a l m o l a r g

i

=

h

i "

T

s

f r e e e n t h a l p y i s d e f i n e d by: ( 1 3 )

i

E q u a t i o n (12) w i l l be shown t o a l l o w t h e f o r m u l a t i o n o f an e f f i c i e n c y m e a s u r e , w h i c h c a n be used t o a n a l y s e g r o w t h and p r o d u c t f o r m a t i o n i n m i c r o o r g a n i s m s , i t s d e v e l o p m e n t w i l l be undertaken i n the next s e c t i o n . The t h e r m o d y n a m i c

efficiency.

The e n e r g y and e n t r o p y c o n t e n t o f c h e m i c a l s u b s t a n c e s . The t h e r m o d y n a m i c t h e o r y o u t l i n e d above c a n , i n p r i n c i p l e , be s t r a i g h t f o r w a r d l y a p p l i e d t o t h e d e s c r i p t i o n o f m i c r o b i a l growth and p r o d u c t f o r m a t i o n . I n o r d e r t o p e r f o r m s u c h an a n a l y s i s , t h e r m o d y n a m i c d a t a a r e needed r e g a r d i n g t h e compounds w h i c h a r e exchanged w i t h t h e environment, i . e . t h e p a r t i a l molar e n t h a l p i e s

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13.

ROELS

Macroscopic

Thermodynamics

and

Growth

301

and e n t r o p i e s o f t h e compounds i n v o l v e d i n t h e p r o c e s s e s i n t h e s y s t e m need t o be known. I n p r i n c i p l e t h e p a r t i a l m o l a r q u a n t i t i e s , e n t h a l p y a s w e l l as e n t r o p y , a r e f u n c t i o n s o f t h e c o n c e n t r a t i o n s o f e a c h and e v e r y c h e m i c a l compound p r e s e n t , i . e . d e f i n i t e v a l u e s c a n n o t be a t t r i b u t e d t o a s i n g l e compound. I n the approximation t o the e n e r g e t i c s o f m i c r o b i a l growth presented h e r e , i d e a l i t y o f t h e m i x t u r e o f compounds i n v o l v e d w i l l be assumed. T h i s i m p l i e s t h e p a r t i a l m o l a r t h e r m o d y n a m i c q u a n t i t i e s to be e q u a l t o t h e s p e c i f i c m o l a r q u a n t i t i e s , t h e s e l a t t e r q u a n t i t i e s depend o n i n t e n s i v e v a r i a b l e s l i k e t e m p e r a t u r e and p r e s s u r e and t h e c o n c e n t r a t i o n o f t h e compound c o n s i d e r e d o n l y . To a good d e g r e e o f a p p r o x i m a t i o n , e n t h a l p y c a n , a t a g i v e n t e m p e r a t u r e and p r e s s u r e , be assumed i n d e p e n d e n t o f t h e c o n c e n t r a ­ t i o n o f t h e compound u n d e r c o n s i d e r a t i o n . The f r e e e n t h a l p y i s , h o w e v e r , by v i r t u e o f t h e n t r o p c o n t r i b u t i o t that quantit (eqn. 1 3 ) , d e f i n i t e l y c o n c e n t r a t i o relationship holds: g

L

= g? + R T l n C

(14)

i

i n w h i c h g? i s t h e f r e e e n t h a l p y a t a g i v e n t e m p e r a t u r e and p r e s s u r e and u n i t c o n c e n t r a t i o n o f t h e compound, w h i c h i s c a l l e d standard free enthalpy. C. i s t h e c o n c e n t r a t i o n o f compound i . As a f i r s t a p p r o a c h s t a n d a r d q u a n t i t i e s , i . e . a s s u m i n g u n i t c o n c e n t r a t i o n s , w i l l be u s e d i n t h e p r e s e n t e v a l u a t i o n o f g r o w t h and product formation. One f u r t h e r c o n v e n i e n t c o n v e n t i o n needs t o be d i s c u s s e d . E n e r g y , and hence a l s o d e r i v e d q u a n t i t i e s l i k e e n t h a l p y and f r e e e n t h a l p y , c a n n o t be a t t r i b u t e d a d e f i n i t e v a l u e ; i t s m a g n i t u d e c a n o n l y be d e f i n e d w i t h r e s p e c t t o a g i v e n r e f e r e n c e s t a t e w h i c h i s a t t r i b u t e d a zero energy l e v e l . A convenient r e f e r e n c e s t a t e f o r t h e e v a l u a t i o n o f g r o w t h and p r o d u c t f o r m a t i o n i n m i c r o ­ o r g a n i s m s i s o b t a i n e d i f C 0 , H 0 , 0 and N a r e a s s i g n e d a z e r o e n e r g y l e v e l . The e n e r g y o f a compound t h u s becomes e q u a l t o i t s e n e r g y o f c o m b u s t i o n t o C 0 , H 0 and N . T h i s c o n v e n t i o n c a n be m o t i v a t e d by t h e f a c t t h a t m i c r o o r g a n i s m s c a n u n d e r no c i r c u m ­ stances d e r i v e u s e f u l energy from processes i n which o n l y C 0 , H 0 , 0 and N a r e i n v o l v e d . The m o l a r f r e e e n t h a l p i e s and e n t h a l p i e s _ o f c o m b u s t i o n a t s t a n d a r d c o n d i t i o n s w i l l be termed Ag°. and A h , r e s p e c t i v e l y . ^ From e q n . (7) i t i s c l e a r t h a t t h e e n f n a l p y o f c o m b u s t i o n , A h ° ^ , equals t h e heat o f combustion. The f r e e e n t h a l p y o f c o m b u s t i o n , A g . , i s m a r k e d l y d e p e n d e n t on t h e c o n c e n t r a t i o n s o f t h e r e a c t a n t s i n v o l v e d ( e q n . ( 1 4 ) ) and most b i o l o g i c a l p r o c e s s e s t a k e p l a c e i n aquous s o l u t i o n s a t a h y d r o g e n i o n c o n c e n t r a t i o n c o r r e s p o n d i n g t o a pH o f 7 r a t h e r t h a n a t u n i t c o n c e n t r a t i o n o f t h e H - i o n , c o r r e s p o n d i n g t o a pH o f z e r o . The f r e e e n t h a l p i e s o f c o m b u s t i o n t o l i q u i d w a t e r , t h e HC0 i o n (the p r e d o m i n a n t f o r m i n w h i c h C 0 e x i s t s a t a pH o f 7) and N a t a pH o f 7 c a n t h u s be c o n s i d e r e d more r e l e v a n t t o b i o l o g i c a l 9

2

2

2

2

2

2

2

2

2

2

2

0

C 1

0

3

2

2

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

302

BIOCHEMICAL

ENGINEERING

t r a n s f o r m a t i o n s . The f r e e e n t h a l p y o f c o m b u s t i o n u n d e r t h e s e c o n d i t i o n s w i l l be i n d i c a t e d A g ! . The e n t h a l p y o f c o m b u s t i o n i s h a r d l y a f f e c t e d by t h e pH. T^e f r e e e n t h a l p i e s and e n t h a l p i e s o f c o m b u s t i o n a r e known t o obey r e g u l a r i t i e s ( 6 , 8 ) . T h e s e c a n be t r e a t e d u s i n g t h e c o n c e p t o f t h e d e g r e e o f r e d u c t i o n a s i n t r o ­ d u c e d by M i n k e v i c h and E r o s h i n (_7) and e x t e n d e d and g e n e r a l i z e d by t h e p r e s e n t a u t h o r ( 5 , 6 ) . The g e n e r a l i z e d d e g r e e o f r e d u c t i o n , γ., o f a compound w i t h r e s p e c t t o m o l e c u l a r n i t r o g e n i s d e f i n e d by: 0

Ύ

=

ί

4

+

a

i"

2

b

( 1 5 )

i

I n w h i c h a. and b. a r e t h e number o f m o l e s o f Η and 0 p r e s e n t i n one C-mole ( b e i n g t h e amount c o n t a i n i n g 12 grams o f c a r b o n ) o f coumpound i . F o r a component i t h e n t h a l p i e d fre e n t h a l p i e s o f combustio Ag°. r e s p e c t i v e l y , a r e approximation uniqu f u n c t i o n o f t h e d e g r e e o f r e d u c t i o n , γ., as i n t r o d u c e d i n e q n . ( 1 5 ) . A s t a t i s t i c a l a n a l y s i s o f d a t a f o r some 60 o r g a n i c compounds o f b i o l o g i c a l s i g n i f i c a n c e revealed the existence of the f o l l o w i n g r e g u l a r i t i e s : 0

Ah .

= 115γ.

CL

Ag°.

(16)

' 1

= 94.4γ. + 86.6

(17)

The r e s i d u a l e r r o r o f t h e e s t i m a t e i s 18 k J f o r b o t h e q n s . ( 1 6 ) and ( 1 7 ) . E q u a t i o n (16) s t a t e s t h a t t h e h e a t o f c o m b u s t i o n p e r C-mole i s more o r l e s s d i r e c t l y p r o p o r t i o n a l t o t h e d e g r e e o f r e d u c t i o n . As i s a p p a r e n t f r o m eqn. (17) s u c h a s i m p l e p r o p o r ­ t i o n a l i t y r e l a t i o n does n o t a p p l y t o f r e e e n t h a l p i e s o f combustion. E q u a t i o n s (16) and (17) show t h a t s y s t e m a t i c d e v i a t i o n s b e t w e e n f r e e e n t h a l p i e s and h e a t s o f c o m b u s t i o n must e x i s t . F o r s u b s t r a t e s o f a low degree o f r e d u c t i o n the f r e e e n t h a l p i e s o f combustion exceed t h e heats o f combustion, f o r s u b s t r a t e s of a h i g h d e g r e e o f r e d u c t i o n t h e r e v e r s e a p p l i e s . T h i s phenomenon c a n be i l l u s t r a t e d i f t h e e n t r o p y c o n t r i b u t i o n t o t h e f r e e enthalpy o f combustion, T A s . , i s c a l c u l a t e d . I t i s obtained from the equation: 0

Ag°. 6

C1

0

0

CI

CI

= Ah . - TAs .

(18)

I n f i g . 2 t h e r e l a t i o n i s shown b e t w e e n t h e s a i d e n t r o p y c o n t r i ­ b u t i o n and t h e d e g r e e o f r e d u c t i o n u s i n g d a t a f o r a v a r i e t y o f o r g a n i c compounds. A d e f i n i t e t r e n d c a n i n d e e d be shown t o e x i s t ( a p a r t f r o m an i n c i d e n t a l o u t l y e r ) : The e n t r o p y c o n t r i b u t i o n i n c r e a s e s w i t h i n c r e a s i n g degree o f r e d u c t i o n . I n v i e w o f the o b s e r v a t i o n t h a t f r e e e n t h a l p y changes a t a pH o f 7 may w e l l be more r e l e v a n t i n m i c r o b i o l o g i c a l p r o c e s s e s , t h e e n t r o p y c o n t r i b u -

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13.

Macroscopic

ROELS

501 ο

Thermodynamics

ι 2.5

and

303

Growth

ι 5

ί­ 7.5

Γ Figure 2. The entropy contribution, T A s ° (kJ/C-mole), to the free enthalpy of combustion at standard conditions, as a function of the degree of reduction, y, of the compounds considered, for acids (%), carbohydrates (A), alkanes (Ο), ethene and ethyne (O), alcohols (%), acetone (|Λ aldehydes (A), and amino acids (*). c

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

304

BIOCHEMICAL

ENGINEERING

0 f

t i o n t o t h e f r e e e n t h a l p y o f c o m b u s t i o n a t a pH o f 7, T A s , was a l s o c a l c u l a t e d . T h e s e v a l u e s a r e p l o t t e d as a f u n c t i o n o? t h e d e g r e e o f r e d u c t i o n i n f i g . 3. The f e a t u r e s o f f i g s . 2 and 3 a r e s e e n t o be v e r y much a l i k e , e x c e p t f o r t h e a c i d s , w h i c h have a m a r k e d l y h i g h e r T A s a t a pH o f 7, i . e . t h e i r f r e e e n t h a l p y o f c o m b u s t i o n i s îower a t t h a t pH. T h i s d i f f e r e n c e b e t w e e n s t a n d a r d c o n d i t i o n s and a s i t u a t i o n i n w h i c h t h e c o n c e n ­ t r a t i o n s d i f f e r f r o m u n i t y , e.g. a t a pH o f 7, i s c h a r a c t e r i s t i c f o r a l i m i t a t i o n o f t h e use o f s t a n d a r d f r e e e n t h a l p y changes i n t h e a n a l y s i s o f p r o c e s s e s , where t h e c o n c e n t r a t i o n s a t t h e l o c a l e o f t h e p r o c e s s may d i f f e r f r o m u n i t y : t h e Ag° v a l u e s c a n o n l y be a p p l i e d t o an a p p r o x i m a t e a n a l y s i s . F o r d e t a i l e d c o n s i d e r a t i o n s the A g v a l u e s at the c o n c e n t r a t i o n s at the l o c a l e o f e n e r g y g e n e r a t i o n a r e n e e d e d . S t i l l , as w i l l be shown, t h e approximate analyses g r e a t l c o n t r i b u t t th understandin of m i c r o b i a l energetics 0 f

Q

T h e r e a l s o e x i s t compounds o f w h i c h t h e e n e r g y r e l e a s e d on t h e i r c o m b u s t i o n does d e f i n i t e l y n o t f o l l o w t h e t r e n d s i n d i c a t e d by e q n s . (16) and ( 1 7 ) . E x a m p l e s a r e o x y g e n and n i t r i c a c i d w h i c h have a " h e a t o f c o m b u s t i o n " w h i c h i s c l o s e t o z e r o and a d e g r e e o f r e d u c t i o n o f -4 and -5 r e s p e c t i v e l y . By v i r t u e o f t h i s f e a t u r e t h e s e compounds can s e r v e as v e r y e f f i c i e n t " e l e c t r o n a c c e p t o r s " . The t h e r m o d y n a m i c e f f i c i e n c y . The t h e r m o d y n a m i c t h e o r y d e v e l o p e d e a r l i e r was shown t o r e s u l t i n eqn. ( 1 2 ) , a r e s t r i c t i v e e q u a t i o n r e g a r d i n g the f l o w s o f m a t t e r exchanged w i t h the e n v i r o n ­ ment by an open s y s t e m . On eqn. (12) a d e f i n i t i o n o f t h e t h e r m o ­ d y n a m i c e f f i c i e n c y c a n be b a s e d i f t h e d i s s i p a t i o n , ΤΠ , i s compared t o t h e t o t a l o f t h e f l o w s o f f r e e e n t h a l p y e n t e r i n g t h e s y s t e m . However, a p r o b l e m w h i c h was a l r e a d y i n d i c a t e d above has t o be t a c k l e d . The amount o f e n e r g y c a n n o t be s p e c i f i e d i n a u n i q u e way and i t can o n l y be d e f i n e d w i t h r e f e r e n c e t o a b a s e l e v e l , w h i c h i s a r b i t r a r i l y a t t r i b u t e d z e r o e n e r g y c o n t e n t . As s o o n as s u c h a r e f e r e n c e s t a t e has been c h o s e n , t h e t h e r m o d y n a m i c e f f i c i e n c y i s e a s i l y c a l c u l a t e d . The p r o c e d u r e i s i l l u s t r a t e d i n f i g . 4. The t h e r m o d y n a m i c e f f i c i e n c y , fL,» i s d e f i n e d e q u a l t o t h e r a t i o o f t h e f r e e e n t h a l p y g a i n e d i f t h e compounds l e a v i n g t h e s y s t e m were t r a n s f o r m e d t o t h e r e f e r e n c e s t a t e , t o t h a t , w h i c h w o u l d be o b t a i n e d i f t h i s p r o c e d u r e were a p p l i e d t o t h e compounds e n t e r i n g t h e s y s t e m . I t i s e a s i l y u n d e r s t o o d t h a t η , i s c o n s t r a i n e d between z e r o , i f a l l t h e f r e e e n t h a l p y e n t e r i n g trie s y s t e m i s d i s s i p a t e d and u n i t y i f Ag!j e q u a l s Ag^ , i . e . i f t h e d i s s i p a t i o n equals zero. I t i s important to r e a l i z e t h a t the f o r m e r c o n s t r a i n t s t r o n g l y depends on t h e c o r r e c t c h o i c e o f t h e reference state. A p p l i c a t i o n s of the

theory

A e r o b i c g r o w t h w i t h o u t p r o d u c t f o r m a t i o n . The a p p l i c a t i o n of the theory to a e r o b i c growth without f o r m a t i o n of products

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13.

Macroscopic

ROELS

Thermodynamics

and

305

Growth

k J/C-mole

100

50

Π Ο

Θ

Δ*

*

-50

*

*

*

** *

7.5

2.5 Υ

Figure 3. The entropy contribution, T A S (kJ/C-mole), to the free enthalpy of combustion at a pH of 7, as a function of the degree of reduction, y, of the com­ pounds considered; symbols as in Figure 2. C

0 /

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

306

BIOCHEMICAL

ENGINEERING

w i l l now be shown. F i g u r e 5 shows t h e s y s t e m and t h e exchange f l o w s f o r t h i s c a s e . The e l e m e n t a r y c o m p o s i t i o n s and t h e h e a t s o f c o m b u s t i o n o f t h e compounds exchanged w i t h t h e e n v i r o n m e n t a r e i n d i c a t e d . A e r o b i c g r o w t h i s f o r t h e p r e s e n t a n a l y s i s assumed t o i n v o l v e u p t a k e o f a n i t r o g e n s o u r c e , a c a r b o n s o u r c e and o x y g e n and t r a n s p o r t t o t h e e n v i r o n m e n t o f c a r b o n d i o x i d e , w a t e r and new b i o m a s s . The b i o m a s s i s assumed t o be one compound, w h i c h c a n be c h a r a c t e r i z e d f u l l y by i t s e l e m e n t a l c o m p o s i t i o n . As t h e e n t h a l p y as w e l l as t h e f r e e e n t h a l p y o f c o m b u s t i o n , i . e . t h e e n t h a l p y and f r e e e n t h a l p y c o n t e n t w i t h r e s p e c t t o t h e r e f e r e n c e s t a t e adopted i n t h e p r e s e n t a n a l y s i s , i s zero f o r oxygen, carbon d i o x i d e and w a t e r , i t i s e a s i l y u n d e r s t o o d t h a t t h e thermodynamic e f f i c i e n c y c a n be d e f i n e d a s f o l l o w s : Φ Ag° n'th . u

-

—

^

—

(19

^

cN i n which Φ , and Φ^ a r e t h e f l o w s o f b i o m a s s ( C - m o l e / h r ) , s u b s t r a t e ^ C - m o l e / h r ) and n i t r o g e n s o u r c e ( m o l e / h r ) t o o r f r o m t h e s y s t e m ( a s i n d i c a t e d i n f i g u r e 5 ) . Ag° and A g ° a r e t h e f r e e e n t h a l p i e s _ o f c o m b u s t i o n o f a C-mole o i b i o m a s s and s u b s t r a t e r e s p e c t i v e l y . A g ^ i s t h e f r e e e n t h a l p y o f combustion o f a mole of t h e n i t r o g e n source. E q u a t i o n (19) c a n a l s o be w r i t t e n a s : g

η,.

Ag° — A o / r g

s

+

(20) ( /c )Ai» C )

4

N

In the formulation o f t h i s equation a balance f o r atomic n i t r o g e n i s u s e d t o r e l a t e t h e f l o w s Φ , and Φ . Y i sa yield factor • Ν χ sx · f o r b i o m a s s o n s u b s t r a t e o n a p e r C-mole b a s e ; C-moles o f b i o m a s s p r o d u c e d p e r C-mole o f s u b s t r a t e consumed, t h u s i t i s d e f i n e d by: f f

%

γ " = φ /φ SX X s

(21)

A n o t h e r u s e f u l e f f i c i e n c y measure i s t h e s o - c a l l e d e n t h a l p y e f f i c i e n c y o f g r o w t h , η^, i t i s by a n a l o g y o b t a i n e d i f t h e Ag°. i n eqn. (20) a r e r e p l a c e d by t h e r e s p e c t i v e A h . . As was alreaày i n d i c a t e d t h e e n t h a l p y e f f i c i e n c y does n o t have t h e f u n d a m e n t a l p r o p e r t i e s o f t h e thermodynamic e f f i c i e n c y a s t h e r e s t r i c t i o n f o l l o w i n g from t h e a p p l i c a t i o n o f t h e second law o f thermodynamics ( s e e e q n . ( 1 1 ) ) d o e s n o t pose an u p p e r l i m i t t o Φ^. H e n c e , p r o c e s s e s f o r w h i c h η„ e x c e e d s u n i t y c a n by no means be e x c l u d e d . I t c a n e a s i l y b e shown t h a t t h e e f f i c i e n c y m e a s u r e s d e v e l o p e d a b o v e , i . e . η^, and η^, a l l o w t h e f o r m u l a t i o n o f e x p r e s s i o n s f o r t h e d i s s i p a t i o n ΤΠ and t h e h e a t p r o d u c t i o n (-Φ„). The f o l l o w i n g S n 0

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13.

ROELS

FREE

Macroscopic

Thermodynamics

and

307

Growth

ENTHALPY

ENTERING

SYSTEM

FREE

ENTHALPY

LEAVING

FREE

ENTHALPY

OF

REFERENCE

SYSTEM

STATE

Figure 4. The thermodynamic efficiency, ηα, of a process. A g / and A g / are the amounts of free enthalpy gained when the compounds entering and leaving the system, respectively, are transformed to the reference state.

c

_\h°-0

co

2

_H 0 2

cs

W

Figure 5.

W

CHa

b

Nc

i° i i

System and flows for thermodynamic analysis of aerobic growth formation of products.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

without

BIOCHEMICAL

308 equations

ENGINEERING

hold: (22)

(23) I n eqn. (22) D e q u a l s t h e d i s s i p a t i o n ΤΠ . For a e r o b i c growth w i t h o u t product f o r m a t i o n the a b s o l u t e m a g n i t u d e second t e r m a p p e a r i n g a t t h e l e f t hand s i d e o f eqn. (11) c a n be shown t o be s m a l l as compared t o Φ^/Τ, i . e . t h e exchange o f h e a t l a r g e l y e x c e e d s t h e exchange o f " c h e m i c a l e n t r o p y " ( 5 , 6^. T h i s i m p l i e s t h a t D and a r e , t o a good a p p r o x ­ i m a t i o n e q u a l and t h i s , o f c o u r s e , a l s o a p p l i e s t o η * Π^· I n t h i s c a s e an a n a l y s i s b a s e d on an e n t h a l p y e f f i c i e n c y o f g r o w t h i s more o r l e s s v a l i of t h e s e c o n d law as t As has been shown e a r l i e r (6) t h e v e r y f a c t t h a t eqn. (16) i s more o r l e s s v a l i d i m p l i e s t h a t h e a t p r o d u c t i o n and oxygen consumption, Φ , are p r o p o r t i o n a l a c c o r d i n g to the f o l l o w i n g equation : a n a

Φ„ = 460

Φ

(24)

ο

The a p p r o x i m a t e v a l i d i t y o f t h i s e q u a t i o n i s e a s i l y u n d e r s t o o d as f o l l o w s . The d e g r e e o f r e d u c t i o n γ. i n d i c a t e s t h e number o f moles o f e l e c t r o n s a v a i l a b l e f o r t r a n s f e r t o o x y g e n on c o m p l e t e c o m b u s t i o n o f a C-mole o f a compound t o C0 , H 0 and N . On t r a n s f e r t o oxygen t h e e n e r g y o f t h e e l e c t r o n s i s d i s s i p a t e d , r e s u l t i n g i n a h e a t p r o d u c t i o n o f 115 k J p e r mole o f e l e c t r o n s . On a e r o b i c g r o w t h p a r t o f t h e e n e r g y c o n t e n t o f t h e s u b s t r a t e and the n i t r o g e n source i s conserved i n the form o f newly s y n t h e s i z e d biomass, the e l e c t r o n s c o r r e s p o n d i n g to the remainder a r e t r a n s f e r r e d t o o x y g e n and p r o v i d e d i s s i p a t i o n . As f o u r moles o f e l e c t r o n s a r e a c c e p t e d by one m o l e o f o x y g e n eqn. (16) shows 460 k J t o be g e n e r a t e d f o r e a c h m o l e o f oxygen consumed. The v a l i d i t y o f eqn. (24) shows t h a t a t r e a t m e n t can a l s o be b a s e d on o x y g e n e f f i c i e n c y o f g r o w t h C5"\7) · A s u b s t a n t i a l body o f d a t a on a e r o b i c g r o w t h w i t h o u t p r o d u c t f o r m a t i o n s u p p o r t e d by ammonia as a n i t r o g e n s o u r c e has r e c e n t l y been r e v i e w e d ( 9 ) . From t h e s e d a t a t h e v a l u e s o f η (- η ) and t h e d i s s i p a t i o n p e r u n i t b i o m a s s p r o d u c e d (D/Φ , k J / C - m o l e ) were c a l c u l a t e d . The r e s u l t s were a v e r a g e d f o r e a c h o f t h e c a r b o n s o u r c e s c o n s i d e r e d and a r e shown i n f i g s . 6 and 7. A l t h o u g h , not u n e x p e c t e d l y , i t i s c l e a r t h a t c o n s i d e r a b l e s c a t t e r i s e x i s t e n t i n b o t h f i g s . 6 and 7,some g l o b a l r e g u l a r i t i e s seem t o be p r e s e n t , w h i c h a r e i n d i c a t e d i n t h e f i g u r e s . F o r s u b ­ s t r a t e s w i t h a d e g r e e o f r e d u c t i o n l o w e r t h a n about 5, t h e thermo­ dynamic e f f i c i e n c y a v e r a g e s 0.58 ( t h e o n l y s i g n i f i c a n t o u t l y e r b e i n g t h e v e r y low e f f i c i e n c y o b s e r v e d f o r g r o w t h s u p p o r t e d by 2

2

2

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13.

ROELS

Macroscopic

Thermodynamics

and

Growth

309

0.25

Figure 6. Thermodynamic efficiency, η , of aerobic growth with NH as the nitrogen source, plotted as a function of the degree of reduction, γ, of the substrate. Theoretical limits due to the second law and C-limitation. Shown are averages of experimental data for methane (%), n-alkanes (A), methanol (J^), ethanol (*ψ), glycerol (®), mannitol (O), acetic acid (Δλ lactic acid glucose (*), formalde­ hyde (VA gluconic acid (S), succinic acid (@), citric acid (®), malic acid (®), formic acid (®), oxalic acid (A)ιη

S

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

310

BIOCHEMICAL

A

Î

1270

ENGINEERING

1240

I·

Figure 7. Dissipation of aerobic growth (kJ/C-mole of biomass produced) for aerobic growth with ΝΗ as a nitrogen source as a function of the degree of reduction of substrate. Theoretical limits due to second law and C-limitation. Average of experimental data for various substrates, symbols as in Figure 6. Ά

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

13.

ROELS

Macroscopic

Thermodynamics

and

311

Growth

o x a l i c a c i d ) , t h i s corresponds to a d i s s i p a t i o n of roughly 400 k J / m o l e o f b i o m a s s p r o d u c e d . F o r s u b s t r a t e s w i t h a d e g r e e o f r e d u c t i o n e x c e e d i n g 5 t h e thermodynamic e f f i c i e n c y p r o g r e s s i v e l y d e c r e a s e s and t h e d i s s i p a t i o n i n c r e a s e s up t o 1400 kJ/C-mole f o r t h e c a s e o f g r o w t h s u p p o r t e d by methane. I n f i g s . 6 and 7 t h e r e s t r i c t i o n s o f u n i t e f f i c i e n c y and z e r o d i s s i p a t i o n r e s p e c t i v e l y , a s imposed by t h e s e c o n d law a r e i n d i c a t e d as w e l l as a l i m i t imposed by a l i m i t a t i o n o f a d i f f e r e n t n a t u r e , i . e . c a r b o n l i m i t a t i o n . The l a t t e r l i m i t m e r i t s a more t h o r o u g h d i s c u s s i o n . The d e g r e e o f r e d u c t i o n , γ , o f b i o ­ mass f r o m a v a r i e t y o f s o u r c e s a v e r a g e s 4.8 (5,6,10) and hence by v i r t u e o f eqn. (16) i t s e n e r g y c o n t e n t i s a b o u t 550 k J / C - m o l e . I f g r o w t h i s s u p p o r t e d by a s u b s t r a t e o f a d e g r e e o f r e d u c t i o n e x c e e d i n g 4.8 i t s e n e r g y c o n t e n t w i l l e x c e e d t h e s a i d 550 k J / C - m o l e and h e n c e , eve i f a l lsubstrat carbo fixed i n b i o m a s s , a thermodynami be o b t a i n e d . A c o m p l e t e x p l o i t a t i o energy p r e s e n t h e s u b s t r a t e w o u l d r e q u i r e f i x a t i o n o f a d d i t i o n a l low e n e r g y c a r b o n e.g. f r o m C0 . T h i s i s , however, e x c l u d e d , as o n l y one c a r b o n s o u r c e i s assumed t o be s u p p l i e d . On o b s e r v a t i o n o f f i g . 6 i t becomes c l e a r t h a t t h e t r e n d s o b s e r v e d i n t h e e x p e r i m e n t a l v a l u e s o f t h e thermodynamic e f f i c i e n c y mimic t h e shape o f t h e t h e o r e t i c a l r e s t r i c t i o n s a t a l e v e l o f a b o u t 60%. The d e v i a t i o n between t h e t h e o r e t i c a l l i m i t and t h e v a l u e s a c t u a l l y o b s e r v e d i s q u i t e e a s i l y u n d e r s t o o d i n g e n e r a l terms i n t h e r e g i o n o f low d e g r e e s o f r e d u c t i o n , where the energy a v a i l a b l e i n the s u b s t r a t e r a t h e r than i t s carbon c o n t e n t l i m i t s the v a l u e s o f Y . The t h e o r e t i c a l l i m i t o f u n i t y sχ · c a n n e v e r be r e a c h e d as any p r o c e s s needs a n o n - z e r o d i s s i p a t i o n t o proceed at a non-zero r a t e (2-4). In f a c t the r a t e at which a p r o c e s s p r o c e e d s , e.g. t h e r a t e o f g r o w t h o f t h e amount o f biomass, i s to a c e r t a i n extent i n c r e a s i n g w i t h i n c r e a s i n g d i s s i p a t i o n . V a r i o u s o p t i m a l i t y p r i n c i p l e s ( 1 1 ) , may d i c t a t e an o p t i m a l thermodynamic e f f i c i e n c y o f r o u g h l y t h e m a g n i t u d e o b s e r v e d h e r e ( 1 1 , 1 2 ) . The b e h a v i o u r a t h i g h d e g r e e s o f r e d u c t i o n i s l e s s e a s i l y u n d e r s t o o d on f u n d a m e n t a l g r o u n d s . The t h e r m o ­ dynamic e f f i c i e n c y c o u l d w e l l a p p r o a c h t h e t h e o r e t i c a l l i m i t c l o s e r with a s u f f i c i e n t l y l a r g e d i s s i p a t i o n . A p p a r e n t l y o t h e r phenomena t o w h i c h t h e f o r m a l m a c r o s c o p i c t r e a t m e n t p r o v i d e s no c l u e s , l i m i t t h e maximum c o n s e r v a t i o n o f s u b s t r a t e c a r b o n i n b i o m a s s t o a b o u t 2/3 o f t h e maximum. O b v i o u s l y one has t o r e s o r t t o b i o ­ c h e m i c a l t h e o r y t o o b t a i n c l u e s t o the n a t u r e o f t h e mechanisms u n d e r l y i n g t h e phenomenon. T h e r e e x i s t s s t i l l a n o t h e r u s e f u l q u a n t i t y , w h i c h has been used t o s y s t e m a t i z e t h e e x p e r i m e n t a l d a t a on t h e e f f i c i e n c y o f g r o w t h s u p p o r t e d by v a r i o u s c a r b o n s o u r c e s ; i t i s P a y n e s y i e l d on a v a i l a b l e e l e c t r o n s , Υ , ( 1 3 ) . I t i s d e f i n e d as t h e amount o f b i o m a s s p r o d u c e d p e r mole o f e l e c t r o n s a v a i l a b l e f o r t r a n s f e r t o o x y g e n on c o m p l e t e c o m b u s t i o n . N u m e r i c a l l y t h e number o f m o l e s o f e l e c t r o n s a v a i l a b l e f o r t r a n s f e r t o o x y g e n on 2

M

1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

312

BIOCHEMICAL

ENGINEERING

c o m b u s t i o n o f a C-mole o f a g i v e n s u b s t r a t e i s e q u a l t o t h e d e g r e e o f r e d u c t i o n , γ., as d e f i n e d by eqn. ( 1 5 ) . As a f i r s t a p p r o x i m a t i o n , t a k i n g i n t o account the f a c t t h a t biomass from a«-·• vVW a. rAi.^ eW tWy^ νo fΛ. I mUX i.V c.rLVUo b iJLaj. a l sIo7uWUr1c.eU^t7 s can beVJ t.w eW lI— lJ. J- r e p r e s e n t e d by t h e COU c a n be c o n s i d e r e d composition formula C H O . 5 N 0 . 2 » / p r o p o r t i o n a l t o X]^ ( o r r a t h e r n ) (§, 6 ) Y

l e 8

C

0

e

H

Υ

, av/e

= 5.85

η., th

(25)

F i g u r e 8 shows t h e d a t a d e p i c t e d i n f i g s . 6 and 7 i n a p l o t o f Y . v e r s u s t h e d e g r e e o f r e d u c t i o n γ. The t r e n d s and t h e o r e t i c a l l i m i t s a r e a l s o shown. Growth w i t h e l e c t r o preceeding s e c t i o n a cas e l e c t r o n a c c e p t i n g m o i e t y . Oxygen i s , h o w e v e r , by no means t h e o n l y compound, w h i c h c a n p e r f o r m s u c h f u n c t i o n . O t h e r examples a r e n i t r a t e and s u l p h a t e . The c h a r a c t e r i s t i c f e a t u r e o f an e l e c t r o n a c c e p t o r i s t h a t f r e e e n t h a l p y i s gained i n the o v e r a l l p r o c e s s o f t r a n s f e r o f an e l e c t r o n f r o m a g i v e n s o u r c e (a s u b s t r a t e ) to the acceptor. T h i s f r e e enthalpy i s p a r t l y d i s s i p a t e d t o p r o v i d e t h e n e c e s s a r y i r r e v e r s i b i l i t y and i t c a n be u s e d t o t r a n s f e r c a r b o n ( - d i o x i d e ) f r o m a low e n e r g y l e v e l t o a h i g h e n e r g y one. I n t a b l e I a summary i s p r o v i d e d o f t h e e n e r g y b e c o m i n g a v a i l a b l e on t r a n s f e r o f one m o l e o f e l e c t r o n s f r o m g l u c o s e t o a g i v e n e l e c t r o n a c c e p t o r engaged i n a g i v e n reduction process. Table

I.

F r e e e n t h a l p y g a i n e d a t pH = 7 and s t a n d a r d c o n d i t i o n s on t r a n s f e r o f one m o l e o f e l e c t r o n s f r o m g l u c o s e t o a g i v e n e l e c t r o n a c c e p t o r (14)

e l e c t r o n acceptor + * (NH ) N +

4

2

S

moles of e l e c t r o n s accepted 6

(HS~) 2-

SO, 4

(HS

)

0

1

Ag ^ ^ kJ 79.1

^Sai/^ kjfmole 13.2

2

27.7

13.9

8

150.7

18.8

6

171.9

28.7

9

S 0

3 N0 ~ 2

(HS~) +

6

435.5

72.6

+

598.4

74.8

(NH ) 4

N0 "

(NH )

8

N0 "

(N ) 2

5

559.5

111.9

(H 0)

4

473.9

118.5

3

3

°2 *

4

2

I n b r a c k e t s reduced

form of e l e c t r o n a c c e p t o r

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Macroscopic

ROELS

Thermodynamics

and Growth

313

'av/e g DM/mole 6h

SECOND

4H

2h

1h

Figure 8. Yield on electrons available for transfer to oxygen, Yav/e, (g DM/mole av/e) for aerobic growth with NH as a nitrogen source. Theoretical limits due to the second law and C-limitation. Average of experimental data for various substrates, symbols as in Figure 6. 3

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

314

ENGINEERING

The v a l u e s o f t h e f r e e e n t h a l p y g a i n e d p e r m o l e o f e l e c t r o n s t r a n s f e r r e d a r e a r r a n g e d i n o r d e r o f i n c r e a s i n g m a g n i t u d e . The " e f f i c i e n c y " o f an e l e c t r o n a c c e p t o r t h u s i n c r e a s e s f r o m t h e t o p to t h e b o t t o m o f t h e t a b l e and f a i t h i n l i f e ' s u n i v e r s a l s t r i v i n g f o r more o p t i m a l g r o w t h w o u l d assume p r e f e r e n c e f o r t h e e l e c t r o n a c c e p t o r s a t t h e b o t t o m o f t h e t a b l e i f two o r more e l e c t r o n acceptors are simultaneously a v a i l a b l e . Growth w i t h o u t e x t e r n a l l y s u p p l i e d e l e c t r o n a c c e p t o r s . I n a number o f c a s e s g r o w t h i s o b s e r v e d t o t a k e p l a c e w i t h o u t an i d e n t i f i a b l e seperate e l e c t r o n a c c e p t o r b e i n g p r e s e n t . I n such case t h e s u b s t r a t e o r a s u b s t r a t e d e r i v e d moiety i s both donor and a c c e p t o r o f e l e c t r o n s . F o r s i m p l i c i t y ' s s a k e o n l y t h e c a s e o f a n a e r o b i c g r o w t h on a s i n g l e c a r b o n s o u r c e w i t h f o r m a t i o n o f a s i n g l e p r o d u c t and NH^ as t h e n i t r o g e n s o u r c e w i l l be t r e a t e d I t i s e a s i l y understoo be b a s e d o n a b a l a n c e o eqn. ( 1 6 ) . T a b l e I I shows t h e f l o w s o f t h e v a r i o u s compounds and t h e i r c o n t e n t o f e l e c t r o n s a v a i l a b l e f o r t r a n s f e r t o oxygen on f o r m a t i o n o f Φ C-moles of b i o m a s s . χ Table I I .

A degree o f r e d u c t i o n balance f o r anaerobic growth w i t h o u t e x t e r n a l e l e c t r o n a c c e p t o r s

molecular species

degree of reduction

substrate N-source

Y

(NH^)

contribution to degree o f reduction balance

flow

γ Φ /Y" 's X SX 3ο.Φ 1 χ

Φ /Υ" χ

s

X

3

C φ

Y

Φ

SX

1 χ B i o m a s s (CH ,0, N -) a1 b1 c1 4

x

- γ Φ χ χ

χ

Product

- γ φ Ρ Ρ

φ Y

P

Ρ

2

0

Φ /Υ" --Φ -φ χ sx χ ρ

0

H 0

0

Φ

0

co 2

W

By v i r t u e o f t h e f a c t t h a t no e x t e r n a l e l e c t r o n a c c e p t o r s are present the c o n t r i b u t i o n s t o the degree o f r e d u c t i o n balance as shown i n t h e l a s t c o l u m n o f t a b l e 2 must add up t o z e r o , i t follows : Φ

Φ

70 cp) l a r g e s p h e r i c a l - c a p b u b b l e s are f r e q u e n t l y e n c o u n t e r e d and t h e r e l e v a n t correlation is : Sh

Non-Newtonian. F l o y

= 1.31

Pe

1 / 2

(8)

Effects

When t h e l i q u i d phase e x h i b i t s n o n - N e w t o n i a n b e h a v i o r , t h e mass t r a n s f e r c o e f f i c i e n t w i l l c h a n g e due t o a l t e r a t i o n s i n t h e f l u i d v e l o c i t y p r o f i l e a r o u n d t h e submerged p a r t i c l e s . The t r e n d s f o r b o t h m a s s t r a n s f e r and d r a g c o e f f i c i e n t a r e a n a l o g o u s . As b e f o r e f o r N e w t o n i a n f l u i d s , two t y p e s o f i n t e r f a c i a l b e h a v i o r need t o be c o n s i d e r e d . For

mobile-surface p a r t i c l e s i n power-law

fluids»

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Hirose

342

BIOCHEMICAL

ENGINEERING

and Moo-Young (1969) have o b t a i n e d a c o r r e l a t i o n f a c t o r f o r k, f o r s i n g l e b u b b l e s , b a s e d on s m a l l p s e u d o p l a s t i c d e v i a t i o n s r r o m N e w t o n i a n b e h a v i o r (0.7 < η < 1.0). They a l s o p r o v i d e some d a t a on d r a g c o e f f i c i e n t s a s f u n c t i o n s o f t h e power-law and Bingham plastic f l u i d s , with mobile i n t e r f a c e s , using perturbation a n a l y s i s , and p r o v i d e d c o r r e l a t i o n f a c t o r s f o r t h e e n h a n c e m e n t o f mass t r a n s f e r . F o r r i g i d s u r f a c e b e h a v i o r , t h e mass t r a n s f e r c o e f f i c i e n t s c a n be o b t a i n e d f r o m t h e r e s u l t s o f W e l l e k a n d H u a n g ( 1 9 7 0 ) . M o o - Y o u n g a n d H i r o s e ( 1 9 7 2 ) showed t h a t an a d d i t i o n a l e f f e c t o f " i n t e r f a c i a l s l i p " by a d d i t i v e s can o c c u r i n p r a c t i c e . Effect

Of

Bulk

Mixing

PattPrns

In a d d i t i o n t c o e f f i c i e n t , k » and t h gas and l i q u i d phase mass b a l a n c e e q u a t i o n s f o r t h e s p e c i e s t r a n s f e r r e d d e p e n d s o n t h e f l o w b e h a v i o r o f b o t h gas and l i q u i d phase· L

In low v i s c o s i t y l i q u i d s i t i s r e a s o n a b l y w e l l e s t a b l i s h e d t h a t i n s m a l l s t i r r e d - t a n k s t h e l i q u i d phase can be c o n s i d e r e d t o be " p e r f e c t l y m i x e d " ( W e s t e r t e r p , e t a l . . 1 9 6 3 ) . Under t h e s e c o n d i t i o n s , t h e g a s p h a s e h a s a l s o g e n e r a l l y b e e n assumed t o be w e l l m i x e d i n t a n k s o p e r a t i n g above c r i t i c a l i m p e l l e r s p e e d . In l a r g e t a n k s , h o w e v e r , t h e s i t u a t i o n i s l e e s c l e a r , and c a r e must be t a k e n t o e s t a b l i s h t h e b e h a v i o r o f b o t h p h a s e s . I n c a s e s where the d e g r e e o f gas a b s o r p t i o n i s h i g h , t h e a s s u m p t i o n s o f w e l l m i x e d o r p l u g - f l o w o f t h e g a s p h a s e may p r e d i c t s i g n i f i c a n t l y d i f f e r e n t gas a b s o r p t i o n r a t e s . S h a f t l e i n and R u s s e l l ( 1 9 6 8 ) p r e s e n t d e s i g n e q u a t i o n s f o r v a r i o u s m o d e l s o f g a s and liquid flows. INTRAPARTICLE BIOREACTION RATES

General Concepts In some b i o c h e m i c a l s y s t e m s t h e l i m i t i n g m a s s t r a n s f e r s t e p s h i f t s from a g a s - l i q u i d or s o l i d - l i q u i d i n t e r f a c e (as discussed e a r l i e r ) to the i n t e r i o r of s o l i d p a r t i c l e s . The most i m p o r t a n t c a s e s a r e s o l i d s u b s t r a t e s and c e l l a g g r e g a t e s ( s u c h as m i c r o b i a l f l o e s , c e l l u l a r t i s s u e s , e t c . ) and i m m o b i l i z e d enzymes (gel-entrapped or s u p p o r t e d i n s o l i d m a t r i c e s ) . In the former, d i f f u s i o n of o x y g e n ( o r o t h e r n u t r i e n t s ) t h r o u g h t h e p a r t i c l e l i m i t s m e t a b o l i c r a t e s , w h i l e i n the l a t t e r , s u b s t r a t e r e a c t a n t or p r o d u c t d i f f u s i o n i n t o o r out o f t h e enzyme c a r r i e r o f t e n l i m i t s the o v e r a l l g l o b a l b i o r e a c t i o n r a t e s . G e n e r a l i z e d mass b a l a n c e s

f o r the

a b o v e s c e n a r i o s can

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

be

15.

MOO-YOUNG

AND

BLANCH

Biological

Reactor

Design

s e t up and v a r i o u s c a s e s where mass t r a n s f e r r e s i s t a n c e w i t h i n p a r t i c l e may become i m p o r t a n t can be i d e n t i f i e d .

343 the

Oxygen Transfer in Mold f fil l e t s M a r s h a l l and A l e x a n d e r (1960) d i s c o v e r e d t h a t f o r s e v e r a l p e l l e t - f o r m i n g f u n g i a "cube r o o t " g r o w t h curve f i t t h e i r data s i g n i f i c a n t l y b e t t e r t h a n t h e s t a n d a r d e x p o n e n t i a l growth model. I t was s u g g e s t e d t h a t t h i s was p r o b a b l y due t o t h e e f f e c t s o f i n t r a p a r t i c l e d i f f u s i o n ; a n u t r i e n t was n o t d i f f u s i n g i n t o t h e p a r t i c l e f a s t enough t o m a i n t a i n u n r e s t r i c t e d g r o w t h . I t was s o o n r e a l i z e d t h a t o x y g e n was t h e l i m i t i n g n u t r i e n t . P h i l l i p s (1966) m e a s u r e d o x y g e n d i f f u s i o n i n p e l l e t s of ΡΡΠ i ci 11 i iim chrysogenum by f i r s t a s s u m i n g t h a t d i f f u s i o n i s t h e mechanism that s u p p l i e p e l l e t and t h a t t h e mas comparatively small. Y a n o e t . a l . ( 1 9 6 1 ) and Koyayashi» e t a l . (1973 b) d i d t h e same w i t h A s p e r g i l l u s n i g e r p e l l e t s . By t a k i n g i n t o a c c o u n t t h e e f f e c t o f i n t r a p a r t i c l e diffusion» K o b a y a s h i and S u z u k i ( 1 9 7 6 ) w e r e a b l e t o c h a r a c t e r i z e t h e k i n e t i c b e h a v i o r of t h e e n z y m e g a l a c t o s i d a s e w i t h i n m o l d p e l l e t s o f HûJLLiexfillâ. vinacea. K o b a y a s h i , e t a l . ( 1 9 7 3 b) s t u d i e d t h r e e c a s e s : (1) u n i f o r m r e s p i r a t i o n a c t i v i t y t h r o u g h o u t m y c e l i a l p e l l e t s * (2) r e s p i r a t i o n a c t i v i t y as a f u n c t i o n of age d i s t r i b u t i o n w i t h i n t h e p e l l e t * (3) r e s p i r a t i v e a c t i v i t y a d a p t a t i o n to the l o c a l oxygen c o n c e n t r a t i o n w i t h i n the p e l l e t . I n c a s e 1» i t was f o u n d t h a t t h e e f f e c t i v e n e s s f a c t o r ( E ) i s e q u a l t o t h e r a t i o of the s p e c i f i c r e s p i r a t i o n r a t e of a p e l l e t to the r e s p i r a t i o n r a t e of w e l l dispersed filamentous mycelia. The t h e o r e t i c a l and e x p e r i m e n t a l r e s u l t s f o r e a c h c a s e a r e g i v e n i n F i g u r e 4. I t i s seen t h a t the t h r e e c a s e s c o n s i d e r e d gave s i m i l a r r e s u l t s and i t i s d i f f i c u l t t o d i s c r i m i n a t e b e t w e e n them w i t h the l i m i t e d e x p e r i m e n t a l d a t a available. f

Immobilized

Enzyme

Kinetics

I n t r a p a r t i c l e d i f f u s i o n c a n h a v e a s i g n i f i c a n t e f f e c t on t h e k i n e t i c b e h a v i o r of enzymes i m m o b i l i z e d o n s o l i d c a r r i e r s o r entrapped i n gels. In t h e i r b a s i c a n a l y s i s of t h i s p r o b l e m . M o o - Y o u n g and K o b a y a s h i ( 1 9 7 2 ) d e r i v e d a g e n e r a l m o d u l u s and effectiveness factor. The r e s u l t s a l s o p r e d i c t e d possible m u l t i p l e s t e a d y - s t a t e s as w e l l as u n s t a b l e s i t u a t i o n s f o r c e r t a i n s y s t e m s . W h i l e t h e s e r e s u l t s a r e v e r y i n t e r e s t i n g i t s h o u l d be r e m e m b e r e d t h a t t h e y a r e p r i m a r i l y m a t h e m a t i c a l and a w a i t extensive experimental support data.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

344

BIOCHEMICAL

ENGINEERING

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

15.

Biological

MOO-YOUNG AND BLANCH

Enzymatic D e g r a d a t i o n of

Insoluble

Reactor

Design

345

Substrates

When t h e s u b s t r a t e i n a b i o r e a c t o r i s a w a t e r - s o l u b l e material (e.g., c e l l u l o s e , o i l s ) , the e f f e c t s of i n t r a p a r t i c l e m a s s t r a n s f e r may be i m p o r t a n t . In such systems, e x t r a c e l l u l a r enzymes c a n b r e a k down s u b s t r a t e e v e n t u a l l y i n t o w a t e r s o l u b l e c o m p o n e n t s , as p r o d u c t s , o r as i n t e r m e d i a t e s f o r c o n s u m p t i o n by m i c r o - o r g a n i s m s ( O k a z a k i and Moo-Young, 1 9 7 8 ) . I f a s o l i d s u b s t r a t e i s s u f f i c i e n t l y p o r o u s , t h e enzyme can d i f f u s e i n t o i t and d e g r a d a t i o n can proceed i n s i d e the m a t e r i a l . The w a t e r - s o l u b l e s u b s t r a t e f r a g m e n t s must a l s o d i f f u s e out o f t h e s o l i d m a t r i x t h r o u g h t h e s e same p o r e s i n t o t h e b u l k s o l u t i o n w h e r e t h e y may be s u b j e c t t o f u r t h e r e n z y m a t i c a t t a c k . The r e a c t i o n may c o n c u r r e n t l y p r o c e e d a t t h e e x t e r i o r o f t h e m a t r i x s u r f a c e and f o r much o f t h e d e g r a d a t i o n t h e e f f e c t i v e n e s s f a c t o r and g e n e r a l m o d u l u s i s c o n v e n i e n t i n s o l v i n g the r e l e v a n t d i f f e r e n t i a l e q u a t i o n s . BIOREACTOR EQUIPMENT PERFORMANCE Bubble-Columns

P n e u m a t i c a l l y a g i t a t e d g a s - l i q u i d r e a c t o r s may show w i d e v a r i a t i o n s i n height to d i a m e t e r r a t i o s . In the p r o d u c t i o n of baker's y e a s t , a tank-type c o n f i g u r a t i o n w i t h a r a t i o of 3 to 1 i s common i n d u s t r i a l l y . Tower t y p e s y s t e m s have h e i g h t t o d i a m e t e r r a t i o s of 6 to 1 or more. As w o u l d be e x p e c t e d , t h e b e h a v i o r o f b o t h gas and l i q u i d p h a s e s may be q u i t e d i f f e r e n t i n t h e s e c a s e s . I n g e n e r a l t h e gas phase r i s e s through the l i q u i d phase i n p l u g - f l o w , under the a c t i o n of g r a v i t y , i n both types of system. A v a r i e t y o f c o r r e l a t i o n s f o r k.a a r e a v a i l a b l e i n t h e l i t e r a t u r e f o r b u b b l e - c o l u m n s . G e n e r a l l y ^ h e y a r e of t h e f o r m k a L

= const. V

n

(9)

where η i s u s u a l l y i n t h e r a n g e o f 0 . 9 t o u n i t y . Y o s h i d a and A k i t a ( 1 9 6 5 ) c o r r e l a t e t h e o v e r a l l mass t r a n s f e r c o e f f i c i e n t s i n b u b b l e columns i n t h e f o r m : k

-

i ° a

V

„

2

=

o

-

6

1/2

rri 0.62

_3

^

2

0.31 1

Φ -

1

( 1 0 )

A r e c e n t r e v i e w o f b u b b l e - c o l u m n s by S c h u g e r l . e t a l . ( 1 9 7 7 . 1978) examines s i n g l e and m u l t i s t a g e columns and a v a r i e t y of l i q u i d phases. A c o r r e l a t i o n f o r k a i s proposed f o r porous and p e r f o r a t e d p l a t e s p a r g e r s (cgs u n i t s ) : T

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

346

BIOCHEMICAL

k.a

= 0.0023 (V / d )

1

,

5

ENGINEERING

8

(11)

R

L

S

D

Many o f t h e a v a i l a b l e c o r r e l a t i o n s f o r k a h a v e b e e n o b t a i n e d on s m a l l s c a l e e q u i p m e n t , and have n o t t a k e n c o g n i z a n c e o f t h e u n d e r l y i n g l i q u i d hydrodynamics. B h a v a r a j u , e t a l . (1978) propose a design procedure b a s e d on t h e d i f f e r e n c e i n bubble s i z e c l o s e t o t h e o r i f i c e and i n t h e l i q u i d b u l k . P r o v i d e d t h e l i q u i d i s t u r b u l e n t * t h e e q u i l i b r i u m b u b b l e s i z e i n t h e b u l k w i l l be independent of t h e s i z e a t f o r m a t i o n . The h e i g h t o f t h e r e g i o n around t h e o r i f i c e where t h e bubble f o r m a t i o n p r o c e s s o c c u r s i s a f u n c t i o n o f s p a r g e r g e o m e t r y and gas f l o w r a t e and i n l a b o r a t o r y s c a l e e q u i p m e n t t h i s h e i g h t may be s i g n i f i c a n t f r a c t i o n o f t h e t o t a l l i q u i d h e i g h t (up t o 3 0 % ) . I n p l a n t s c a l e e q u i p m e n t * h o w e v e r , t h i s g e n e r a l l y r e p r e s e n t s l e s s t h a n 5% o f t h e t o t a l l i q u i d height. Thus c o r r e l a t i o n s d e v e l o p e d on s m a l l s c a l e a p p a r a t u s need t o be r e v i e w e a r e a w i t h column h e i g h t L

Systems w i t h S t a t i o n a r y

Intpmak

Several laboratory scale devices which i n c l u d e i n t e r n a l e l e m e n t s t o enhance mass t r a n s f e r r a t e s have a p p e a r e d . These include d r a f t - t u b e s , m u l t i p l e sieve p l a t e s staged along the length o f t h e c o l u m n , and s t a t i c m i x i n g e l e m e n t s . A c o n s i d e r a b l e l i t e r a t u r e e x i s t s on d r a f t - t u b e columns* w h e r e l i q u i d i s c i r c u l a t e d due t o a b u l k d e n s i t y d i f f e r e n c e b e t w e e n t h e i n n e r c o r e a n d t h e s u r r o u n d i n g a n n u l a r s p a c e . The downcoming l i q u i d i n t h e a n n u l a r s p a c e e n t r a i n s a i r b u b b l e s * and t h u s h o l d u p i n t h e c e n t r a l c o r e and a n n u l a r r e g i o n w i l l be different. S e v e r a l r e p o r t s o n s m a l l s c a l e a i r l i f t columns as b i o r e a c t o r s have a p p e a r e d . C h a k r a v a r t y . e t a l . (1973) examined gas h o l d u p a t v a r i o u s p o s i t i o n s i n a 10 cm d i a m e t e r c o l u m n . A r e c t a g u l a r a i r l i f t h a s b e e n r e p o t e d ( G a s n e r , 1974) and a i r l i f t s w i t h e x t e r n a l r e c i r c u l a t i o n ( K a n a z a w a . 1 9 7 5 ) have been p r o p o s e d . The o v e r a l l mass t r a n s f e r c o r r e l a t i o n s f o r a i r l i f t d e v i c e s a r e u s u a l l y expressed a s :

k.

a

L·

= const.

(12)

V S

I n d u s t r i a l l y , p l a n t s c a l e a i r l i f t d e v i c e s h a v e b e e n u s e d by J a p a n e s e , B r i t i s h , F r e n c h a n d USA c o m p a n i e s m a i n l y f o r SCP p r o d u c t i o n and w a s t e t r e a t m e n t S t a t i c m i x i n g e l e m e n t s have been i n c o r p o r a t e d i n t o a i r l i f t devices with the o b j e c t i v e s o f p r o v i d i n g a d d i t i o n a l m i x i n g and h e n c e g r e a t e r mass t r a n s f e r c a p a b i l i t i e s . S t a t i c mixers are b e c o m i n g i n c r e a s i n g l y m o r e common i n o x i d a t i o n ponds f o r

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

15.

MOO-YOUNG A N D BLANCH

Biological

Reactor

Design

347

b i o l o g i c a l wastewater t r e a t m e n t . H e r e , f i n e b u b b l e s may be produced as t h e g a s - l i q u i d m i x t u r e passes through t h e m i x i n g element. These a r e u s u a l l y 18-24 i n c h e s i n d i a m e t e r , and a r e placed over sparger pipes. A f a i r l y intense l i q u i d c i r c u l a t i o n c a n be d e v e l o p e d b y s u c h m i x e r s d u e t o e n t r a i n m e n t b y t h e g a s - l i q u i d j e t r i s i n g from the m i x i n g element. Mpchaniral

Non-Viscous

Stirred

Tanks

Systems.

The p r e v i o u s s e c t i o n s d e a l t w i t h g a s - l i q u i d c o n t a c t i n g w i t h o u t m e c h a n i c a l a g i t a t i o n i n such d e v i c e s a s b u b b l e - c o l u m n s a n d a i r l i f t towers. To o b t a i n b e t t e r g a s - l i q u i d contacting, mechanical a g i t a t i o n i s o f t e n r e q u i r e d . The d i s c u s s i o n i s confined to baffled sparge A e r a t i o n by s u r f a c t i o wastewater treatment f a c i l i t i e s ( Z l o k a r n i k , 1978). For p a r t i c u l a t e s , such as c e l l s , i n s o l u b l e s u b s t r a t e s , o r i m m o b i l i z e d - e n z y m e s , t h e i n t e r f a c i a l a r e a c a n be d e t e r m i n e d f r o m d i r e c t a n a l y s e s s u c h as by m i c r o s c o p i c e x a m i n a t i o n . F o r gas b u b b l e s and l i q u i d d r o p s , a c a n be e v a l u a t e d f r o m s e m i - e m p i r i c a l correlations. Two c a s e s a r e i d e n t i f i e d : (a)

For "coalescing** air-water

dispersions,

Ρ "°· a = 0.55 φ

4

V

0 5 0

5

s

and -0.17 = 0.27 C l ) V Β γ s 0

d

U

2

, + 9 χ 10 *

7

,

Z

/

n

( b ) F o r " n o n - c o a l e s c i n g " a i r - e l e c t r o l y t e s o l u t i o n dispersions» 0.7 a = 0.15 (I)

0.3 V

and d

B = °· Ψ 89

Ρ "°·

V

1 7

0 17

3

I n t h e e q u a t i o n , (P/V) i s i n W a t t s / m , and V

g

i s i n m/s.

American Chemical Society Library 1155 16th St., N.W.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Washington, D.C. Society: 20036Washington, DC, 1983.

348

BIOCHEMICAL

ENGINEERING

It is seen that there is a significant effect of e l e c t r o l y t e s on t h e c o r r e l a t i o n s * E l e c t r o l y t e s and s u r f a c t a n t s i n h i b i t bubble coalesence r e s u l t i n g i n the f o r m a t i o n of smaller b u b b l e s and i n c r e a s e d i n t e r f a c i a l a r e a than n o r m a l l y found i n the c l e a n water system. A v e r y h i g h gas f l o w r a t e » l i q u i d b l o w - o u t f r o m t h e v e s s e l may o c c u r * In a d d i t i o n , t h e above equations are applicable p r o v i d e d t h a t t h e i m p e l l e r i s n o t f l o o d e d by t o o h i g h a g a s flow r a t e and t h e r e i s no g r o s s s u r f a c e - a e r a t i o n due t o g a s b a c k - m i x i n g at the surface of the l i q u i d . Equations are available to c a l c u l a t e these c r i t e r i a (Calderbank, 1959; W e s t e r t e r p » 1963)· The e f f i c i e n c y o f g a s - l i q u i d c o n t a c t i n g has p r e s e n t e d i n terms o f t h e f u n d a m e n t a l s o f k. a n d a the o v e r a l l correlation applicability. Severa correlations. They u s u a l l y take the form

m

ρ k a L

and t h e i r r a n g e s o f and a i r l i f t d e v i c e s

= const.

applicability i n F i g u r e 5.

(^)

are

a l r e a d y been separately:

V

g

(17)

n

compared

to

bubble

columns

I n r e c e n t y e a r s , e x t e n s i v e s t u d i e s have b e e n c a r r i e d o u t u s i n g p h y s i c a l r a t h e r than c h e m i c a l r e a c t i o n measurements f o r t h e evaluation of k . On t h i s b a s i s . S m i t h V a n t R i e t and M i d d l e t o n (197 7) f o u n d t n a t i n g e n e r a l , t h e f o l l o w i n g c o r r e l a t i o n s a p p l y t o a w i d e v a r i e t y o f a g i t a t o r t y p e s , s i z e s and D/T r a t i o s : f

a

(a)

For

"coalescing" air-water

dispersion

k a = 0.01 ^)

ν

L

(b)

For

β

"non-coalescing"* a i r - e l e c t r o l y t e

Ρ ° ·

l ^ a = 0 . 0 2 (|)

4

7

5

ν

0

·

(18)

4

solution

β

dispersions

0 4 ϋ

(19)

·*

-1 3 Both e q u a t i o n s a r e i n SI u n i t s k . a i n s » (P/V) i n W/m · V in m . The a c c u r a c y o f t h e c o r r e l a t i o n s i s ± 20% and ± 35% w i t h 95% c o n f i d e n c e f o r t h e a b o v e two e q u a t i o n s , respectively. g

From

Figure

5»

it

is

seen

that

for

comparable

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

power

MOO-YOUNG A N D BLANCH

Figure 5. Aeration efficiencies electrolyte systems). Reproduced,

Biological

Reactor

of various gas-liquid with permission, from Springer-V erlag.

Design

contacting devices Ref. 38. Copyright

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

349

(air1981,

350

BIOCHEMICAL

ENGINEERING

i n p u t s * t h e m a g n i t u d e o f k ^ a o b t a i n e d i s a b o u t t h e same w h e t h e r m i x i n g i s done m e c h a n i c a l l y i n s t i r r e d - t a n k s o r p n e u m a t i c a l l y i n bubble-columns or a i r l i f t d e v i c e s . However, only mechanically a g i t a t e d systems are capable of a t t a i n i n g h i g h v a l u e s of k a r q u i r e d ( e . g . * i n some a n t i b i o t i c f e r m e n t a t i o n s and t h e a c t i v a t e d s l u d g e method o f t r e a t i n g w a s t e w a t e r ) . Non-mechanically a g i t a t e d s y s t e m s would r e s u l t i n l i q u i d blowout b e f o r e r e a c h i n g these h i g h aeration rates. L

It s h o u l d be stressed that none of the overall c o r r e l a t i o n s f o r k a had u n i v e r s a l a p p l i c a b i l i t y . The p r o b l e m i s t h a t any s c a l e - u p p r o c e d u r e b a s e d o n e q u a l i z i n g k ^ a o f b o t h s c a l e s a c c o r d i n g t o a g i v e n c o r r e l a t i o n may c a u s e o t h e r p h y s i c a l c r i t e r i a t o be v i o l a t e d . A l s o * d e p e n d i n g on b i o l o g i c a l demands and t o l e r a n c e s * o t h e r c r i t e r i a may be m o r e i m p o r t a n t . F o r example* i n c r e a s i n g t h e k a c a n sometime in highly turbulent fermentatio L

L

Viscous Systems Two t y p e s

of

viscous

fermentations

need

t o be

(a) m y c e l i a l fermentations ( e . g . * molds* v i s c o s i t y i s due t o t h e m i c r o b i a l n e t w o r k c o n t i n u o u s aqueous p h a s e .

distinguished:

a c t i n o m y c e t e s ) where t h e structure dispersed in

(b) p o l y s a c c h a r i d e f e r m e n t a t i o n s w h e r e t h e v i s c o s i t y i s due t o polymers i n the continuous aqueous p h a s e r e s u l t i n g i n an e s s e n t i a l l y homogeneous* v i s c o u s l i q u i d . The f i r s t t y p e o f f e r m e n t a t i o n b r o t h c a n be s i m u l a t e d b y m a t e r i a l s u c h as p a p e r p u l p * w h i c h has a m a c r o s c o p i c s t r u c t u r e analogous t o f u n g a l h y p h a e * s u s p e n d e d i n w a t e r . The second t y p e may be s i m u l a t e d by aqueous p o l y m e r s o l u t i o n s o f known p r o p e r t i e s . Sideman* e t a l . (1966) have p r o p o s e d t h e f o l l o w i n g form o f a general c o r r e l a t i o n for the l i q u i d phase mass transfer coefficient.

D

A L

(

L

σ

>

(

M

a

>

V

A d d i t i o n a l d i m i n s i o n l e s s g r o u p s be i n c o r p o r a t e d t o a c c o u n t f o r geometric v a r i a b l e s * e . g . H / T » D/T. T h e a b o v e e q u a t i o n c a n be a l t e r e d t o r e l a t e k a t o t h e s p e c i f i c power i n p u t . L

L

L o u c a i d e s and McManamey ( 1 9 7 3 ) e x a m i n e d r a t e s i n p a p e r pulp supensione s i m u l a t i n g filamentous fermentation media. Tank g e o m e t r i e s and i m p e l l e r g e o m e t r i e s were b o t h v a r i e d ; vessel

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

15.

Biological

MOO-YOUNG A N D BLANCH

Reactor

351

Design

volumes ranging from 5 to 72 l i t e r s * Analogous t o the r e s u l t s f o r n o n - v i s c o u s solutions» k a as found t o c o r r e l a t e v e i l w i t h v a r i a t i o n s i n tank diameter* L

k a = C j (T/H ) Ν D ζ-Τ .5 L

(21)

L

By v a r y i n g the i m p e l l e r blade dimensions» v a r i a t i o n s i n power per u n i t volume were made a t a c o n s t a n t i m p e l l e r speed* A t low power p e r u n i t volumes t h e r e was a l i n e a r i n c r e a s e i n k^a » w h i c h c o r r e l a t e d w i t h P/V w i t h an exponent of 0.9 t o 1.2* Hteyond the breakpoint* the exponent r e l a t i n g the P/V dependence was 0*53* I n both r e g i o n s , the k a dependen t h e 0*3 power. Tfies e a r l i e r by B l a k e b r o u g h and Sambamurthy (1966)· and Hamer and Blakebrough (1963)* obtained i n s m a l l e r s c a l e v e s s e l s * a l s o u s i n g paper p u l p s u s p e n s i o n s . Other r e f e r e n c e s on t h e a e r a t i o n o f v i s c o u s non-Newtonian f e r m e n t a t i o n b r o t h a r e Banks (1977)· and Blanch and Bhavaraju (1976).

NOMENCLATURE a

s p e c i f i c i n t e r f a c i a l area (based on d i s p e r s i o n volume)

C

Concentration of s o l u t e i n bulk l i q u i d

C

Concentration of s o l u t e i n bulk media ( f o r i n t r a p a r t i c l e d i f f u s i o n case)

D

D i l u t i o n r a t e ; i m p e l l e r diameter

(generally)

L i q u i d phase d i f f u s i v i t y d

Diameter of p a r t i c l e as an equi-volume

sphere

Bubble diameter Effectiveness factor L i q u i d height i n r e a c t o r L i q u i d phase mass t r a n s f e r c o e f f i c i e n t C o n t i n u e d on n e x t page

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

352

BIOCHEMICAL ENGINEERING V o l u m e t r i c l i q u i d phase mass t r a n s f e r

coefficient

m

An e x p o n e n t

Ν

Speed o f

Ρ

Agitator

power r e q u i r e m e n t s f o r u n g a s s e d

Agitator

requirements f o r g a s - l i q u i d

Ρ

agitator systems

dispersions

g Τ

Temperature; tank diameter

V

Volume o f r e a c t o r c o n t e n t s

V

Superficial

6

VVM

gas v e l o c i t y

Volume

&£££k L e t t e r s Ρ

Viscosity

P

Apparent v i s c o s i t y

a

Viscosity

( d y n a m i c ) o f c o n t i n u o u s phase (dynamic)

(dynamic) of d i s p e r s e d

phase

ν

K i n e m a t i c v i s c o s i t y o f c o n t i n u o u s phase

Ρ

D e n s i t y o f c o n t i n u o u s phase

Φ

Holdup o f d i s p e r s e d

phase.

A b b r e v i a t i o n s f o r D i m e n s i o n l e s s Groups Gr

G r a s h o f number f o r mass t r a n s f e r ( b a s e d o n p a r t i c l e environment d e n s i t y d i f f e r e n c e )

Nu

N u s s e l t number

Pe

P e c l e t number ( s i n g l e

Pr

P r a n d t l number

Re

R e y n o l d s number f o r p a r t i c l e s

Re

particles)

R e y n o l d s numbers f o r i s o t r o p i c

turbulence

e Sh

Sherwood

number

Se

S c h m i d t number

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

15.

MOO-YOUNG AND BLANCH

Biological

Reactor

353

Design

Literature Cited 1.

Banks, G.T., in "Topics in Enzymes and Fermentation Biotechnology", Wiseman (Ad.), John Wiley and Sons, 1977, 1, 72.

2.

Batchelor, G.K., Proc. Camb. Phil. Socl., 1951, 47, 359

3.

Bhavaraju, S.M., Mashelkar, R.A., Blanch, H.W., 1978, 24 1063; AIChE J., 24, 1070

AIChE J.,

4.

Bhavaraju, S.M., Russell, T.W.F., Blanch, H.W., 1978, 24, 454

AIChE J.,

5. Blakebrough, Ν., Sambamurthy 8, 25.

K., Biotechnol. Bioeng., 1966

6.

Blanch, H.W., 18. 745.

7.

Calderbank, P.H., Trans. Inst. Chem. Engrs., 1959, 37, 173.

8. 16, 9.

Bhavaraju, S.M., Biotechnol. Bioeng., 1976,

Calderbank, P.H., Moo-Young, M. Chem. Eng. Sci., 1961 39. Calderbank, P.H., Moo-Young, M., Trans. Inst. Chem. Engrs., 1961, 39, 337.

10. Chakravarty, Y., Begum, S., Singh, A.D., Baruah, J.N. Iyengar, M.S., Biotechnol. Bioeng. Symp., 1973, No. 4 363. 11.

Finn, R.K., Bact. Rev., 1954, 18. 245.

12.

Gasner, L.L., Biotechnol, Bioeng., 1974, 16, 1179

13.

Hadamard, J . , Compt. Rend. Acad. Sci., 1911, 152, 1735.

14.

Hamer, G., Blakebrough, Ν., J . Appl. Chem., 1963, 13, 517

15.

Higbie, R.,

16.

Hirose, T., Moo-Young, M., Can. J . Chem. Eng., 1969, 47, 265.

17.

Kanazawa, M., in "SCP II," Tannenbaum and Wang (Eds.), MIT Press, 1975.

18.

Kobayashi, H., Suzuki, M., Biotechnol. Bioeng., 1976, 18, 37.

19.

Kobayashi, T., Moo-Young, M., Biotechnol. Bioeng., 1973 a, 15, 47.

Trans.

Amer.

Inst.

Chem.

Engrs.,

1935, 31, 365.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

354

BIOCHEMICAL

ENGINEERING

20. Kobayashi, T., van Dedem, Β., Moo-Young. M., Biotechnol. Bioeng., 1973 b., 15,. 27. 21.

Levich, V.G., "Physicochemical Hydrodynamics," 1962, Prentice-Hall.

22.

Loucaides, R., McManamey, W.J., Chem. Eng. Sci., 1973, 28, 2165.

23.

Marshall, K.C., Alexander, M., J . Bacteriol., 1960, 80, 412.

24.

Moo-Young, M., Hirose, T., Can. J . Chem. Eng., 1972, 50 128.

25. Moo-Young, M. Kobayashi, 50, 128. 26.

Okazaki, M., Moo-Young. M., Biotechnol. Bioeng., 1978, 20, 637.

27.

P h i l l i p s , H.H., Biotechnol. Bioeng., 1966, 8, 456.

28.

Schugerl, K., Oels, U., Lucke, J., Adv. Biochem. Eng., 1977, 7, 1.

29.

Schugerl, Κ., Lucke, J., Lehman, J., Wagner, F., Adv. Biochem. Eng., 1978, 8, 63.

30.

Shaftlein, R.W., Russell, T.W.F.,Ind.Eng,Chem.,1968, 60(5), 13.

31.

Sideman, S., Hortacsu, O., Fulton, J.W., Ind.Eng,Chem., 1966, 58(7), 32.

32.

Smith, J . , Van't Riet. K., Middleton, J . , Second European Conf. on Mixing, April 1977, Preprint.

33.

Wellek, R.M., Huang, C.C., Ind. Eng, Chem. Fund., 1970, 2 , 480.

34.

Westerterp, Κ., Chem. Eng. Sci., 1963, 18, 157.

35. Yano, T., Kodama, T., Yamada, K., Agr. Biol. Chem., 1961, 25, 589. 36.

Yoshida, F., Akita, Κ., AIChE J., 1965, 11, 9.

37.

Zlokarnik, M., Adv. Biochem. Eng., 1978, 8, 133.

38.

Moo-Young, Μ., Blanch, H.W., 18, 2.

Adv. Biochem. Eng., 1981,

RECEIVED June 29, 1982 In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16 Reactor Design Fundamentals Hydrodynamics,MassTransfer,HeatExchange,Control,and Scale-up ALES PROKOP Kuwait Institute for Scientific Research, Biotechnology Department, P.O. Box 24885, Kuwait

For the convenience of d i s c u s s i n g the above subject it i s h e l p f u l t and s y n t h e s i s ) , i . e . i n t o s e v e r a l orders of s t r u c t u r a l and f u n c t i o n a l h i e r a r c h y , i n c l u d i n g b i o l o g i c a l and p h y s i c a l l e v e l s (such as molecular, cellular, p o p u l a t i o n , r e a c t o r and t e c h n o l o g i c a l l i n e ) , and to s e l e c t from a number of elementary events systemic phenomena p l a y i n g a d e c i s i v e r o l e a t each l e v e l of h i e r a r c h y . This approach allows an i n t e g r a l d e s c r i p t i o n during process synthesis while maintaining the s p e c i f i c prop e r t i e s of each l e v e l . The b i o r e a c t o r l e v e l is distinguished by the f o l l o w i n g fundamental events and f u n c t i o n s : b i o r e a c t o r hydrodynamics, mass t r a n s f e r , heat exchange, b i o r e a c t o r c o n t r o l and its scale-up. This review will emphasize r e a c t o r s employed i n m i c r o b i a l p r o t e i n production and the systems approach i s intended as a methodological a i d in process research and development. R e c e n t l y , t h e author advocated t h e a p p l i c a t i o n o f t h e systems a p p r o a c h i n t h e a n a l y s i s and s y n t h e s i s o f a b i o t e c h n o l o g i c a l p r o c e s s ( 1 ) . The h i e r a r c h y o f a b i o l o g i c a l s y s t e m i n v o l v e s s t r u c t u r a l , f u n c t i o n a l , d e s c r i p t i v e , c o n t r o l a n d dynamic o r g a n i z a t i o n . S t r u c t u r a l and f u n c t i o n a l h i e r a r c h i e s o f a b i o t e c h n o l o g i c a l p r o c e s s a r e d e p i c t e d i n T a b l e s I and I I . I n T a b l e I I a c o m p a r t m e n t a l l e v e l i s o m i t t e d . T h i s i s p o s s i b l e as l o n g as t h e t r a n s l o c a t i o n o f s u b s t a n c e s between o r g a n e l l e s and c y t o p l a s m i s n o t i m p o r t a n t . The scheme o f f u n c t i o n s s h o u l d be u n d e r s t o o d i n b o t h d i r e c t i o n s , i . e . , f r o m h i g h e r l e v e l s t o l o w e r ( a n a l y s i s ) and v i c e v e r s a ( s y n t h e s i s ) , r e p r e s e n t i n g b a s i c a n d a p p l i e d r e s e a r c h . The f i r s t On l e a v e f r o m : I n s t i t u t e o f M i c r o b i o l o g y , C z e c h o s l o v a k Academy K I S R 620 o f S c i e n c e s , 142 20 P r a g u e 4, C z e c h o s l o v a k i a

0097-6156/83/0207-0355$06.50/0 ©

1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

356

BIOCHEMICAL

Table

I

ENGINEERING

S t r u c t u r a l and F u n c t i o n a l H i e r a r c h i e s of a B i o t e c h n o l o g i c a l Process

Level

S t r u c t u r a l Elements

Function

Molecular

Atoms,

Synthesis of macromolecules

molecules

Organelles Macromolecules

Duplication of organelles, metabolic manifestation of c e l l s

Cell

Translocation of substances, complex b i o c h e m i c a l r e a c t i o n s , morphological d i f f e r e n t i a t i o n , cell cycle

Organelles

Population Cells

Growth and m u l t i p l i c a t i o n , i n t e r a c t i o n between c e l l s

Reactor

Mass t r a n s f e r , h e a t diffusion, etc.

Elementary zones of r e a c t o r

B i o t e c h n o ­ U n i t equipment logical process (line)

Unit

exchange,

operations

I n t e r n a t . J . G e n e r a l Systems 1982, j $ ( l ) , T a b l e V I I ( 1 )

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16.

Reactor

PROKOP

Table I I

Design

357

Fundamentals

Hierarchy of Functions

of B i o t e c h n o l o g i c a l

Processes

Molecular Level 1.1. C a t a b o l i c and a n a b o l i c m a n i f e s t a t i o n s o f l i v i n g 1.1.1. E n e r g y f o r m a t i o n 1.1.2. S y n t h e t i c p r o c e s s e s 1.1.3. M a c r o m o l e c u l a r d e c a y 1.2. C o n t r o l mechanisms 1.2.1. R e a c t i o n mechanisms 1.2.2. E p i g e n e t i 1.2.3. B i o c h e m i c a 1.2.4. R e p r o d u c t i o n mechanisms

systems

S t r u c t u r a l H i e r a r c h y o f C e l l s (Compartments) 2.1. T r a n s l o c a t i o n o f s u b s t a n c e s 2.2. Complex b i o c h e m i c a l n e t w o r k 2.3. M o r p h o l o g i c a l d i f f e r e n t i a t i o n 2.4. C e l l c y c l e 2.5.

Genetic

phenomena a t l e v e l o f

organelles

Population 3.1.

D i s p e r s e d growth 3.1.1. P u r e c u l t u r e 3.1.2. M i x e d c u l t u r e 3.2. A g g r e g a t e d g r o w t h B i o r e a c t o r and O t h e r E q u i p m e n t 4.1. M a c r o - and m i c r o - m i x i n g o f e q u i p m e n t c o n t e n t s 4.2. Mass t r a n s f e r 4.3. Heat e x c h a n g e 4.4. B i o r e a c t o r c o n t r o l and o f o t h e r e q u i p m e n t 4.5. S c a l e - u p Technological Line 5.1. B a t c h p r o c e s s e s 5.2. C o n t i n u o u s p r o c e s s e s Internat.J.General

Systems 1982,

8(1), Table V I I I

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

(1)

BIOCHEMICAL

358

ENGINEERING

l e v e l ( m o l e c u l a r ) i n T a b l e I I i s c o n s i d e r e d quasihomogeneous ( r e a c t i o n s o c c u r r i n g i n a s o l u t i o n ) , the second i s represented by a c e l l c o n s i d e r e d a s a two-phase s y s t e m , composed o f o r g a n e l l e s h o m o g e n e o u s l y d i s p e r s e d i n t h e c y t o p l a s m . The p o p u l a t i o n l e v e l i s m a n i f e s t e d b y d i f f e r e n t m o r p h o l o g i c a l s t a t e s ( d i s p e r s e d and a g g r e ­ g a t e d ) o f a p o p u l a t i o n . The l e v e l s o f t h e r e a c t o r and t e c h n o l o g i ­ c a l l i n e a r e d i s t i n g u i s h e d by fundamental f u n c t i o n s t y p i c a l f o r chemico-technological processes. The r e a c t o r l e v e l i s d i s t i n g u i s h e d b y t h e f o l l o w i n g f u n d a ­ m e n t a l e v e n t s and f u n c t i o n s : m a c r o - and m i c r o - m i x i n g o f r e a c t o r ( e q u i p m e n t ) c o n t e n t s and t h e c o r r e s p o n d i n g mass t r a n s f e r a n d h e a t e x c h a n g e i n v o l v e t h e d e t e r m i n a t i o n o f e l e m e n t a r y zones o f r e a c t o r , mass t r a n s f e r and h e a t e x c h a n g e b e t w e e n them and a l s o b e t w e e n i n d i v i d u a l phases ( l i q u i d , gaseous, s o l i d ) ; b i o r e a c t o r c o n t r o l and s c a l e - u p ( 2 ) . I f n o n - h o m o g e n e i t i e s o f r e a c t o r p e r f o r m a n c e i n s p a c e and t i m e a r e e x p e c t e d and momentum t r a n s p o r t As a s o l u t i o n t o momentum t r a n s p o r t ( N a v i e r - S t o k e s e q u a t i o n ) i s u s u a l l y n o t a v a i l a b l e f o r b i o r e a c t o r v e l o c i t y f i e l d , we a r e l e f t w i t h mass and h e a t b a l a n c e s . A l o c a l b a l a n c e d e s c r i b i n g m i x i n g , f l o w and i n t e r f a c e t r a n s f e r , i n c l u d i n g r e a c t i o n i s known a s t h e d i s p e r s e d model ( 3 ) :

— —

+

Vc..

at

u

V D V C .

+

ij

-k-id«) \

\

(

c

iks

+

r..

ij

ij

-

°ik > • °

( i )

where s u b s c r i p t i d e n o t e s s y s t e m component, j i s t h e number o f a phase i n t h e f - p h a s e s y s t e m , k i s a p h a s e o t h e r t h a n j , s u b s c r i p t i k s d e n o t e s c o n c e n t r a t i o n n e a r t h e i n t e r f a c i a l a r e a on s i d e j , and u i s t h e l o c a l v e l o c i t y o f p h a s e s j . The l a s t t e r m d e n o t e s the t r a n s p o r t between phases. A l i m i t e d a p p l i c a t i o n o f t h i s s y s t e m o f p a r t i a l d i f f e r e n t i a l e q u a t i o n s was made f o r a s t i r r e d t a n k r e a c t o r (STR) w i t h a n e g l e c t o f t r a n s f e r t e r m (4_) as w e l l as f o r a t u b u l a r r e a c t o r ( 5 ) . Hydrodynamics E l e m e n t a r y r e g i o n s o f b i o r e a c t o r . A more s i m p l e d e s c r i p t i o n of the flow c h a r a c t e r i s t i c s o f a r e a c t o r than that by a l o c a l mass b a l a n c e i s done b y i n t r o d u c i n g t h e r e s i d e n c e t i m e d i s t r i b u ­ t i o n c o n c e p t (RTD), w h i c h p r o v i d e s m a c r o - m i x i n g c h a r a c t e r i s t i c s (determination of the elementary regions o f the r e a c t o r ) . I n f a c t , u s i n g t h e r e s i d e n c e t i m e c o n c e p t a p a r t i c u l a r s i t u a t i o n may be d e s c r i b e d b y m i x e d - t y p e m o d e l s c o n s i d e r i n g " t h e r e a c t o r a s

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16.

PROKOP

Reactor

Design

Fundamentals

359

c o n s i s t i n g o f i n t e r c o n n e c t e d f l o w s b e t w e e n and a r o u n d t h e s e r e ­ g i o n s " ( 6 ) . The f o l l o w i n g k i n d s o f e l e m e n t a r y r e g i o n s a r e u s e d i n t h e c o n s t r u c t i o n o f m i x e d m o d e l s : two t y p e s o f i d e a l z o n e s ( p l u g f l o w and p e r f e c t l y s t i r r e d = b a c k m i x e d ) , d i s p e r s e d p l u g f l o w and deadwater. I n a d d i t i o n t o these r e g i o n s , the f o l l o w i n g k i n d s o f f l o w may be u s e d : b y - p a s s , r e c y c l e and c r o s j s - f l o w . The above n o n i d e a l i t i e s i n m i x i n g may be d e s c r i b e d e i t h e r b y means o f d i s p e r ­ sed o r d i s c r e t e ( s t a g e - w i s e ) models, t h e l a t t e r c o n s i d e r i n g a s e r i e s o f i d e a l l y mixed v e s s e l s . Residence time d i s t r i b u t i o n . The above d i s t r i b u t i o n o f l i ­ q u i d , g a s e o u s and s o l i d ( c e l l s ) p h a s e s i s u s u a l l y m e a s u r e d b y a stimulus-response experiment. Frequently, r a d i o a c t i v e t r a c e r s are u s e d ( 7 , 8 ) . I n t h e a b s e n c e o f m i c r o o r g a n i s m s and f o r l i q u i d RTD, a pH t r a c e r i s q u i t e c o n v e n i e n t e - t y p e model f o r i n t e r p r e t i n Micro-mixing c h a r a c t e r i s t i c s . I t i s w e l l established that t h e RTD c o n c e p t does n o t c h a r a c t e r i z e a l l a s p e c t s o f m i x i n g . To c l a r i f y t h i s a concept o f s e g r e g a t i o n has been i n t r o d u c e d ( 1 0 ) . M i c r o - m i x i n g f a l l s , t h e n , b e t w e e n two l i m i t i n g c a s e s o f maximum m i x e d n e s s and c o m p l e t e s e g r e g a t i o n , and i s t y p i c a l f o r r e a c t o r zones s m a l l e r than the elementary r e g i o n s d e f i n e d above, u s u a l l y a t t h e l e v e l o f i n d i v i d u a l c e l l s , b u b b l e s , m o l e c u l e s and t h e i r c l u m p s . M i c r o - m i x i n g c h a r a c t e r i s t i c s , h o w e v e r , c a n n o t be e x t r a c t e d f r o m RTD d a t a . F o r t u n a t e l y , t h e r e a c t o r p e r f o r m a n c e i s n o t o f t e n too s e n s i t i v e t o m i c r o - m i x i n g . F o r example, f o r growth o f y e a s t s on h y d r o c a r b o n s , where one c a n assume an i n f l u e n c e o f t h e d e g r e e o f o i l d r o p and c e l l s e g r e g a t i o n , t h e d i f f e r e n c e s b e t w e e n c o m p l e ­ t e s e g r e g a t i o n and maximum m i x e d n e s s i s a p p r e c i a b l e o n l y f o r l o n g ­ e r c u l t i v a t i o n t i m e s ( 1 1 ) . Some p r o g r e s s c a n be e x p e c t e d f r o m t h e o r e t i c a l and e x p e r i m e n t a l i n v e s t i g a t i o n o f t h e e f f e c t o f t h e gas phase ( b u b b l e ) s e g r e g a t i o n o n mass t r a n s f e r and o x y g e n u t i l i ­ z a t i o n e f f i c i e n c y i n connection with d i f f e r e n t reactor designs. F o r a l m o s t a l l p r a c t i c a l c a s e s maximum s u b s t r a t e c o n v e r s i o n i s a c h i e v e d a t maximum m i x e d n e s s . Mass T r a n s f e r Mass t r a n s f e r i n v o l v e s e s t a b l i s h i n g a t r a n s f e r b e t w e e n t h e e l e m e n t a r y r e g i o n s o f t h e r e a c t o r and b e t w e e n i n d i v i d u a l p h a s e s ( i n t e r f a c i a l mass t r a n s f e r c o e f f i c i e n t s : gas phase mass t r a n s f e r , l i q u i d p h a s e mass t r a n s f e r , mass t r a n s f e r w i t h r e a c t i o n , l i q u i d s o l i d mass t r a n s f e r ) , a s w e l l a s o t h e r e l e m e n t a r y phenomena and p r o c e s s e s c o n n e c t e d w i t h mass t r a n s f e r : g a s p h a s e phenomena and p r o c e s s e s ( g a s h o l d - u p , b u b b l e s i z e , i n t e r f a c i a l a r e a and b u b b l e c o a l e s c e n c e / r e d i s p e r s i o n ) , v o l u m e t r i c mass t r a n s f e r and power c o n s u m p t i o n d u r i n g mass t r a n s f e r ( 2 ) .

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

360

BIOCHEMICAL

ENGINEERING

I n t e r f a c i a l mass t r a n s f e r c o e f f i c i e n t s . T h e o r e t i c a l and e x p e r i m e n t a l i n v e s t i g a t i o n s o f many a u t h o r s h a v e shown t h a t d u r i n g t h e a b s o r p t i o n o f s p a r i n g l y s o l u b l e g a s e s s u c h as o x y g e n , t h e gas phase c o e f f i c i e n t ( k ) i s s e v e r a l o r d e r s i n m a g n i t u d e h i g h e r t h a n t h e l i q u i d phase mass t r a n s f e r c o e f f i c i e n t ( k _ ) . B e c a u s e o f t h e above f a c t and a l s o due t o t h e h i g h v a l u e o f H e n r y ' s Law c o n s t a n t f o r o x y g e n , t h e l i q u i d p h a s e mass t r a n s f e r c o e f f i c i e n t d e t e r m i n e s t h e o v e r a l l r a t e o f mass t r a n s f e r . I n d e a l i n g w i t h i n t e r f a c i a l phenomena, two e x t r e m e c a s e s a r e e n c o u n t e r e d : mass t r a n s f e r by m o l e c u l a r d i f f u s i o n and c o n v e c t i o n f r o m r i g i d i m m o b i l e s p h e r e s , r e p r e s e n t e d by gas b u b b l e s w i t h c o n t a m i n a t e d s u r f a c e s and d e s c r i ­ bed by t h e F r B s s l i n g e q u a t i o n ( e . g . , i n ( 1 2 ) ) , and mass t r a n s f e r by c o n v e c t i o n f r o m m o b i l e s p h e r e s , d e s c r i b e d by t h e B o u s s i n e s q e q u a t i o n (e.g., i n ( 1 3 ) ) . In p r a c t i c e , the l a t t e r system i s r a r e ­ l y a c h i e v e d s i n c e f e r m e n t a t i o n media w i t h e l e c t r o l y t e s p r o t e i n s p r o d u c t s o f m e t a b o l i s m an m a t e r i a l may h i n d e r t h gas b u b b l e s . V a r i o u s t h e o r e t i c a l and e x p e r i m e n t a l c o r r e l a t i o n s f o r p r e d i c t i n g k^ f o r b u b b l e s w i t h i m m o b i l e i n t e r f a c e s h a v e b e e n p r e s e n t e d i n r e v i e w s ( 1 4 , 15) i n v o l v i n g s i t u a t i o n s w i t h c r e e p i n g f l o w ( t y p i c a l f o r a i r - l i f t r e a c t o r s ) and l o w - h i g h Re numbers, and a l s o e f f e c t s o f n o n - N e w t o n i a n f l u i d on mass t r a n s f e r f r o m m o v i n g b u b b l e s . These c o r r e l a t i o n s a r e o f i m p o r t a n c e i n p o l y s a c c h a r i d e and a n t i b i o t i c p r o d u c t i o n s . The e f f e c t o f s u r f a c e - a c t i v e compounds on k^ and a i s d i f f e r e n t i a l b e c a u s e o f t h e i r d i f f e r e n t i n f l u e n c e on s u r f a c e t e n s i o n ( i n c r e a s e o r d e c r e a s e ) . T h e s e phenomena h a v e not y e t been i n c o r p o r a t e d i n t o a s u f f i c i e n t l y g e n e r a l t h e o r y . ç

Mass t r a n s f e r w i t h r e a c t i o n . The p r e c e d i n g s i t u a t i o n i n v o l ­ v e d o n l y a p h y s i c a l mass t r a n s f e r b e t w e e n g a s - l i q u i d o r s o l i d - l i ­ q u i d i n t e r f a c e s . In the presence of microorganisms, oxygen uptake by r e s p i r i n g c e l l s w i t h i n t h e r e l a t i v e l y s t a g n a n t l i q u i d r e g i o n a d j a c e n t t o b u b b l e s submersed i n a c e l l s u s p e n s i o n may l e a d t o e n h a n c e d o x y g e n t r a n s f e r r a t e s . U s i n g an enhancement c o n c e p t o f A s t a r i t a , B l a n c h (16) p r e s e n t e d r u l e s f o r i t s p r e d i c t i o n : t h e d i f f u s i o n t i m e f o r t h e o x y g e n o f gas b u b b l e s a s c e n d i n g t h r o u g h a l i q u i d , e s t i m a t e d f r o m b u b b l e d i a m e t e r and a s c e n d i n g a i r v e l o c i t y , dg / u , s h o u l d be g r e a t e r o r a t l e a s t o f t h e same o r d e r as t h e r e a c t i o n t i m e , e v a l u a t e d from d i s s o l v e d oxygen c o n c e n t r a t i o n , o x y g e n u p t a k e r a t e and b i o m a s s d e n s i t y , C ^ / ( Q Q X ) . S o b o t k a e t a l . (17) h a v e shown t h a t t h e c e l l f l o t a t i o n 2 mechanism c a n be s u c c e s s f u l l y u t i l i z e d to obtain a b e t t e r f i t f o r experimental growth d a t a , c o n s i d e r i n g g a s - s o l i d ( c e l l s ) a b s o r p t i o n of oxygen ( i t may amount up t o a h a l f o f t o t a l a b s o r p t i o n ) i n a d d i t i o n t o the p r e v a i l i n g t y p i c a l oxygen path t o c e l l s v i a d i s s o l v e d oxygen ( F i g u r e 1 ) . C o n c l u s i o n of t h i s work, p r o v i d i n g enhanced a b s o r p t i ­ on ( r e d u c e d b u b b l e s l i p v e l o c i t y due t o e l e c t r o l y t e , a l c o h o l s and o t h e r s u r f a c e - a c t i v e compounds; o x y g e n l i m i t a t i o n o f g r o w t h ; h i g h r e s p i r a t i o n r a t e ; h i g h c e l l d e n s i t y a t the i n t e r f a c e ) are i n f u l l R

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983. 2

T

0

Figure 1. Fitting data to one-phase (liquid) and two-phase (liquid and gas) oxygen uptake models. Key: *, oxygen in outlet gas (y scale); O, biomass concentration (X scale); ·, dissolved oxygen concentration; dashed line, one-phase model; solid line, two-phase model; X , biomass concentration at the interface. Reprinted, with permission, from Ref. 17. Copyright 1981, John Wiley & Sons, Inc.

362

BIOCHEMICAL

ENGINEERING

a c c o r d w i t h B l a n c h ' s a r g u m e n t a t i o n . Enhanced a b s o r p t i o n i s , i n f a c t , o n l y a p p a r e n t , b e c a u s e o f t h e p a r a l l e l pathway o f o x y g e n utilization. I n t r a p a r t i c l e mass t r a n s f e r . F o r some p r a c t i c a l s i t u a t i o n s mass t r a n s f e r l i m i t i n g s t e p i s l o c a l i z e d i n t h e i n t e r i o r o f a s o ­ l i d phase. T h i s i s t h e case f o r c e r t a i n m y c e l i a l f e r m e n t a t i o n s where t h e o x y g e n t r a n s f e r v i a p e l l e t o r m y c e l i a l clump i n t e r i o r may l i m i t g r o w t h o r p r o d u c t i o n p r o c e s s e s . T h i s s i t u a t i o n , e m p l o y ­ i n g t h e e f f e c t i v e n e s s c o n c e p t , i s r e v i e w e d b y Moo-Young and B l a n c h ( 1 4 ) . I n t h e f o l l o w i n g , some o t h e r e l e m e n t a r y phenomena and p r o c e s s e s c o n n e c t e d w i t h mass t r a n s f e r a r e r e v i e w e d . Gas p h a s e phenomena and p r o c e s s e s . T h e s e i n c l u d e gas h o l d ­ up, b u b b l e s i z e , i n t e r f a c i a coalescence/redisper s i o n . Gas h o l d - u p and b u b b l physico-chemical propertie , c o n f i g u r a t i o n and o n o p e r a t i o n c o n d i t i o n s . The i n i t i a l b u b b l e d i a m e t e r a t o r i f i c e i s an o r d e r o f m a g n i t u d e s m a l l e r t h a n t h e e q u i l i b r i u m b u b b l e s i z e a n d , a t some d i s t a n c e f r o m t h e gas d i s t r i ­ b u t o r , t h e s i z e o f b u b b l e s i s dependent o n l y on b r o t h p r o p e r t i e s and on l o c a l t u r b u l e n c e . I n b u b b l e c o l u m n , on t h e o t h e r h a n d , d i f f e r e n t r e g i o n s c a n be o b s e r v e d , w h e r e b u b b l e d i a m e t e r i s e i t h e r determined by o r i f i c e c h a r a c t e r i s t i c s o r by a p a r t i c u l a r t u r b u l e n c e . A d i s t i n c t i o n must be made b e t w e e n c o a l e s c i n g m e d i a ( w a t e r ) and n o n - c o a l e s c i n g m e d i a w i t h e l e c t r o l y t e s , a l c o h o l s and o t h e r s u r f a c e - a c t i v e a d d i t i o n s . I n media w i t h a c l e a n i n t e r f a c e ( c o a l e s c i n g ) , an a v e r a g e e q u i l i b r i u m s i z e o f b u b b l e s , d e t e r m i n e d by a n e x t e n t o f p a r a l l e l p r o c e s s e s o f c o a l e s c e n c e and r e d i s p e r ­ s i o n , i s h i g h e r because o f enhanced c o a l e s c e n c e . Under these c o n d i t i o n s , t h e s e c o n d a r y b u b b l e s , a r i s i n g f r o m p r i m a r y ones a t t h e o r i f i c e , c o a l e s c e e a s i l y a t some d i s t a n c e f r o m t h a t s p a c e . On t h e o t h e r h a n d , d i s p e r s i o n o f gas b u b b l e s i s e n h a n c e d i n t h e presence o f e l e c t r o l y t e s o r a l c o h o l s . T h i s e f f e c t i s e x p l a i n e d on t h e b a s i s o f c o m p l e x phenomena c o n n e c t e d w i t h w a t e r s t r u c t u r e changes n e a r t h e i n t e r f a c e ( 1 8 ) . The i n f l u e n c e o f e l e c t r o l y t e s and a l c o h o l s i s d i f f e r e n t i a t e d : t h e c o n c e n t r a t i o n o f e l e c t r o l y t e s a t t h e f r e s h i n t e r f a c e d e c r e a s e s w i t h b u b b l e age w h e r e a s t h a t o f a l c o h o l s i n c r e a s e s . These phenomena h a v e , no d o u b t , an i m p a c t on r e a c t o r d e s i g n a s b u b b l e p a t h and age c a n c o n s i d e r a b l y i n f l u e n c e gas h o l d - u p and i n t e r f a c i a l a r e a ( m e c h a n i c a l l y - m i x e d r e a c t o r s v s . v e r t i c a l m u l t i - s t a g e r e a c t o r s o r b u b b l e c o l u m n s ) . However, no sound t h e o r e t i c a l b a s i s h a s b e e n p u t f o r w a r d f o r g e n e r a l i z i n g t h e e f f e c t o f a l c o h o l s , e l e c t r o l y t e s and o t h e r s u r f a c e - a c t i v e com­ p o u n d s . S i m i l a r l y , no q u a n t i t a t i v e d e s c r i p t i o n o f a b u b b l e b e h a ­ v i o u r d u r i n g mass t r a n s f e r i n t h e p r e s e n c e o f m i c r o o r g a n i s m s , i n c l u d i n g b u b b l e c o a l e s c e n c e and r e d i s p e r s i o n and c e l l a d s o r p t i o n and d e s o r p t i o n , h a s b e e n s u g g e s t e d . E v e n a s i m p l e measurement o f bubble s i z e o r o f t o t a l i n t e r f a c i a l area i n a c e l l suspension

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16.

Reactor

PROKOP

Design

363

Fundamentals

p r e s e n t s a p r o b l e m . The same a p p l i e s t o a n a s s e s s m e n t o f c o a l e s c e n c e / r e d i s p e r s i o n r a t e s and mechanisms a l t h o u g h some methods f o r c o a l e s c e n c e f r e q u e n c y measurement h a v e b e e n s u g g e s t e d ( 1 9 , 2 0 ) . Some f u r t h e r t h e o r e t i c a l c o n s i d e r a t i o n s and c o r r e l a t i o n s f o r p r e ­ d i c t i n g b u b b l e s i z e , gas h o l d - u p a n d i n t e r f a c i a l a r e a were r e v i e w e d ( 1 6 , 1 5 ) . Gas h o l d - u p and p r e s s u r e d r o p a r e o f i m p o r t a n ­ ce i n a r a t i o n a l d e s i g n o f a i r - l i f t r e a c t o r s ( 2 1 ) . V o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t k _ a . This represents t h e most i m p o r t a n t d e s i g n p a r a m e t e r b e c a u s e and a a r e d i f f i ­ c u l t t o measure u n d e r r e a l c o n d i t i o n s . The k ^ a measurement methods were r e v i e w e d b y S o b o t k a e t a l . ( 2 2 ) . The most r e l i a b l e v a l u e s a r e o b t a i n e d b y b a l a n c e m e t h o d s . The model o f S i n c l a i r and R y d e r ( 2 3 ) may s e r v e a s a good e x a m p l e o f t h e a p p l i c a t i o n o f t h e above g e n e r a l b a l a n c e e q u a t i o n ( 1 ) w i t h a d o u b l e s u b s t r a t e l i m i t a t i o n o f growth (carbo f i t t i n g o f t h i s m o d e l , compose s u b s t r a t e and b i o m a s s b a l a n c e s , t o g r o w t h d a t a p r o v i d e s a p o s s i ­ b i l i t y o f e s t i m a t i n g L a a s one o f s e v e r a l e v a l u a t e d model p a r a ­ m e t e r s . An e x t e n s i o n or* t h i s model w i t h a p r o v i s i o n f o r a n a l t e r ­ n a t i v e oxygen uptake from t h e gaseous phase has been proposed by Sobotka e t a l . ( 1 7 ) . F o r k ^ a p r e d i c t i o n i n b u b b l e c o l u m n s , an e m p i r i c a l e q u a t i o n o f A k i t a and Y o s h i d a ( 2 4 ) , w h i c h d e s c r i b e s f a i r l y w e l l v a r i o u s d a t a o b t a i n e d f r o m l a r g e s c a l e e q u i p m e n t , c a n be u s e d : Sh

( a D

c

) = 0.6 e j '

1

5

0

, c°' . Bo ' S

6 2

. Ga°'

3 1

(2)

c o n t a i n i n g d i m e n s i o n l e s s Sherwood, S c h m i d t , B o d e n s t e i n and G r a s h o f numbers, i n t e r f a c i a l a r e a a , b u b b l e c o l u m n d i a m e t e r D and gas h o l d - u p ε . A s i m i l a r e q u a t i o n may be a p p l i c a b l e t o b u b b l e c o l u m n s p r o v i d e d w i t h t h e two-phase n o z z l e ( e j e c t o r ) , a s i n d i c a ­ t e d f r o m k ^ a v s . ε^ dependence ( F i g u r e 2 ) . Two-phase n o z z l e s and m u l t i - o r i f i c e spargers a r e s u i t e d f o r i n d u s t r i a l r e a c t o r s because of h i g h v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t s . The m a i n f e a t u r e of two-phase n o z z l e i s i n p r e s e r v i n g t h e e n e r g y o f t h e j e t , u t i ­ l i z e d f o r the p r o d u c t i o n o f a h i g h i n t e r f a c i a l a r e a , by suppres­ s e d c o a l e s c e n c e i n s u i t a b l e m e d i a and b y a s u i t a b l e g u i d e t u b e (momentum t r a n s f e r t u b e , ( 2 6 ) ) . The i n d u s t r i a l a p p l i c a t i o n s i n ­ v o l v e t h o s e i n SCP p r o d u c t i o n ( 2 7 ) a n d i n w a s t e w a t e r t r e a t m e n t ( 2 8 ) . The c o r r e l a t i o n o f t h e t y p e o f e q . ( 2 ) c a n , p e r h a p s , be o f use i n p r e d i c t i n g k ^ a f o r s t i r r e d - t a n k r e a c t o r s , b a s e d o n a s i n g l e m e a s u r e d v a l u e (gas h o l d - u p ) . C o r r e l a t i o n s b a s e d o n power i n p u t and s u p e r f i c i a l v e l o c i t y a r e t h e most f r e q u e n t ( 2 9 ) . E f f e c t o f v i s c o s i t y o n k ^ a a n d power c o n s u m p t i o n d u r i n g mass t r a n s f e r . The e f f e c t o f v i s c o s i t y o n k ^ a i s o f i m p o r t a n c e i n s e v e r a l h i g h l y v i s c o u s N e w t o n i a n and n o n - N e w t o n i a n f e r m e n t a t i o n s . Some c o r r e l a t i o n s d e s c r i b i n g l ^ a d e c r e a s e w i t h v i s c o s i t y have

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

364

BIOCHEMICAL

ENGINEERING

+ - V L = 1.70 10 ms 3

S

1

A - V L 0.86. 1Ô ms S

1 ' 4

6

8

10

S

' 20

3

1

1

30

Gas hold-up £q {%) Figure 2.

The k a dependence on € , bubble column with two-phase nozzle (3 mm ID), electrolyte solution plus ethanol (0.1% v/v) (25). L

0

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16.

Reactor

PROKOP

Design

365

Fundamentals

b e e n s u m m a r i z e d i n ( 1 5 ) . From t h i s p a p e r , t h e H e n z l e r ' s c o r r e l a ­ t i o n f o r 1-2% CMC s o l u t i o n s i n b u b b l e c o l u m n s ( f l o w b e h a v i o u r r e p ­ resentative f o r p e n i c i l l i n fermentation) i s u s e f u l :

where v ^ i s t h e s u p e r f i c i a l a i r v e l o c i t y and υ k i n e m a t i c v i s c o s i ­ t y . R e u s s e t a l . ( 3 0 ) s u g g e s t e d a much s i m p l e r e q u a t i o n f o r s t i r red-tank reactor: g

V

Ρ

T

—

a

= f (

§

)

(4)

G V L S > i n v o l v i n g two d i m e n s i o n l e s s g r o u p s ( i svolumetric a i r flow rate, r e a c t o r v o l u m e ) . Power c o n s u m p t i o n i n g a s s e d s y s t e m s , Ρ , i s then c a l c u l a t e d from: ^ V

Ρ /Ρ g o

(

0

= 0.0312 R e '

0 6 4

U

0

Fr" '

1 5 6

0

Na" '

3 8

( A _ a

).8

(

5

)

i

i n v o l v i n g R e y n o l d s a n d F r o u d e numbers o f i m p e l l e r , a e r a t i o n num­ b e r Na and r a t i o o f t a n k a n d i m p e l l e r d i a m e t e r . The a p p l i c a b i l i t y of eq.(4) f o r p r e d i c t i n g k^a d u r i n g f e r m e n t a t i o n o f P.chrysogenum and A . n i g e r i s shown i n F i g u r e 3. T h u s , t h e b a s i c p h y s i c a l p r o ­ p e r t i e s o f c u l t i v a t i o n broths ( i n t h i s case v i s c o s i t y ) a r e i n c o r ­ p o r a t e d i n t o c o r r e l a t i o n s f o r t r a n s p o r t phenomena t o g e t h e r w i t h k e y d e s i g n p a r a m e t e r s ( k ^ a and power c o n s u m p t i o n ) . N i s h i k a w a e t a l . (31; have r e c e n t l y proposed t h e t w o - r e g i o n model ( b u b b l i n g - and a g i t a t i o n - c o n t r o l l e d ) f o r e s t i m a t i n g k a i n a mixed r e a c t o r . Exponents f o r v i s c o s i t y terms a r e d i f f e r e n t f o r d i f f e r e n t regions. P r e d i c t i o n s by dimensionless c o r r e l a t i o n s a r e a p p l i c a b l e f o r b o t h non-Newtonian and Newtonian l i q u i d s . F o r b u b b l e c o l u m n s f i t t e d w i t h a two-phase n o z z l e a n d e l e c ­ t r o l y t e s o l u t i o n s , k a c a n be p r e d i c t e d f r o m power f o r a e r a t i o n Ε and f r o m power f o r l i q u i d c i r c u l a t i o n v i a n o z z l e Ε (Figure 4 ) . a ρ T

L

Heat Exchange H e a t e x c h a n g e i n v o l v e s h e a t g e n e r a t i o n and t r a n s f e r i n a n d between e l e m e n t a r y r e g i o n s o f a b i o r e a c t o r and t h a t o f i n d i v i d u a l phases o f a r e a c t o r ( 2 ) . A r a t i o n a l s t a r t f o r these c o n s i d e r a t i ­ ons i s t h e g e n e r a l l o c a l h e a t b a l a n c e , s i m i l a r t o t h a t o f mass transfer:

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

366

BIOCHEMICAL

ENGINEERING

Figure 3. Correlation of Reuss as applied for k a estimate during mold fermentations. Reprinted, with permission, from Ref. 30. Copyright 1981, Pergamon Press Ltd. L

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

PROKOP

Reactor

Design

Fundamentals

367

Figure 4. The k/.a dependence on E and E ; bubble column with two-phase nozzles (3-5 mm ID), electrolyte solution plus ethanol (0-0.1 % v/v) (25). e

p

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

368

BIOCHEMICAL

ENGINEERING

3 ρ . C . T. T . .

+ V . c . P

J

PJ

+Vk

iJ

ej

.

V T .

j

+

ΣΔΗ

n j

r.. ij

a t f -k-l(k«) \

\

T

T

< j s -

j

> -

(6)

0

where Ρ i s s p e c i f i c d e n s i t y , C i s m o l a r h e a t , Τ i s a b s o l u t e tem­ perature, k i s e f f e c t i v e thermal c o n d u c t i v i t y , Δ Η i s heat of r e a c t i o n , h i s h e a t t r a n s f e r c o e f f i c i e n t and T. i s t h e t e m p e r a ­ t u r e a t t h e i n t e r f a c e a r e a . The f i r s t t e r m o f tftîs b a l a n c e i s a n a c c u m u l a t i o n term a c c o u n t i n g f o r heat c a p a c i t y ; t h e second term i s heat t r a n s p o r t due t o c o n v e c t i o n , w h i c h i s i m p o r t a n t i n t u b u ­ l a r r e a c t o r s . The t h i r d t e r r e p r e s e n t h e a t b a c k m i x i n d be i m p o r t a n t i n b i o r e a c t i o n nes o r i n a deep l a y e r clumps f o u r t h t e r m c h a r a c t e r i s e s h e a t g e n e r a t i o n due t o a r e a c t i o n and the f i f t h i s t h e i n t e r f a c e h e a t t r a n s f e r . I n b i o r e a c t o r s t h a t a r e t h o r o u g h l y m i x e d o n l y t h e a c c u m u l a t i o n and h e a t g e n e r a t i o n terms are s i g n i f i c a n t and t h e t e m p e r a t u r e f i e l d i s u n i f o r m . The b o u n d a ­ ry c o n d i t i o n s o f t h i s s i m p l i f i e d e q u a t i o n a r e r e p r e s e n t e d by the o v e r a l l heat t r a n s f e r from the c u l t i v a t i o n b r o t h t o the c o o l i n g o r h e a t i n g ( s t e r i l i z a t i o n ) medium. The amount o f h e a t g e n e r a t e d i n a b i o r e a c t o r c a n be e a s i l y e v a l u a t e d f r o m t h e above s i m p l i f i e d h e a t b a l a n c e ^ r e s u l t i n g i n a v o l u m e t r i c rate o f heat g e n e r a t i o n , Q ( J . l t .h ) . Cooney e t a l . (32) o b t a i n e d b y means o f dynamic c a l o r i m e t r y . F o r a r o u g h e s t i m a t i o n o f Q , a p p l i c a b l e u n d e r o x y g e n l i m i t a t i o n and w i t h c e l l s a s t h e s o l e r e a c t i o n p r o d u c t , M i n k e v i c h and E r o s h i n ( 3 3 ) derived a t h e o r e t i c a l formula: A

f

f

= 818 Na

f

= 818

y k a — L

(7)

T

H

w h e r e ^ N a ^ i s t h e maximum o x y g e n t r a n s f e r o f a b i o r e a c t o r ( i n g.lt .h ) , y i s t h e mole f r a c t i o n o f oxygen i n t h e e x i t gas and H i s H e n r y *s c o n s t a n t .The c o e f f i c i e n t 818 h a s t h e m e a n i n g o f h e a t g e n e r a t i o n p e r 1 g o f oxygen consumed. Cooney e t a l . ^ ^ u s i n g d i r e c t m e a s u r e m e n t s , f o u n d t h i s c o e f f i c i e n t t o be 822 J . g oxy­ gen. E q . ( 7 ) seems t o be u s e f u l f o r p r e d i c t i n g t h e d e s i g n o f h e a t e x c h a n g e r s . Q i s a l s o c o r r e l a t e d t o b i o m a s s y i e l d and p r o d u c t i ­ vity ( X ) : 2

f

y

k Q

f

=

(

k

i

"

>

~ T —

υ

x

(

8

)

x/s where k^ and k^ a r e c o n s t a n t s t h a t c a n be d e r i v e d f r o m t h e h e a t s of c o m b u s t i o n o f s u b s t r a t e and c e l l s . T h u s , c a n be a s s e s s e d

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16.

PROKOP

Reactor

Design

Fundamentals

369

for

a g i v e n s u b s t r a t e and e x p e c t e d y i e l d and p r o d u c t i v i t y ( 3 4 ) . The o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t i s composed o f a m i n i ­ mum o f t h r e e c o n t r i b u t i o n s , t h e m a j o r o f w h i c h i s t h e c o e f f i c i e n t of h e a t t r a n s f e r from g a s - l i q u i d phase t o h e a t exchanger-wall. P o l l a r d and T o p i w a l a ( 3 5 ) r e p o r t e d v a l u e s o f h e a t t r a n s f e r c o e f ­ f i c i e n t s i n g a s - l i q u i d bioreactors f o rvarious configurations of h e a t e x c h a n g e r ( c o i l , j a c k e t ) . These a u t h o r s q u e s t i o n e d t h e a p p l i ­ c a t i o n o f c u r r e n t l y used c o r r e l a t i o n s o b t a i n e d i n l i q u i d media (36) t o g a s - l i q u i d s y s t e m s . The i n t r o d u c t i o n o f a i r a f f e c t s t h e heat t r a n s f e r c o e f f i c i e n t . A novel theory f o r p r e d i c t i n g heat t r a n s f e r i n b u b b l e column r e a c t o r s was p u t f o r w a r d b y Deckwer ( 3 7 ) . B l a k e b r o u g h and McManamey ( 3 8 ) m e a s u r e d t h e h e a t t r a n s f e r o f m o l d f e r m e n t a t i o n s i n an a i r - l i f t r e a c t o r . The e f f e c t s o f non-Newto­ n i a n a e r a t e d l i q u i d s o n h e a t t r a n s f e r c o e f f i c i e n t were s h o r t l y r e v i e w e d b y P a c e and R i g h e l a t Process Synthesis

at Reactor Level

The o v e r a l l d e s c r i p t i o n (model) o f a r e a c t o r i s o b t a i n e d through p r o c e s s s y n t h e s i s by combining models o f r e a c t o r hydrody­ n a m i c s , mass t r a n s f e r and h e a t e x c h a n g e w i t h an a p p r o p r i a t e c e l l ( s u b c e l l u l a r ) o r p o p u l a t i o n model ( 1 ) . D e s c r i p t i o n o f a p o p u l a t i o n should take i n t o c o n s i d e r a t i o n p o s s i b l e d i s p e r s e d o r aggregated (the d i s t i n c t morphological appearances o f a c u l t u r e : p e l l e t s , m y c e l i u m , f l o c k s , g r o w t h on r e a c t o r w a l l i n t h e f o r m o f m i c r o b i a l f i l m ) forms o f p o p u l a t i o n . Biomass s u p p o r t p a r t i c l e s a r e g a i n i n g a p p r e c i a b l e importance i n a e r o b i c (40) as w e l l as i n a n a e r o b i c processes. The d e s c r i p t i o n h i e r a r c h y a c q u i r e s d i f f e r e n t w a y s : p h y s i c a l p r o c e s s e s i n mass and e n e r g y b a l a n c e s ; i n f o r m a t i o n p r o c e s s i n g and c o n t r o l ; o p t i m i z a t i o n o f the system a t t h e r e a c t o r l e v e l o r as a w h o l e ( 4 1 ) . The most e l a b o r a t e c o n c e p t o f d e s c r i p t i v e h i e r a r c h y , i n c l u d i n g a s e t o f p r o g r a m s , was p u b l i s h e d and r o u t i n e l y u s e d b y K l i r ( 4 2 ) . As d e s c r i p t i v e h i e r a r c h y u s u a l l y f o l l o w s s t r u c t u r a l and f u n c t i o n a l h i e r a r c h y , i t i s t h u s a s s u r e d t h a t t h e m o d e l l e d o b j e c t p o s s e s s e s enough s t r u c t u r a l and f u n c t i o n a l f e a t u r e s , o t h e r ­ w i s e t h e r e a c t o r c o n t r o l b y means o f s u c h m o d e l s w o u l d n o t s a t i s ­ f a c t o r i l y respond t o changing c o n d i t i o n s . Reactor

Control

Reactor c o n t r o l concerns the system p r o p e r t i e s from the c o n t r o l v i e w p o i n t , and t h e d e t e r m i n a t i o n o f c r i t e r i a o f c o n t r o l and o p t i m i z a t i o n . S y s t e m p r o p e r t i e s i n c l u d e d y n a m i c p r o p e r t i e s s u c h a s t h e n a t u r e o f s y s t e m r e s p o n s e t o s m a l l and l a r g e d i s t u r ­ b a n c e s . R e g u l a r t r a n s i e n t r e a c t o r o p e r a t i o n may be o f f u t u r e i m p o r t a n c e e v e n f o r some p r o d u c t f o r m a t i o n p r o c e s s e s ( 4 3 ) . E l u c i ­ dation of input operating v a r i a b l e s a f f e c t i n g a process i s then valuable f o r reactor c o n t r o l . In t h i s connection the parametric

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

370

BIOCHEMICAL

ENGINEERING

s e n s i t i v i t y o f t h e s e v a r i a b l e s , d e f i n e d as a r e l a t i v e o r a b s o l u t e change i n an o p t i m i z a t i o n c r i t e r i o n on t h e i r change ( 4 4 ) , i s r e ­ q u i r e d . The d e c i s i v e p a r a m e t e r s s e r i o u s l y a f f e c t i n g t h e s y s t e m a r e d e f i n e d i n t h i s way. The c r i t e r i o n o f c o n t r o l and o p t i m i z a ­ t i o n i s c o n v e n i e n t l y s e t up, e.g., as t h e maximum b i o l o g i c a l t i t r e , maximum p r o d u c t i v i t y , l o w e s t r u n n i n g c o s t s , e t c . C o n t r o l and d y n a m i c h i e r a r c h i e s may s e r v e as a good g u i d e l i ­ ne f o r s e t t i n g up p r o p e r c o n t r o l . C o n t r o l h i e r a r c h y o f b i o l o g i c a l l e v e l s i s i n T a b l e I I I , c o n t r o l l o o p s and g o a l f u n c t i o n s ( c o n t r o l and o p t i m i z a t i o n c r i t e r i a ) o f b i o l o g i c a l l e v e l s a r e i n T a b l e I V . The c o m p l e x i t y o f b i o l o g i c a l phenomena i s r e f l e c t e d i n t h e p r e s e n ­ ce o f m u l t i p l e l o c a l g o a l f u n c t i o n s o f d i f f e r e n t s u b s y s t e m s , w h i c h may a c t i n an a c c o r d o r o p p o s i t e l y . N o t e t h a t T a b l e IV has b e e n d e v e l o p e d f o r e c o s y s t e m s . The i m p l e m e n t a t i o n o f c o n t r o l h i e r a r c h y i n t h e m o d e l l i n g and c o n t r o l f b i o l o g i c a l s y s t e m ha t t b e e n c a r r i e d o u t . The c o n t r o namic h i e r a r c h y of tim d i v i d u a l s u b s y s t e m s ) . The r e l a x a t i o n t i m e i s c o n s i d e r e d t o be t h e t i m e f o r a change f r o m one s t a t e t o a n o t h e r (due t o r e a c t i o n , d i f f u s i o n , change i n t h e a d j o i n i n g l e v e l , e t c . ) . T a b l e V p r e s e n t s a v e r a g e r e l a x a t i o n t i m e s o f some c e l l u l a r s u b s y s t e m s . As a p p e a r s f r o m t h i s t a b l e , s l o w (and l i m i t i n g ) p r o c e s s e s g i v e r i s e t o s t r u c ­ t u r a l e l e m e n t s , s e r v i n g as b a s i s f o r f a s t p r o c e s s e s . U s u a l l y , responses of h i g h e r l e v e l s of the system t o d i s t u r b a n c e s coming from the s u p e r i o r l e v e l are s l o w e r than responses a t the n e x t lower l e v e l . B e s i d e s r e l a x a t i o n times of b i o l o g i c a l subsystems of c e l l s , t h e s e l e c t i o n o f s y s t e m i c phenomena may p r o c e e d v i a an u t i l i z a t i o n o f , e.g., c e l l g e n e r a t i o n t i m e , r a t e o f s u b s t r a t e c o n s u m p t i o n , r e s p i r a t i o n r a t e , o x y g e n t r a n s f e r and o f t h e homogen i z a t i o n t i m e o f a r e a c t o r , t o m e n t i o n some. The above d i s c u s s i o n may i n v o l v e b o t h c o n t r o l and d y n a m i c s o f s t e a d y s t a t e ( s i n g l e and m u l t i p l e ) , u n s t e a d y s t a t e ( t r a n s i t i o n b e t w e e n two s t a t e s ) and u n s t a b l e o p e r a t i o n s o f t h e b i o r e a c t o r r e s u l t i n g from t y p i c a l n o n - l i n e a r response of b i o l o g i c a l systems. In s p i t e of the f a c t t h a t the s t a b i l i t y a n a l y s i s of n o n - l i n e a r systems i s q u i t e advanced, e x p e r i m e n t a l c o n f i r m a t i o n of m u l t i p l e s t e a d y s t a t e s and i n s t a b i l i t i e s l a g s b e h i n d ( f o r a r e v i e w o f t h e o r y and e x p e r i m e n t s see ( 4 5 ) ) . An e x c e l l e n t e x a m p l e o f e x p e r i ­ mental demonstration of unstable operation of a continuous reactor i s i n (46). Reactor Scale-Up On t h e b a s i s o f a r e a c t o r m o d e l , i n v o l v i n g enough s t r u c t u r a l and f u n c t i o n a l f e a t u r e s o f b i o l o g i c a l and e n g i n e e r i n g (physical) p r o p e r t i e s o f a b i o t e c h n o l o g i c a l p r o c e s s , new c r i t e r i a f o r a s c a l e - u p may e v o l v e . The employment o f o n l y one c r i t e r i o n , t a k e n f r o m one a r b i t r a r y l e v e l o f a h i e r a r c h y , i n the m o d e l l i n g and s u b s e q u e n t s c a l e - u p f r e q u e n t l y f a i l s , as i s a p p a r e n t f r o m numerous

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16.

PROKOP

Reactor

Design

371

Fundamentals

Table I I I Control Hierarchy

of B i o l o g i c a l

Levels

Dynamic B e h a v i o u r

The H i g h e s t Mechanism

1

Mass and e n e r g y change ( s t e a d y number o f s t r u c t u r a l e l e m e n t s and s t e a d y p a r a m e t e r s

D i r e c t and f e e d - b a c k control

2

F u n c t i o n a l dynamics (steady number o f s t r u c t u r a l e l e m e n t s , changing parameters)

Adaptation

3

S t r u c t u r a l dynamics ( c h a n g i n g number o f s t r u c t u r a l elements )

Organization

4

Developmental dynamics (changing goal function)

Development

Control Level

Internat.J.General

Control

Systems 1982, 8 ( 1 ) , T a b l e I V ( 1 )

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

Development

Change i n g o a l function of a subsystem

Change i n g o a l function of population

Change i n g o a l f u n c t i o n of ecosystem

I n t e r n a t . J . G e n e r a l Systems 1982, J K 1 ) , T a b l e V (1)

Change i n g o a l function of i n d i ­ vidual cells

Change i,n r a t i o o f different populations

Change i n r a t i o o f s t r u c t u r a l elements

Change i n f u n c t i o n Change-over from one t o a n o t h e r of subsystems b i o c h e m i c a l pathway

Organization (selection)

kinetics

Adaptation of trophic levels

Multiple

Adaptation

S t a b i l i z a t i o n of a number o f p o p u l a t i o n s

Optimization of energy f l o w o f each trophic level

Trophic

Adaptation of populations

S t a b i l i z a t i o n of Stabilization of r a t i o o f i n d i v i d u a l a number o f subsystems individuals

Simple

D i r e c t and feed-back

Physiological adaptation of subsystems

Optimization of structural elements o f population

Optimization of subsystems o f a c e l l by controlling individual subsystems

Optimization of individual subsystems by controlling biochemical pathways

Goal function

kinetics

H i e r a r c h y Population

Levels

S t r u c t u r a l Cellular

C o n t r o l Loops and G o a l s o f B i o l o g i c a l

Molecular

T a b l e IV

16.

PROKOP

Table V

Reactor

Design

373

Fundamentals

Dynamic H i e r a r c h

System (Subsystem)

R e l a x a t i o n Time, s

. . C e l l m u l t i p l i c a t i o n , DNA r e p l i c a t i o n

10

-

10

mRNA s y n t h e s i s on o p e r o n * T r a n s l o c a t i o n of substances i n t o c e l l s

3 10 1 10 1

-

4 10 3 10 2

P r o t e i n s y n t h e s i s i n polysomes

10

-

10

Allosteric control Glycolysis

2

o f enzyme s y n t h e s i s

i n cytoplasm

Oxidative phosphorylation

4

10° 10 * -

10

-2 10

i n mitochondria —6

E n z y m a t i c r e a c t i o n and t u r n o v e r

10

—3 -

10

Bond b e t w e e n enzyme and s u b s t r a t e 10 I n t e r n a t . J . G e n e r a l Systems 1982, 8 ( 1 ) , T a b l e V I ( 1 )

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

374

BIOCHEMICAL

ENGINEERING

examples of a p p l i c a t i o n s of e n g i n e e r i n g c r i t e r i a ( e . g . , i n ( 2 9 ) ) . The n e g l e c t o f b i o l o g i c a l f e a t u r e s o f b i o t e c h n o l o g i c a l p r o c e s s e s f r e q u e n t l y l e a d s t o an u n r e s o l v e d c a s e o f s i m u l t a n e o u s m a i n t e n a n ­ ce o f t h e n u m e r i c a l v a l u e s o f a l l d i m e n s i o n l e s s g r o u p s o f p h y s i ­ c a l p a r a m e t e r s (mass t r a n s f e r , power i n p u t p e r u n i t v o l u m e , m i x i n g time, e t c . ) . For example, a s i n g l e c r i t e r i o n of constant m i x i n g t i m e w o u l d v i o l a t e an i n v a r i a n c y o f gas p h a s e d y n a m i c s . M a c r o m i x i n g o f t h e f l u i d phase d e t e r m i n e s , t o a c o n s i d e r a b l e e x t e n t , t h e b e h a v i o u r o f t h e gas p h a s e , i . e . , t h e r e s i d e n c e t i m e d i s t r i ­ b u t i o n o f gas b u b b l e s . I n r e a c t o r s c a l e - u p , a c o n s i d e r a b l e d i f f e ­ r e n c e i n gas p h a s e r e s i d e n c e t i m e c a n be e x p e c t e d as t h e l i q u i d f l o w p a t h s ( l o o p s ) g r o w w i t h i n c r e a s i n g r e a c t o r s c a l e . The m a i n t e ­ n a n c e o f m i x i n g t i m e w o u l d r e s u l t i n an i n c r e a s e i n o x y g e n u t i l i ­ z a t i o n e f f i c i e n c y . Some l i m i t e d e x p e r i m e n t a l d a t a f o r d i f f e r e n t r e a c t o r designs are a v a i l a b l e i n (47) Q u a l i t a t i v e l y new c r i t e r i a scheme o f t h e h i e r a r c h i c a c e s s , suggest a need f o r m a i n t a i n i n g s i m i l a r i t y between systems o f d i f f e r e n t s i z e s o f l a b o r a t o r y and p l a n t l e v e l s , i . e . , t h e i d e n t i t y o f v a l u e s o f p a r a m e t e r s and c o n s t a n t s (1,2) · Such a scale-up procedure would r e q u i r e a r e p e t i t i o n of systemic f e a t u ­ res of d e c i s i v e l e v e l s of h i e r a r c h y i n v o l v i n g those of b i o t e c h n o ­ l o g i c a l and p h y s i c a l n a t u r e on t h e l a b o r a t o r y and p l a n t s c a l e and w o u l d assume t h e i n v a r i a n c e o f t h e s y s t e m i c phenomena o f a g i v e n l e v e l w i t h r e s p e c t t o t h e s c a l e . The m e t h o d o l o g y o f s c a l e up v i a m o d e l l i n g and s i m u l a t i o n i s y e t t o be d e v e l o p e d .

Conclusions F u r t h e r d e v e l o p m e n t o f r e a c t o r d e s i g n i s hampered by a l a c k o f a p p r o p r i a t e t h e o r y o f some e l e m e n t a r y phenomena. T h i s s i t u a ­ t i o n l e a d s t o e m p i r i c a l c o r r e l a t i o n s t h a t may be o f some p r a c t i ­ c a l u s e . Systems a p p r o a c h a i d s i n c r e a t i n g a g u i d e l i n e f o r r a t i o ­ n a l b i o r e a c t o r d e s i g n , e s p e c i a l l y on t h e b a s i s o f sound b i o l o g i ­ c a l theory.

Literature Cited 1. Prokop, A. Internat.J.General Systems 1982, 8(1) 2. Prokop, A. Acta B i o t e c h n o l o g i c a (DDR) 1981, 1(3) 269-278. 3. B i r d , B.; Stewart, W.E.; L i g h t f o o t , B.N. "Transport Phenomena"; J.Wiley: New York, 1980. 4. T u r i a n , R.M.; Fox, G.E.; R i c e , P.A. Can.J.Chem.Eng. 1975, 53, 431-437.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

16.

PROKOP

Reactor

Design

Fundamentals

375

5. Deckwer, W.-D. Chem.Ing.Technik 1977, 49, 213-233. 6. L e v e n s p i e l , O. "Chemical Reaction E n g i n e e r i n g . An I n t r o d u c t i o n to the Design of Chemical Reactors"; J.Wiley: New York, 1962. 7. Prokop, Α.; E r i c k s o n , L.E.; Fernandez, J . ; Humphrey, A.E. Biotechnol.Bioeng. 1969, 11, 945-966. 8. L a i n e , J . ; Kuoppamäki, R. Ind.Eng.Chem., Proc.Des.Develop. 1979, 18, 501-506. 9. E i n s e l e , A. Chem.Rundschau 1976, 29, 53-55. 10. Danckwerts, P.V. Chem.Eng.Sci. 1958, 8, 93-102. 11. B a j p a i , R.K.; Ramkrishna, D.; Prokop, A. Biotechnol.Bioeng. 1977, 19, 1761-1772. 12.Skelland, A.H.P. " D i f f u s i o n a l Mass T r a n s f e r " ; J.Wiley: New York, 1974. 13. A i b a , S.; Toda, K. J.Gen.Appl.Microbiol. 1964, 10, 157-162. 14. Moo-Young, M.; Blanch H.W "Advance i Biochemical Enginee r i n g " ; F i e c h t e r , Α. pp.1-69. 15. Deckwer, W.-D. "Advances i n Biotechnology"; Moo-Young, M.; Vezina, C.; Robinson, W.C., Eds.; Pergamon Press: Oxford, 1981; V o l . 1 . 16. Blanch, H.W. "Annual Reports on Fermentation Processes"; P e r l man, D., Ed.; Academic Press: New York, 1979; V o l . 3 , pp.47-74. 17.Sobotka, M.; Votruba, J . ; Prokop, A. Biotechnol.Bioeng. 1981 23, 1193-1202. 18. Z i e m i n s k i , S.A.; Whittermore, R.C. Chem.Eng.Sci. 1971, 26, 509-520. 19. K o e t s i e r , W.T.; Thoenes, D. Proc.5th Europ.2nd Internat.Symp. on Chemical Reaction Engineering; Amsterdam, May 2-4, 1972, E l s e v i e r : Amsterdam, 1972; pp.(B3-15)-(B3-24). 20. Hassan, I.T.M.; Robinson, C.W. Chem.Eng.Sci. 1980, 35, 12771289. 21. Hsu, Y.C.; Dudukovic', M.P. Chem.Eng.Sci. 1980, 35, 135-141. 22.Sobotka, M.; Prokop, Α.; Dunn, I . J . ; E i n s e l e , A. "Annual Repor­ ts on Fermentation Processes"; Tsao, G.T., Ed; Academic Press: New York, 1981; Vol.5. 2 3 . S i n c l a i r , C.G.; Ryder, D.N. Biotechnol.Bioeng. 1975, 17, 375389. 24. A k i t a , K.; Yoshida, F. Ind.Eng.Chem., Proc.Des.Develop. 1973, 12, 76-80. 25. Prokop, Α.; Janík, P.; Sobotka, M.; Krumphanzl, V. B i o t e c h n o l . Bioeng. ,submitted. 26. Nagel, O.; Kürten, H.; Sinn, R. Chem.Ing.Technik 1970, 42, 474-479. 27. Dimmling, W.; Seipenbusch, R. Process Biochem. 1978, 13(3), 9-12, 14-15, 34. 28. L e i s t n e r , G.; M i l l i e r , G.; S e l l , G.; Bauer, A. Chem.Ing.Technik 1979, 51, 288-294. 29. A i b a , S.; Humphrey, A.E.; Millis, N.F. "Biochemical Engineer i n g " ; Tokyo U n i v e r s i t y Press: Tokyo, 1973, 2nd Ed.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

376

BIOCHEMICAL

ENGINEERING

30. Reuss, M.; B a j p a i , R.K.; Lenz, R.; Niebelschütz, H.; Papalexion, A. "Advances in Biotechnology"; Moo-Young, M.; Vezina, C.; Robinson, W.C., Eds.; Pergamon Press: Oxford, 1981; V o l . 1 . 31. Nishikawa, M.; Nakamura, M.; Hashimoto, K. J.Chem.Eng.Japan 1981, 14, 227-232. 32. Cooney, C. .; Wang, D.I.C.; Mateles, R.I. Biotechnol.Bioeng. 1968, 11, 269-281. 33. Minkevich, I.G.; E r o s h i n , V.K. Folia M i c r o b i o l . 1973, 18, 376-385. 34. Wang, H.Y.; Mou, S.-G.; Swartz, J.R. Biotechnol.Bioeng. 1976, 18, 1811-1814. 35. P o l l a r d , R.; Topiwala, H.H. Biotechnol.Bioeng. 1976, 18, 1517-1535. 36. Edwards, M.F.; Wilkinson, W.L. Chem.Engr.(London) 1972, 265, 328-335. 37. Deckwer, W.-D. Chem.Eng.Sci 38. Blakebrough, N.; McManamey Engrs. 1978, 56, 127-135. 39. Pace, G.W.; R i g h e l a t o , R.C. "Advances in Biochemical Engineer i n g " ; F i e c h t e r , Α., Ed.; Springer: B e r l i n , 1980; Vol.15, pp.41-70. 40. Atkinson, B.; Black, G.M.; Pinches, A. Process Biochem. 1980, 15(4), 24-26, 29-32. 41. Mesarovic', M.D.; Macko, D.; Takahara, Y. "Theory of H i e r a r c h i ­ c a l , M u l t i l e v e l Systems"; Academic Press: New York, 1970. 42. Klir, G.J. " T h e o r e t i c a l Systems Ecology; Advances and Case Studies"; Halfon, E., Ed.; Academic Press: New York, 1979; pp.291-323. 43. P i c k e t t , A.M.; Topiwala, H.H.; Bazin, M.J. Process Biochem. 1979, 14(11), 10, 12, 14-16. 44. Ditmar, P.; Khartman, K.; O s t r o v s k i i , G.M. Theoret.Osnovy Khim. Tekhnol. 1978, 12, 104-111 ( i n Russian). 45. Prokop, A. "Continuous C u l t i v a t i o n o f Microorganisms"; S i k y t a , B.; F e n c l , Z.; Poláĉek, V., Eds.; I n s t i t u t e of M i c r o b i o l o g y : Prague, 1980, pp. 173-187. 46. D i B i a s i o , D.; Lim, H.C.; Weigand, W.A. AIChE J o u r n a l 1981, 27, 284-292. 47.Ovaskainen, P.; L u n d e l l , R.; Laiho, P. Process Biochem. 1976 11(4) 37-39, 55. R E C E I V E D June 1, 1982

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

17 Immobilized Cells Catalyst Preparation and Reaction Performance J. KLEIN and K.-D. VORLOP Technical University of Braunschweig, Institute of Chemical Technology, Federal Republic of Germany Immobilized cells have proven to be effective cata­ lysts i n the enzymati pounds. Such catalyst entrapment of cells i n polymeric carriers, and the methods of ionotropic gelation and polycondensation of epoxids w i l l be described. Depending on enzymatic activity and particle size the transformation may proceed i n the reaction or diffusion controlled re­ gime. Quantitative estimation of the effectiveness factor-Thiele modulus relation w i l l be presented for different reaction types. This includes the experi­ mental determination of the catalytically active c e l l concentration and the effective d i f f u s i v i t y i n the porous polymeric carrier. Transport limitation can also be a controlling factor i n the experimental determination of the operational s t a b i l i t y of such biocatalysts.

A large number of products i n the pharmaceutical and food industry i s obtained from fermentation processes. Examples are amino acids, stereoregular organic acids, antibiotics, ethanol, etc. In a classical fermentation process the product formation is s t r i c t l y coupled to c e l l growth resulting i n a possibly unfav­ orable byproduction of biomass. Furthermore these processes are typically performed as batch operations. As has been shown already on an industrial scale, fermenta­ tion can be substituted by heterogeneous catalysts with resting microbial cells immobilized i n polymeric carriers. Repeated use of the once formed biomass, continuous process operation, and elim­ ination of costly separation steps of product solution from bio­ mass are obvious advantages of this new technology. Some p r i n c i ­ pal aspects of a) immobilization methodology, b) catalyst effect­ iveness, and c) operational s t a b i l i t y shall be outlined i n this contribution. 0097-6156/83/0207Ό377$06.00/0 © 1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

378

ENGINEERING

Polymer Entrapment V a r i o u s methods h a v e b e e n p r o p o s e d f o r w h o l e c e l l i m m o b i l i z a ­ t i o n i n c l u d i n g a d s o r p t i o n and c o v a l e n t a t t a c h m e n t t o a p r e f o r m e d c a r r i e r , c r o s s l i n k i n g , f l o c c u l a t i o n , m i c r o e n c a p s u l a t i o n , and e n ­ t r a p m e n t . P h y s i c a l e n t r a p m e n t i n a p o r o u s m a t r i x i s by f a r t h e most f l e x i b l e and most commonly u s e d t e c h n i q u e . Considering the f a c t t h a t t h e p o l y m e r n e t w o r k has t o be f o r m e d i n t h e p r e s e n c e o f t h e f i n a l l y entrapped b i o l o g i c a l m a t e r i a l , the performance c r i t e r i a of c h e m i c a l and p h y s i c a l n a t u r e a r e as f o l l o w s : (1) The n e t w o r k f o r m a t i o n has t o p r o c e e d u n d e r m i l d c o n d i ­ t i o n s (pH and t e m p e r a t u r e ) i n an aqueous e n v i r o n m e n t ; (2) t h e n e t w o r k has t o be c h e m i c a l l y s t a b l e u n d e r v a r i o u s r e ­ a c t i o n c o n d i t i o n s (pH, b u f f e r s o l u t i o n , i o n i c and n o n i o n i c s u b ­ strates, etc.); (3) t h e s i z e and t h e r a b l y as b e a d s ) has t (4) t h e p o s s i b i l i t y f o r a l a r g e v a r i a t i o n o f b i o m a s s c o n t e n t i n t h e c a t a l y s t s h o u l d be g i v e n ; (5) t h e c a t a l y s t b e a d s s h o u l d be m e c h a n i c a l l y s t a b l e t o be used i n v a r i o u s r e a c t o r c o n f i g u r a t i o n s (packed bed, f l u i d i z e d bed, s t i r r e d tank). A p p r o p r i a t e p o l y m e r i c c a r r i e r s c a n be o b t a i n e d f r o m p o l y m e r i c , o l i g o m e r i c , and monomeric p r e c u r s o r s . Due t o unwanted c h e m i c a l i n ­ t e r a c t i o n of such chemicals w i t h the c e l l m a t e r i a l l a r g e r s i z e of t h e s e p r e c u r s o r s i s f a v o r a b l e . The i o n o t r o p i c g e l a t i o n , s t a r t i n g f r o m p o l y e l e c t r o l y t e s and t h e p o l y c o n d e n s a t i o n , s t a r t i n g f r o m o l i ­ g o m e r i c epoxy r e s i n s , a r e t y p i c a l p r o b l e m s o l u t i o n s . I o n o t r o p i c G e l a t i o n of P o l y e l e c t r o l y t e s T h i s method o f n e t w o r k f o r m a t i o n i s d e f i n e d as a c r o s s l i n k i n g r e a c t i o n of p o l y e l e c t r o l y t e s w i t h lower molecular weight m u l t i v a ­ lent counterions. C o n s i d e r i n g t h e p o l y m e r i c component, a n i o n i c ( e . g . , a l g i n a t e , CMC (I) o r c a t i o n i c ( c h i t o s a n (2)) substances can be u s e d . T h i s v a r i e t y o f p o l y m e r s and t h e a p p r o p r i a t e c o u n t e r i o n s a r e s u m m a r i z e d i n F i g u r e 1. The c h o i c e o f t h e p o l y m e r i s d e t e r ­ m i n e d by t h e pH r e g i o n o f t h e r e s p e c t i v e b i o c a t a l y t i c r e a c t i o n , s i n c e a l l i o n o t r o p i c g e l s a r e r e v e r s i b l e s t r u c t u r e s w h i c h c a n be r e d i s s o l v e d by i n c r e a s e ( a l g i n a t e ) o r d e c r e a s e ( c h i t o s a n ) o f pH b e ­ yond c e r t a i n l i m i t s . A second important c r i t e r i o n i s the i o n i c c o m p o s i t i o n o f t h e r e a c t i o n medium and t h e p o s s i b i l i t y o f i n s o l u b l e byproduct o r complex f o r m a t i o n w i t h the network forming i o n s . I n a t y p i c a l a l g i n a t e entrapment process the c e l l s are sus­ pended i n a 3% s o d i u m a l g i n a t e s o l u t i o n and t h i s v i s c o u s s u s p e n ­ s i o n i s p r e c i p i t a t e d d r o p w i s e i n a 1% C a C l 2 s o l u t i o n . A f t e r 30 m i n u t e s s t a b l e C a - a l g i n a t e g e l s a r e f o r m e d where t h e c e l l s a r e i m ­ m o b i l i z e d i n a macroporous s t r u c t u r e . F o l l o w i n g to t h i s p r e c i p i ­ t a t i o n p r o c e s s a p a r t i a l d r y i n g s t e p c a n be a p p l i e d w h i c h r e s u l t s i n a homogeneous s h r i n k i n g o f t h e p a r t i c l e s , t h u s i n c r e a s i n g c o n -

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

KLEIN

A N D VORLOP

Immobilized

POLYELECTROLYTES

Cells

379

as Catalysts

MULTIVALENT COUNTERIONS

POLYANIONS ALGINAT '""cOO^

Χ

CARBOXYMETHYLCELLULOSE

φ

CARBOXY-GUARGUM

Ca . Fe . Zn 2 +

Al \ 3

2 +

Fe

2 +

...

3 +

COPOLY-STYRENEMALEIC ACID POLYCATIONS CHITOSAN

Fe(CN)

6

4

\

Fe(C^

3

"

POLY-PHOSPHATE /

^ΝΗ3

Φ

Χ

θ

POLY-ALDEHYDO-CARBONIC ACID P0LY-1-HYDR0XY-1SULF0NATE-PR0PEN-2 ALGINATE

Figure 1. Summary of polymer-counterion systems to be used in ionotropic gelation for whole cell entrapment. Reprinted, with permission, from Ref. 13. Copy­ right 1982, Plenum Publishing Corp.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

380

ENGINEERING

s i d e r a b l y t h e m e c h a n i c a l s t a b i l i t y as w e l l a s t h e p a c k i n g d e n s i t y of the entrapped c e l l s i t s e l f . A l l these f a c t o r s are very advanta­ geous f o r t h e b i o c a t a l y t i c a p p l i c a t i o n . The f l e x i b i l i t y o f t h e a l g i n a t e - m e t h o d c a n be d e m o n s t r a t e d a c c o r d i n g t o t h e f o l l o w i n g p a r ­ a m e t e r b o u n d a r y v a l u e s : p o l y m e r c o n c e n t r a t i o n f r o m 0.5 t o 8%, CaC^ c o n c e n t r a t i o n f r o m 0.05 t o 2%, c e l l c o n c e n t r a t i o n (on wet w e i g h t b a s i s ) f r o m 0.1 t o 100%, b e a d d i a m e t e r s f r o m 0.1 t o 5 mm, and p r e p a r a t i o n t e m p e r a t u r e s f r o m 0 t o 80° C. Cells of different s t r u c t u r e ; e.g., a e r o b i c (1) o r a n a e r o b i c m i c r o b e s ( 3 ) , p l a n t c e l l s ( 4 ) , mammalian c e l l s ( 5 ) , c a n be e n t r a p p e d and t h u s s t a b i l i z e d without c o n s i d e r a b l e t o x i c i t y problems. A p r o b l e m o f p r a c t i c a l i m p o r t a n c e i s t h e s c a l e up o f t h e i m ­ m o b i l i z a t i o n p r o c e s s f r o m amounts o f s e v e r a l grams t o s e v e r a l hundred l i t e r s . W h i l e s m a l l amounts c a n e a s i l y be p r e p a r e d u s i n g one c a p i l l a r y o r i f i c e , a b u n d l e o f s u c h c a p i l l a r y i n a s i e v e p l a t e type c o n s t r u c t i o n w i l l g i v i f the c a p i l l a r y c h a r a c t e r i s t i c a r e shown i n F i g u r e 2. Polycondensation

o f Epoxy

Resins

I n t h i s c a s e c o v a l e n t n e t w o r k s o f h i g h m e c h a n i c a l and c h e m i ­ c a l s t a b i l i t y a r e o b t a i n e d as a r e s u l t o f c r o s s l i n k i n g r e a c t i o n of e p o x i d e s w i t h m u l t i f u n c t i o n a l a m i n e s ( 6 ) . The m a i n p r o b l e m s o f t h i s t e c h n i q u e a r e t h e t o x i c i t y o f t h e amino-component and t h e u s u a l l y l o w p o r o s i t y o f t h e p o l y m e r i c n e t w o r k . The t o x i c i t y , mea­ s u r e d by t h e v i a b i l i t y o f i m m o b i l i z e d y e a s t c e l l s , c o u l d be m i n i ­ m i z e d a) by p r o p e r s e l e c t i o n o f e p o x y and amino components and b) by i n t r o d u c t i o n o f a p r e g e l l i n g t i m e i n t h e o r d e r o f 15 m i n u t e s b e f o r e m i x i n g t h e c e l l s w i t h t h e c o n d e n s a t i n g o l i g o m e r s ( 7 ) . The p o r o s i t y o f t h e m a t r i x i s i n t r o d u c e d by t h e i m m o b i l i z e d c e l l s i t ­ s e l f and by an i n t e r m e d i a t e p r e p a r a t i o n o f an i n t e r p e n e t r a t i n g n e t w o r k w i t h an i o n o t r o p i c g e l . The i o n o t r o p i c g e l a t i o n i s a l s o u s e d t o c o n t r o l t h e p a r t i c l e s h a p e and s i z e . A c o m p l e t e scheme o f s u c h a n i m m o b i l i z a t i o n p r o c e s s i s shown i n F i g u r e 3. A g a i n q u i t e h i g h c o n c e n t r a t i o n s (up t o 70% on wet w e i g h t b a s i s ) o f c e l l s c a n be f i n a l l y i n c o r p o r a t e d i n s u c h a p o l y m e r i c s t r u c t u r e . The v i a b i l i t y o f t h e y e a s t c e l l s , and t h u s t h e r e d u c e d t o x i c ­ i t y o f t h e e n t r a p m e n t m e t h o d , c a n be d e m o n s t r a t e d by c e l l g r o w t h i n the m a t r i x , which gives r i s e to a corresponding a c t i v i t y i n ­ crease f o r ethanol p r o d u c t i o n from glucose ( 7 ) . This behavior i s shown i n F i g u r e 4. The f a c t o r o f a c t i v i t y i n c r e a s e compared t o t h e i n i t i a l v a l u e i n c r e a s e s w i t h d e c r e a s i n g i n i t i a l l o a d i n g ; however, i t i s o b v i o u s t h a t an u p p e r l i m i t o f a c t i v i t y w i l l f i n a l l y be reached. The r e a s o n f o r t h i s phenomenon, as w e l l as f o r t h e a c ­ t i v i t y d e c r e a s e w i t h i n c r e a s i n g i n c u b a t i o n t i m e , w i l l become obvious from the d i s c u s s i o n s o f the f o l l o w i n g chapter.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

KLEIN

Immobilized

A N D VORLOP

Cells as Catalysts

381

PRESSURE

Figure 2.

Scheme for catalyst bead formation by ionotropic gelation, including scale-up device.

10g tpoxy resin • 33g curing agent (30%-soUn H^O) * 7 ml H 0

-±

2

±

precondensotion (15m. n.)

mixing periodical injection

6g bake i*s yeast • 2ml • 20g β % alginate- sol.

, Qoooonnnnnooo drying (24h)

0

crosslink!ng (20min)

ο.ο

9r^-> ol

2wt%CaCl2-solution

EP0XY-BEADS alginate-dissolution (40min) in 0.1« phosphate-buffer (pH> 6.0)

Figure 3. Process scheme for preparation of biocatalysts by cell entrapment in epoxy beads. Reprinted, with permission, from Ref. 14. Copyright 1982, Science and Technology Letters.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

382

BIOCHEMICAL

ENGINEERING

Figure 4. Dependence of biocatalytic activities for the batch fermentation of ethanol from glucose with immobilized yeast cells as a function of incubation time (time for cellgrowth in the carrier) for various initial cell loadings in epoxy carriers.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

17.

KLEIN A N D VORLOP

Immobilized

Cells

Effectiveness o f Immobilized C e l l

as Catalysts

383

Catalysts

I t i s a w e l l known f a c t i n h e t e r o g e n e o u s c a t a l y s i s , t h a t t h e c a t a l y t i c a c t i v i t y i s generally not d i r e c t l y proportional to the c o n c e n t r a t i o n o f a c t i v e s i t e s b u t depends a l s o o n h y d r o d y n a m i c c o n d i t i o n s i n t h e s u r r o u n d i n g o f t h e p a r t i c l e s , on p a r t i c l e s i z e and m a t r i x p o r o s i t y . I t i s furthermore w e l l understood, that v a r i o u s t r a n s p o r t phenomena h a v e t o be t a k e n i n t o a c c o u n t , m a i n l y d i f f u s i o n a l transport processes which n e c e s s a r i l y a r e preceding to the r e a c t i o n step i t s e l f . A d i m e n s i o n l e s s number, u s u a l l y c a l l e d T h i e l e - m o d u l u s , c a n be used t o q u a n t i t a t i v e l y account f o r t r a n s p o r t - r e a c t i o n c o u p l i n g phenomena. A s s u m i n g t h e v a l i d i t y o f M i c h a e l i s - M e n t e n r a t e e q u a ­ t i o n - which i s j u s t i f i e d f o r simple enzymatic r e a c t i o n s i n whole c e l l s t o o - t h e f o l l o w i n g e x p r e s s i o n f o r t h e T h i e l e modulus has been d e r i v e d ( 8 ) :

f

where R i s t h e p a r t i c l e r a d i u s , v t h e r a t e o f r e a c t i o n , the M i c h a e l i s c o n s t a n t , S t h e s u b s t r a t e c o n c e n t r a t i o n and D the e f ­ f e c t i v e s u b s t r a t e d i f f u s i v i t y i n the porous c a t a l y s t p a r t i c l e . On t h e o t h e r hand t h e e f f e c t i v e n e s s f a c t o r η i s d e f i n e d a s t h e r a t i o o f t h e e f f e c t i v e r e a c t i o n r a t e ν t o t h e maximum r e a c t i o n rate ν w h i c h w o u l d be o b s e r v e d w i t h o u t t r a n s p o r t l i m i t a t i o n max e

n = ~ -

(2)

max F o r i m m o b i l i z e d c e l l c a t a l y s t s t h e r e a r e two p o s s i b i l i t i e s t o ob­ t a i n t h i s f a c t o r . F i r s t l y , t h e p a r t i c l e s o f l a r g e r r a d i u s can be g r i n d e d down t o s u c h a s m a l l s i z e t h a t p o r e d i f f u s i o n becomes neg­ ligible. I n t h i s case = v ^ + . Due t o t h e s i z e and t h e s i m p l e entrapment o f t h e c a t a l y t i c s p e c i e s l o s s from t h e m a t r i x may b e c o n s i d e r a b l e . Therefore, secondly, the free c e l l a c t i v i t y can be used i n t h e denominator, i f t h e e x a c t c o n c e n t r a t i o n o f c a t a l y t i c a l l y a c t i v e immobilized c e l l s ( X ) known. Since e

Q

i

s

a c t

v.-I.ilfi

(3)

i s t h e s p e c i f i c r e a c t i o n r a t e o f t h e f r e e l y suspended c e l l s , t h e equation ν = ν ' X = v* (4) max act 1

h o l d s , w h i c h f u r t h e r m o r e d e f i n e s v i n E q n . ( 1 ) . B a s e d o n numer­ i c a l calculations t y p i c a l functions

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

384

BIOCHEMICAL ENGINEERING

η - f (Φ)

(5)

h a v e b e e n d e v e l o p e d , w h i c h i n t e r r e l a t e t h e two d i m e n s i o n l e s s p a r ­ ameters and w h i c h c a n be checked e x p e r i m e n t a l l y . To e v a l u a t e t h e a p p l i c a b i l i t y o f E q n . ( 5 ) , t h e p a r a m e t e r s i n Eqns. (1-4) have t o be determined i n d e p e n d e n t l y . T h i s has been done f o r t h e c l e a v a g e r e a c t i o n o f P e n i c i l l i n G t o 6APA w i t h immo­ b i l i z e d E. Qoli c e l l s i m m o b i l i z e d i n e p o x i d e b e a d s ( 9 ) . The r a d i u s R: The r a d i u s o f p a r t i c l e s o b t a i n e d f r o m i o n o t r o p i c g e l a t i o n i s u s u a l l y c o n t r o l l e d w i t h i n v e r y narrow l i m i t s and t h e s i z e c a n e a s i l y b e d e t e r m i n e d by m i c r o s c o p i c m e a s u r e m e n t s . Reaction K i n e t i c s ; The r e a c t i o n r a t e s h a v e b e e n m e a s u r e d a t pH = 7.8 a n d Τ = 37o C, u s i n g a 5% P e n G s u b s t r a t e c o n c e n t r a t i o n . T i t r a t i o n w i t h 0.1 m o l a r NaOH h a s b e e n u s e d t o d e t e r m i n e t h e amount o f p r o d u c t f o r m a t i o n . The K^j v a l u e s o f f r e e a n d i m m o b i l i z e d c e l l s have been o b t a i n e d from e x a m p l e s i n F i g u r e 5. F o l l o w i n enzymes d u r i n g t h e p r o c e s s o f i m m o b i l i z a t i o n , t h e i n e q u a l i t y X £ < ^ m m o b i l . °lds. f o l l o w i n g approach has been developed f o r the determination o f X : i n a c e r t a i n experiment, i n a f i r s t ap­ proximation X - Ximm.; i . e . , 100% o f a l l i m m o b i l i z e d c e l l s a r e assumed t o b e a c t i v e . I n t h i s case, η 0.23 h a s b e e n d e t e r m i n e d . act ^mm. » become l a r g e r , due t o t h e d e c r e a s e o f t h e a C

n

a c t

a c t

β

I

f

x




n

c

c

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

n

466

BIOCHEMICAL

ENGINEERING

F i n a l l y , s u b s t r a t e i s added t o a c o n t i n u o u s r e a c t o r a t a mass f l o w r a t e d S , w h e r e S i s t h e c o n c e n t r a t i o n o f i n f l o w i n g s u b s t r a t e and d i s a d i l u t i o n r a t e e q u a l t o t h e r a t i o o f t h e v o l u m e t r i c i n f l o w r a t e t o t h e volume o f f l u i d i n t h e r e a c t o r . For a constant f l u i d volume, i n f l o w i n g s u b s t r a t e a l s o d i s p l a c e s s u b s t r a t e , b i o m a s s , a n d m e t a b o l i t e a t mass f l o w r a t e s e q u a l , r e s p e c t i v e l y , t o d S , dB - d B + d B , a n d dM. A t t h i s p o i n t , a l l t h e n e c e s s a r y mass c o n c e n t r a t i o n s a n d f l o w s h a v e b e e n d e f i n e d . The r e s u l t i n g r e a c t i o n mechanism i s s c h e m a t i z e d i n F i g u r e 1. The s o l i d l i n e s r e p r e s e n t t h e mass f l o w s , a n d t h e d a s h e d l i n e s show w h i c h c o n c e n t r a t i o n s i n f l u e n c e t h e i r r a t e s . A y i e l d c o e f f i c i e n t Y must be i n t r o d u c e d t o make t h e u n i t s o f S a n d M c o m p a t i b l e w i t h t h o s e o f B a n d Bn. E a c h u n i t o f S consumed i s assumed t o p r o d u c e Y u n i t s o f B. S i m i l a r ­ l y , each u n i t o f M excrete i unit Q

0

c

n

c

R a t e Laws The r a t e o f c h a n g e o f e a c h c o n c e n t r a t i o n shown i n F i g u r e 1 may be o b t a i n e d b y summing a l l i t s mass i n f l o w s a n d o u t f l o w s : dS/dt

•

0

dB /dt = B c

Also, equations

c

- (c - s ) S B

c

= sSB

dB / d t η dM/dt

(6)

= d ( S - S) - c S B / Y

Ξ S

c

c

+ uB

n

- (w + d ) B

- (u + w + d ) B

(8)

n

(9)

= e B / Y - dM.

= M

n

( 7 ) a n d ( 8 ) may be a d d e d t o g e t h e r

dB/dt

(7)

c

= Β

= cSB

c

to yield:

- (w + d ) B

(10)

The r a t e s o f b i o m a s s p r o d u c t i o n a n d m e t a b o l i t e e x c r e t i o n c a n be shown t o s a t u r a t e i n s u b s t r a t e c o n c e n t r a t i o n i f B i s assumed t o a d j u s t much more s l o w l y t o c h a n g e s i n S t h a n B d o e s . So, o n t h e t i m e s c a l e o f c h a n g e s i n B , B 2 0, a n d f r o m e q u a t i o n (8): c

n

c

Β where

η

Κ

Now, f r o m e q u a t i o n s

n

s SB /K C

= (u + w + d ) / s

(5) and

(Ha) (lib)

(11a):

B

c

Z

B K / ( K + S)

(12a)

B

n

ζ

B S / ( K + S)

(12b)

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

22.

QUINLAN

Thermochemical

467

Optimization

Figure 1. Reaction mechanism assumed to govern the rates of microbial biomass production and metabolite excretion in batch (a = 0) and continuous (a > 0) reactors. Symbols defined in text and in legend of symbols. B = B + B . C

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

n

468

BIOCHEMICAL

Substrate Depletion. S u b s t i t u t i o n o f equation (6) y i e l d s t h e f a m i l i a r c o n t i n u o u s - c u l t u r e e q u a t i o n d e p l e t i o n (17,18): S Ζ d ( S - S) - ^ ( B / Y j S / f K

(12a) i n t o for substrate

+ S)

Q

where

ENGINEERING

(13a)

y = cK m

(13b)

The s e c o n d t e r m i n e q u a t i o n (13a) r e p r e s e n t s t h e r a t e o f s u b s t r a t e consumption, o r n u t r i e n t uptake. I t s a t u r a t e s i n s u b s t r a t e con­ c e n t r a t i o n a c c o r d i n g t o a Monod r a t e l a w where b o t h Κ a n d y / Y a r e known t o v a r y w i t h t e m p e r a t u r e a n d d i l u t i o n r a t e ( 1 1 - 2 1 ) . m

Biomass P r o d u c t i o n . S i m i l a r l y , s u b s t i t u t i o n o f equation (12a) i n t o ( 1 0 ) y i e l d s t h l y used f o r continuous c u l t u r Β/Β

ζ

y S/(Κ + S) - (w + d) m

(14)

The f i r s t t e r m i n e q u a t i o n ( 1 4 ) , r e p r e s e n t i n g t h e g r o s s r a t e o f b i o m a s s p r o d u c t i o n , i s i d e n t i c a l w i t h t h e f u n c t i o n Monod ( 2 5 ) o r i g i n a l l y adopted " t o express c o n v e n i e n t l y t h e r e l a t i o n between e x p o n e n t i a l growth r a t e and c o n c e n t r a t i o n o f an e s s e n t i a l n u t r i e n t . Such a r e c t a n g u l a r h y p e r b o l i c f u n c t i o n h a s b e e n d e r i v e d many t i m e s f r o m v a r i o u s r e a c t i o n mechanisms ( 2 6 - 3 0 ) , b u t none h a s a d d r e s s e d the p r e s e n t case o f c o n t i n u o u s c u l t u r e systems where y and Κ have been o b s e r v e d t o v a r y w i t h temperature and d i l u t i o n r a t e . Now, t h r o u g h e q u a t i o n s ( l i b ) a n d ( 1 3 b ) , t h e t e m p e r a t u r e v a r i a t i o n o f y and Κ i s a t t r i b u t a b l e t o t h e m i c r o s c o p i c r a t e c o e f f i c i e n t s c,s,u,w, and t h e i r v a r i a t i o n w i t h d i l u t i o n r a t e i s e x p l i c i t . To e s t i m a t e t h e v a l u e s o f t h e m i c r o - c o e f f i c i e n t s c,s,u,w a s f u n c t i o n s o f t e m p e r a t u r e , e q u a t i o n ( 1 4 ) c a n be r e w r i t t e n a s m

m

Β/Β Ζ V ( S - S ) / ( S + K) B

where

V. Β

S

T

Ξ y

T

- (w + d)

(15a) (15b)

m = (c - s) Κ + u

(15c)

Ξ (w + d ) K / V

(15d)

B

E q u a t i o n (15a) r e p r e s e n t s a Monod r a t e l a w w i t h a t h r e s h o l d s u b ­ s t r a t e c o n c e n t r a t i o n S-j ( F i g u r e 2 ) . I t c a n be l i n e a r i z e d t o a generalized Eadie-Augustinsson equation (31-33): ν ζ V

B

- K(v/S) - V S ( 1 / S ) B

T

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

(16)

22.

QUINLAN

Thermochemical

τ

Optimization

1 GENERIC

1

469

1

1

1

MONOD RATE - SATURATION LAW

WITH THRESHOLD SUBSTRATE CONCENTRATION

I Ο

ι

10

ι

20

ι

30

ι

40

ι

50

S (ppm ELEMENT)

ι

60

I

70

Figure 2. Properties of the rate law for net biomass production in batch (a = 0) and continuous (d > 0) reactors. Symbols defined in text and in legend of symbols.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

470

BIOCHEMICAL

ENGINEERING

where ν i s t h e s p e c i f i c n e t b i o m a s s p r o d u c t i o n r a t e B/B m e a s u r e d i n the reactor a t p a r t i c u l a r values o f substrate concentration, t e m p e r a t u r e , and d i l u t i o n r a t e . A l i n e a r r e g r e s s i o n o f ν v e r s u s v/S and 1/S w i l l y i e l d v a l u e s f o r t h e m a c r o - c o e f f i c i e n t s V g , K, and S- a s f u n c t i o n s o f t e m p e r a t u r e and d i l u t i o n r a t e . The v a l u e s o f t h e m i c r o - c o e f f i c i e n t s a s f u n c t i o n s o f t e m p e r a t u r e c a n t h e n be e s t i m a t e d f r o m e q u a t i o n s ( l i b ) , ( 1 5 c ) , a n d (15d) a s s u m i n g c = s . Metabolite Excretion. S u b s t i t u t i o n o f e q u a t i o n (12b) i n t o (9) y i e l d s a p u r e Monod r a t e l a w f o r m e t a b o l i t e e x c r e t i o n : (M + dM)/(B/Y) Ζ V S / ( S + K)

(17a)

M

where Thermal

V = e m

(17b)

Sensitivity of

Temperature i n f l u e n c e s t h e m a c r o - c o e f f i c i e n t s (K,y ,Vg,V , S.j0 t h r o u g h t h e t e m p e r a t u r e d e p e n d e n c i e s o f t h e m i c r o - c o e f f i c i e n t s ( c , e , s , u , w ) . E a c h o f t h e m i c r o - c o e f f i c i e n t s i s assumed t o obey an A r r h e n i u s temperature l a w o f t h e form ( 3 4 ) : m

where

k

= A exp ( - E / R T )

k

= a positively-valued micro­ scopic rate c o e f f i c i e n t

A

= a positively-valued coefficient that i s p r a c t i c a l l y independent of temperature

A

m

(18)

K

E^ Ξ a p o s i t i v e l y - v a l u e d apparent a c t i v a t i o n energy ( c a l . mol ) l

Ξ t h e e a s c o n s t a n t (1.987 c a l . molK- )

R

Y

T

R

= degrees

1

Kelvin

W i t h i n t h e t e m p e r a t u r e r a n g e 0 - 50°C, e q u a t i o n ( 1 8 ) may be approximated as f o l l o w s ( 1 0 ) : k

ζ a exp (Τ/Θ )

α

Ξ A exp (-1.843 χ 1 0 *

Τ

= degrees

(19a)

α

3

E^)

(19b)

Celsius

θ „ Ξ 1.481 χ 1 0 / E α A 5

A

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

(19c)

22.

QUiNLAN

Thermochemical

Optimization

All

This approximation considerably s i m p l i f i e s the i n v e s t i g a t i o n of thermo-chemical r a t e - o p t i m i z a t i o n c o n d i t i o n s . To i l l u s t r a t e some i n t e r e s t i n g a s p e c t s o f t h e t h e r m a l s e n ­ s i t i v i t y o f the m a c r o - e f f i c i e n t s , s p e c i f i c temperature depend­ e n c i e s w e r e assumed f o r t h e f i v e m i c r o - c o e f f i c i e n t s . The assumed d e p e n d e n c i e s a r e shown i n F i g u r e 3. The p a r a m e t e r v a l u e s w e r e c h o s e n so i n b a t c h c u l t u r e (d = 0) a l l f i v e m a c r o - c o e f f i c i e n t s w o u l d a l w a y s r i s e w i t h t e m p e r a t u r e ( F i g u r e s 4-6) and Κ w o u l d r i s e more r a p i d l y w i t h t e m p e r a t u r e t h a n Vg and i n the tempera­ t u r e r a n g e 20-30°C. T h i s t h e r m a l s e n s i t i v i t y p a t t e r n i s o f t e n seen i n b a t c h c u l t u r e (e.g., 11-14). H a l f - S a t u r a t i o n C o e f f i c i e n t K. ( l i b ) reduces t o :

For batch c u l t u r e , e q u a t i o n

K| I f s r i s e s more r a p i d l y w i t h t e m p e r a t u r e t h a n b o t h n u m e r a t o r t e r m s , then the b a t c h - c u l t u r e h a l f - s a t u r a t i o n c o e f f i c i e n t should always d e c r e a s e as t e m p e r a t u r e i n c r e a s e s . I f s r i s e s more r a p i d l y t h a n t h e n u m e r a t o r t e r m d o m i n a n t a t l o w t e m p e r a t u r e s b u t more s l o w l y t h a n t h e t e r m d o m i n a n t a t h i g h t e m p e r a t u r e s , i t s h o u l d show a t e m p e r a t u r e minimum. I f s r i s e s more s l o w l y t h a n b o t h n u m e r a t o r t e r m s ( F i g u r e 3 ) , i t s h o u l d a l w a y s r i s e w i t h t e m p e r a t u r e ( F i g u r e 4, d = 0) The t h e r m a l s e n s i t i v i t i e s o f t h e b a t c h - c u l t u r e h a l f - s a t u r a t i o n c o e f f i c i e n t s f o r s e v e r a l m i c r o b i a l p r o c e s s e s (11-14) h a v e b e e n observed to resemble the l i n e a r p o r t i o n o f the d = 0 curve i n F i g u r e 4. However, a few d e v i a t i o n s f r o m t h i s p a t t e r n h a v e b e e n s e e n where t h e h a l f - s a t u r a t i o n c o e f f i c i e n t s showed e i t h e r a n e g a t i v e s l o p e o r a maximum ( 1 3 ) . O n l y t h e t h e r m a l maximum i s i n c o n s i s t e n t w i t h e q u a t i o n s (18) - ( 2 0 ) . For continuous c u l t u r e , K

|d > ο -

K

|d = ο

+

(

1

/

s

)

d

( 2 1 )

According to equation (21), the continuous-culture h a l f - s a t u r a t i o n c o e f f i c i e n t equals the b a t c h - c u l t u r e h a l f - s a t u r a t i o n c o e f f i c i e n t augmented by a t e r m t h a t i n c r e a s e s l i n e a r l y w i t h d i l u t i o n r a t e . However, t h e m a g n i t u d e o f t h i s t e r m s h o u l d d e c r e a s e e x p o n e n t i a l l y w i t h i n c r e a s i n g t e m p e r a t u r e b e c a u s e o f t h e f a c t o r 1/s. Thus, a t l o w t e m p e r a t u r e s where t h e d i l u t i o n t e r m may d o m i n a t e t h e b a t c h c u l t u r e h a l f - s a t u r a t i o n c o e f f i c i e n t , the continuous-culture h a l f s a t u r a t i o n c o e f f i c i e n t may d e c l i n e w i t h i n c r e a s i n g t e m p e r a t u r e . I t s h o u l d grow w i t h t e m p e r a t u r e o n l y when t h e b a t c h - c u l t u r e h a l f s a t u r a t i o n c o e f f i c i e n t has a p o s i t i v e s l o p e and d o m i n a t e s t h e d i l u t i o n term. I n t h i s c a s e , i t may h a v e a t h e r m a l minimum ( F i g u r e 4, d > 0 ) . M o r e o v e r , f o r t h e r a n g e o f d i l u t i o n r a t e s where t h e l o c u s o f m i n i m a ( d a s h e d l i n e , F i g u r e 4) p a r a l l e l s t h e

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

472

BIOCHEMICAL

ENGINEERING

Figure 3. Temperature dependencies assumed for the five microscopic rate coefficients defined in Figure 1. The microcoefficients c and s have units (ppm element Khr' , e, u, and w have units Khr'K 1

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

QUINLAN

Thermochemical

473

Optimization

1

4

1 1 1 1 1 1— VARIATION OF HALF - SATURATION COE FFICIENT WITH TEMPERATURE AND DILUTION RATE

3

~d « 100 Khr -ι

LU

/

/ ΙΟ « 5 0

/

1

Lu

_J LU

«25/ -Ο "

ε CL CL

/

/ /

/

BATCH /

d «Ο­ u

• w*d

w « 0.5 exp(T/5.l) u « 10

exp(T/l6.9)

s « 5 0 exp (T/20) I

10

I

I

20

I

30

L

40

TTC) Figure 4. Theoretical thermal sensitivity of the half-saturation coefficient in batch (a = 0) and continuous (a > 0) culture with the parameter values specified in Figure 3. Dashed line, locus of thermal minima ( O).

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

474

BIOCHEMICAL

ENGINEERING

d - 0 curve, the temperature t h a t minimizes the h a l f - s a t u r a t i o n c o e f f i c i e n t r i s e s l i n e a r l y w i t h the l o g a r i t h m o f t h e d i l u t i o n rate. In c o n t i n u o u s c u l t u r e , t h e h a l f - s a t u r a t i o n c o e f f i c i e n t has b e e n o b s e r v e d t o r e s p o n d t o r i s i n g t e m p e r a t u r e s by d e c l i n i n g m o n o t o n i c a l l y (15-17) and by s h o w i n g a minimum ( 1 8 , 1 9 ) . B o t h c a s e s a r e c o n s i s t e n t w i t h t h e d > 0 c u r v e s i n F i g u r e 4. In c o n t r a s t , experiments p r o b i n g i t s response t o r i s i n g d i l u t i o n r a t e s h a v e n ' t shown c l e a r - c u t t r e n d s b e c a u s e o f e x t r e m e ­ l y l a r g e measurement u n c e r t a i n t i e s ( 2 0 , 2 1 ) . I n one i n s t a n c e , no t r e n d c o u l d be d e t e c t e d ( 2 0 ) . I n a n o t h e r , t h e mean v a l u e s showed a maximum, b u t l i n e a r and s a t u r a t i o n c u r v e s c o u l d a l s o be drawn through the + o n e - s t a n d a r d - d e v i a t i o n u n c e r t a i n t y ranges f o r each mean v a l u e ( 2 1 ) . B e t t e r d a t a a r e c l e a r l y needed t o t e s t t h e l i n e a r d e p e n d e n c e on d i l u t i o predicted b equation ( l i b ) and 2 1 ) . M a x i m u m - S p e c i f i c - G r o w t h - R a t e C o e f f i c i e n t V^. e q u a t i o n s ( l i b ) and (13b) c o m b i n e t o y i e l d : w

«|d

= 0

=

c u / s

+

In batch c u l t u r e ,

c w / s

( 2 2 )

The b a t c h - c u l t u r e m a x i m u m - s p e c i f i c - g r o w t h - r a t e c o e f f i c i e n t s h o u l d f a l l w i t h i n c r e a s i n g t e m p e r a t u r e i f s r i s e s more r a p i d l y t h a n b o t h c u and cw. I t s h o u l d show a minimum i f s r i s e s more r a p i d l y t h a n the n u m e r a t o r o f t h e t e r m d o m i n a n t a t l o w t e m p e r a t u r e s b u t l e s s r a p i d l y than the o t h e r term. I t should always i n c r e a s e i f s r i s e s l e s s r a p i d l y t h a n t h e n u m e r a t o r s o f b o t h t e r m s . When c = s , i t a l s o s h o u l d a l w a y s i n c r e a s e ( F i g u r e 5, d = 0 ) . The d a t a (11-14) a v a i l a b l e t o t e s t t h e p r e d i c t e d t h e r m a l s e n ­ s i t i v i t y of the b a t c h - c u l t u r e maximum-specific-growth-rate co­ e f f i c i e n t were o b t a i n e d from s u b s t r a t e consumption e x p e r i m e n t s . From e q u a t i o n ( 1 3 a ) , t h e m a x i m u m - v e l o c i t y c o e f f i c i e n t f o r s u b ­ s t r a t e c o n s u m p t i o n i s V^/Y. D a t a p r e s e n t e d i n t h i s form must be m u l t i p l i e d by a y i e l d c o e f f i c i e n t Y t o c o n v e r t t o y « I f the y i e l d c o e f f i c i e n t i s assumed t o be p r a c t i c a l l y c o n s t a n t , t h e n y / Y s h o u l d show t h e same t h e r m a l s e n s i t i v i t y p a t t e r n as y . The t h e r m a l s e n s i t i v i t y o f y / Y i n b a t c h c u l t u r e i s w e l l d e s c r i b e d by t h e l i n e a r p o r t i o n o f t h e d = 0 c u r v e i n F i g u r e 5, and s o i s t h a t o f y as l o n g as Y i s n e a r l y c o n s t a n t . In continuous c u l t u r e , the maximum-specific-growth-rate co­ e f f i c i e n t i s a c c o r d i n g t o e q u a t i o n s ( l i b ) , ( 1 3 b ) , and ( 2 2 ) : m

m

m

m

m

\|d

> ο • "Jd = ο

+

(

c

/

8

)

d

( 2 3 )

The c o n t i n u o u s - c u l t u r e y s h o u l d i n c r e a s e l i n e a r l y w i t h d i l u t i o n r a t e , and t h e i n f l u e n c e o f t h e d i l u t i o n t e r m s h o u l d grow w i t h r i s i n g t e m p e r a t u r e i f s r i s e s more s l o w l y t h a n c . I f c = s , t h e c o n t i n u o u s - c u l t u r e y should a s y m p t o t i c a l l y approach the d i l u t i o n m

m

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

22.

QUINLAN

Thermochemical

0

475

Optimization

10

20

30

40

T(°C) Figure 5. Theoretical thermal sensitivity of the maximum specific growth-rate coefficient in batch (d = 0) and continuous (d > 0) culture with the parameter values specified in Figure 3.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

476

BIOCHEMICAL

ENGINEERING

r a t e a s t e m p e r a t u r e f a l l s and t h e b a t c h c u l t u r e p a s t e m p e r a t u r e r i s e s ( F i g u r e 5, d > 0 ) . The l i n e a r p o r t i o n s o f t h e d > 0 c u r v e s i n F i g u r e 5 r e s e m b l e the t h e r m a l s e n s i t i v i t i e s o b s e r v e d f o r y (17,18) and y / Y (15,16, 19) i n c o n t i n u o u s c u l t u r e . M o r e o v e r , i n agreement w i t h e q u a t i o n (23) y / Y has b e e n o b s e r v e d t o i n c r e a s e l i n e a r l y w i t h d i l u t i o n r a t e ( 2 0 ) . I t has a l s o b e e n s e e n t o d e c r e a s e s l i g h t l y w i t h i n ­ c r e a s i n g d i l u t i o n r a t e (21), which d i s a g r e e s w i t h equation (23). m

m

m

m

M a x i m u m - V e l o c i t y C o e f f i c i e n t s Vft V^. According to equations ( l i b ) and ( 1 5 c ) , t h e m a x i m u m - v e l o c i t y c o e f f i c i e n t f o r b i o m a s s p r o ­ d u c t i o n depends on t h e m i c r o s c o p i c r a t e c o e f f i c i e n t s a s f o l l o w s : t

V

B

= (1/s) [ ( c - s) w + cu] + [ ( c - s ) / s ] d

(24)

In g e n e r a l , depending e s p e c i a l l t h i s m a x i m u m - v e l o c i t y c o e f f i c i e n t may v a r y i n a c o m p l i c a t e d f a s h i o n w i t h b o t h t e m p e r a t u r e and d i l u t i o n r a t e . However, a s c a p p r o a c h e s s i n v a l u e , the i n f l u e n c e o f a l l the m i c r o - c o e f f i c i e n t s but u v a n i s h e s , and i n t h e l i m i t o f c = s , V

B

= u

(25)

In t h i s s p e c i a l case o n l y , the maximum-velocity c o e f f i c i e n t f o r b i o m a s s p r o d u c t i o n w o u l d show t h e same e x p o n e n t i a l t e m p e r a t u r e dependence i n c o n t i n u o u s c u l t u r e as i t does i n b a t c h c u l t u r e . The m a x i m u m - v e l o c i t y c o e f f i c i e n t f o r m e t a b o l i t e e x c r e t i o n a s g i v e n by e q u a t i o n (17b) i s i d e n t i c a l l y e q u a l t o e. As a r e s u l t , i t should g e n e r a l l y r i s e e x p o n e n t i a l l y w i t h temperature and be i n s e n s i t i v e t o d i l u t i o n r a t e . Thus, the maximum-velocity c o e f f i c i e n t f o r metabolite excretion i n batch culture should a l s o be i d e n t i c a l t o t h a t s e e n i n c o n t i n u o u s c u l t u r e . No t h e r m a l s e n s i t i v i t y d a t a c o u l d be f o u n d f o r Vg o r So, t h e v a l i d i t y o f e q u a t i o n s ( 1 7 b ) , ( 2 4 ) , and (25) a w a i t s t e s t ­ ing. T h r e s h o l d C o e f f i c i e n t S T * F o r b a t c h c u l t u r e and t h e s p e c i a l case c = s, the t h e r m a l s e n s i t i v i t y o f t h e t h r e s h o l d c o e f f i c i e n t i s d e t e r m i n e d a s f o l l o w s by e q u a t i o n s ( 1 5 d ) , ( 2 0 ) , and ( 2 5 ) : S | T

d

m

0

=

(w/s) +

(w/u)

(w/s)

(26)

A t t e m p e r a t u r e s where u d o m i n a t e s w, t h e b a t c h - c u l t u r e t h r e s h o l d c o e f f i c i e n t should f a l l e x p o n e n t i a l l y w i t h temperature i f s r i s e s more r a p i d l y w i t h t e m p e r a t u r e t h a n w. A t t e m p e r a t u r e s where w d o m i n a t e s u, i t s h o u l d a l s o f a l l e x p o n e n t i a l l y w i t h r i s i n g tem­ p e r a t u r e i f s u r i s e s more r a p i d l y t h a n w . I f b o t h terms d e ­ c r e a s e as t e m p e r a t u r e r i s e s , i t s h o u l d a l w a y s d i m i n i s h as tem­ perature r i s e s . I f the term dominant a t low temperatures f a l l s 2

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

22.

Thermochemical

QUINLAN

477

Optimization

w i t h r i s i n g temperature and t h e o t h e r term i n c r e a s e s , i t s h o u l d h a v e a t h e r m a l minimum. I f b o t h t e r m s r i s e w i t h t e m p e r a t u r e , i t s h o u l d a l w a y s r i s e w i t h t e m p e r a t u r e ( F i g u r e 6, d = 0 ) . None o f t h e b a t c h - c u l t u r e t h e r m a l s e n s i t i v i t y e x p e r i m e n t s r e p o r t e d any v a l u e s f o r S^, s o t h e v a l i d i t y o f e q u a t i o n (26) a n d t h e d = 0 c u r v e i n F i g u r e 6 c a n ' t be j u d g e d now. For c o n t i n u o u s c u l t u r e and t h e s p e c i a l c a s e c = s , e q u a t i o n s ( l i b ) , ( 1 5 d ) , and (26) d e t e r m i n e t h e t h e r m a l s e n s i t i v i t y o f t h e t h r e s h o l d c o e f f i c i e n t as f o l l o w s : S | T

d

>

0

- S | T

d

m

0

+ (1/s) [ 1 + 2

(w/u)] d + ( l / s u ) d

2

(27)

According to equation (27), the continuous-culture threshold co­ e f f i c i e n t i s a q u a d r a t i c f u n c t i o n o f d i l u t i o n r a t e when c = s ; however, t h e magnitude o t i a l l y w i t h r i s i n g temperatur l i n e a r t e r m w i l l v a n i s h t o o i f s u r i s e s more r a p i d l y w i t h tem­ p e r a t u r e than w does. The c o n t i n u o u s - c u l t u r e t h r e s h o l d c o ­ e f f i c i e n t s h o u l d i n c r e a s e when t h e b a t c h c u l t u r e t h r e s h o l d c o e f f i c i e n t r i s e s w i t h temperature and dominates t h e d i l u t i o n terms. I t s h o u l d have a t h e r m a l minimum i f a d e c l i n i n g t e r m d o m i n a t e s a t l o w t e m p e r a t u r e and a n i n c r e a s i n g t e r m d o m i n a t e s a t h i g h t e m p e r a t u r e ( F i g u r e 6, d > 0)· The t e m p e r a t u r e a t w h i c h t h i s minimum o c c u r s r i s e s a l m o s t l i n e a r l y w i t h t h e l o g ­ a r i t h m o f t h e d i l u t i o n r a t e as l o n g as t h e l o c u s o f minima ( d a s h e d l i n e , F i g u r e 6) p a r a l l e l s t h e d = 0 c u r v e . In continuous r e a c t o r s , the t h r e s h o l d c o e f f i c i e n t i s i d e n t i ­ c a l w i t h the steady s t a t e substrate c o n c e n t r a t i o n (17,18). For i n c r e a s i n g t e m p e r a t u r e s , i t has b e e n o b s e r v e d t o f a l l (17,18) and show a minimum ( 1 8 ) . T h e s e r e s p o n s e s a r e c o n s i s t e n t w i t h the d > 0 c u r v e s shown i n F i g u r e 6. I t h a s a l s o b e e n o b s e r v e d to i n c r e a s e n o n l i n e a r l y w i t h d i l u t i o n r a t e u n t i l w a s h o u t o c c u r r e d (17,18). I n b o t h i n s t a n c e s , t h e s l o p e a t low d i l u t i o n r a t e s de­ c r e a s e d w i t h r i s i n g t e m p e r a t u r e . The o b s e r v e d r e s p o n s e s t o i n ­ creasing d i l u t i o n rate are also consistent with equation (27). A t t h i s p o i n t , i t w o u l d a p p e a r t h a t one c a n a c c o u n t f o r most of t h e observed e f f e c t s o f temperature and d i l u t i o n r a t e on t h e m a c r o - c o e f f i c i e n t s by s i m p l y a s s u m i n g t e m p e r a t u r e d e p e n d e n c i e s s u c h a s t h o s e shown i n F i g u r e 3 f o r t h e m i c r o - c o e f f i c i e n t s i n e q u a t i o n s (20) - ( 2 7 ) . These e q u a t i o n s w i t h t h e parameter v a l u e s s p e c i f i e d i n F i g u r e 3 w i l l now be u s e d t o a n a l y z e t h e t h e r m a l s e n s i t i v i t y o f t h e n e t b i o m a s s p r o d u c t i o n and m e t a b o l i t e e x c r e t i o n rates. Thermal

S e n s i t i v i t y o f Process Rates

R a t e I s o t h e r m s . D e p e n d i n g on s u b s t r a t e c o n c e n t r a t i o n , t h r e e t h e r m a l s e n s i t i v i t y p a t t e r n s may be s e e n i n b o t h b a t c h a n d c o n ­ t i n u o u s r e a c t o r s when t h e n e t b i o m a s s p r o d u c t i o n r a t e ( a s s p e c i f i e d by e q u a t i o n s ( l i b ) and ( 1 5 ) and F i g u r e s 3, 4, and 6) i s p l o t t e d

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL ENGINEERING

478

1

1

1 1 1 1 1 VARIATION OF T H R E S H O L D S U B S T R A T E CONCENTRATION WITH _ T E M P E R A T U R E AND DILUTION R A T E _

T(°C) Figure 6. Theoretical thermal sensitivity of the threshold coefficient in batch (à = 0) and continuous (à > 0) culture with the parameter values specified in Figure 3. Dashed line, locus of thermal minima (O).

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

22.

QUiNLAN

Thermochemical

Optimization

479

v e r s u s s u b s t r a t e c o n c e n t r a t i o n w i t h t e m p e r a t u r e as a p a r a m e t e r ( F i g u r e 7 ) . A t l o w s u b s t r a t e c o n c e n t r a t i o n s (S < 1 . 2 ) , t h e r a t e d i m i n i s h e s a s t e m p e r a t u r e r i s e s and h e n c e shows a n e g a t i v e t h e r m a l s e n s i t i v i t y ; w h e r e a s , a t h i g h s u b s t r a t e c o n c e n t r a t i o n s (S > 4·4), t h e r a t e i n c r e a s e s w i t h t e m p e r a t u r e and t h u s has a p o s i t i v e t h e r m a l sensitivity. A t i n t e r m e d i a t e s u b s t r a t e c o n c e n t r a t i o n s (1.2 < S < 4 . 4 ) , t h e r a t e f i r s t r i s e s and t h e n f a l l s w i t h i n c r e a s i n g tem­ perature. I n o t h e r words, a t moderate s u b s t r a t e c o n c e n t r a t i o n s , the thermal s e n s i t i v i t y s w i t c h e s s i g n from p o s i t i v e to n e g a t i v e , w h i c h means t h e r a t e goes t h r o u g h a maximum a s t e m p e r a t u r e r i s e s . M o r e o v e r , t h e maximum r a t e i s d e t e r m i n e d by a h i g h e r t e m p e r a t u r e i s o t h e r m a s s u b s t r a t e c o n c e n t r a t i o n i n c r e a s e s . As a c o n s e q u e n c e , t h e optimum t e m p e r a t u r e s h o u l d r i s e when s u b s t r a t e c o n c e n t r a t i o n increases. The r a t e i s o t h e r m s f o m e t a b o l i t excretio (a s p e c i f i e d b e q u a t i o n s ( l i b ) and (17 thermal s e n s i t i v i t y pattern isotherms. T h u s , t h e r a t e o f m e t a b o l i t e e x c r e t i o n may a l s o h a v e an optimum t e m p e r a t u r e t h a t s h i f t s t o h i g h e r v a l u e s a s s u b s t r a t e concentration r i s e s . Rate I s o c o n c e n t r a t e s . The i n c r e a s e o f optimum t e m p e r a t u r e w i t h i n c r e a s i n g s u b s t r a t e c o n c e n t r a t i o n i s p l a i n l y s e e n by p l o t t i n g r a t e v e r s u s t e m p e r a t u r e w i t h s u b s t r a t e c o n c e n t r a t i o n as a p a r a ­ m e t e r ( F i g u r e s 8 and 9 ) . The f a m i l i e s o f r a t e i s o c o n c e n t r a t e s f o r n e t b i o m a s s p r o d u c t i o n and m e t a b o l i t e e x c r e t i o n a l s o a p p e a r qualitatively similar. However, t h e maxima o f c o r r e s p o n d i n g i s o ­ concentrates occur at q u i t e d i f f e r e n t temperatures. For example, when S = 1 ppm, t h e optimum t e m p e r a t u r e f o r t h e n e t b i o m a s s p r o ­ d u c t i o n r a t e w o u l d be a b o u t 16°C ( F i g u r e 8) and t h a t f o r t h e m e t a b o l i t e e x c r e t i o n r a t e w o u l d be a b o u t 28°C ( F i g u r e 9 ) . Note t h a t i f the o p e r a t i n g t e m p e r a t u r e o f t h e r e a c t o r were s e t a t t h e optimum t e m p e r a t u r e f o r t h e m e t a b o l i t e e x c r e t i o n r a t e , t h e n e t b i o m a s s p r o d u c t i o n r a t e w o u l d be s e v e r e l y s u b o p t i m a l ( F i g u r e 8 ) . But i f i t were s e t a t t h e optimum t e m p e r a t u r e f o r t h e n e t b i o m a s s p r o d u c t i o n r a t e , t h e m e t a b o l i t e e x c r e t i o n r a t e w o u l d be o n l y s l i g h t l y suboptimal (Figure 9). S h i f t o f Optimum T e m p e r a t u r e . F i g u r e 10 shows how t h e tem­ p e r a t u r e t h a t maximizes the r a t e o f each process v a r i e s w i t h b o t h s u b s t r a t e c o n c e n t r a t i o n and d i l u t i o n r a t e . I n t h i s regard, the t h e r m a l s e n s i t i v i t i e s o f t h e two p r o c e s s e s d i f f e r s u b s t a n t i a l l y . The optimum o p e r a t i n g t e m p e r a t u r e f o r t h e n e t b i o m a s s p r o ­ d u c t i o n r a t e i s n e a r l y i n s e n s i t i v e t o d i l u t i o n r a t e , but i n ­ creases almost l i n e a r l y w i t h the l o g a r i t h m of s u b s t r a t e con­ c e n t r a t i o n when t h i s c o n c e n t r a t i o n e x c e e d s t h e minimum v a l u e of the t h r e s h o l d c o e f f i c i e n t ( F i g u r e 6 ) . I n c o n t r a s t , t h e optimum o p e r a t i n g t e m p e r a t u r e f o r t h e m e t a b o l i t e e x c r e t i o n r a t e i s s t r o n g l y a f f e c t e d by b o t h d i l u t i o n r a t e and s u b s t r a t e c o n c e n t r a t i o n . As s u b s t r a t e c o n c e n t r a t i o n

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

480

BIOCHEMICAL

1

1 NET

1

1

1

ENGINEERING

Γ

BIOMASS PRODUCTION

S (ppm ELEMENT) Figure 7. Predicted influence of substrate concentration on the rate of net biomass production, with temperature as a parameter. Parameter values correspond to Figures 3-6. Note shift of optimum temperature to higher values with increasing substrate concentration.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

22.

QUiNLAN

Thermochemical

τ

1

481

Optimization

1

NET BIOMASS THEORETICAL RATE

1

τ—

PRODUCTION ISOCONCENTRATES

Τ CO Figure 8. Predicted influence of temperature on the rate of net biomass production with substrate concentration as a parameter. Parameter values correspond to Figures 3-7. Dashed line, locus of thermal rate maxima (O). Note shift of optimum temperature to higher values as substrate concentration rises.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

482

BIOCHEMICAL

ENGINEERING

— ι

1 1 1 1 1 1 METABOLITE EXCRETION T H E O R E T I C A L RATE ISOCONCENTRATES CONTINUOUS CULTURE ! d = 2 5 Khr" 1

0.5

M • dM (B/Y) (Khr ) 1

0.1

0.05 S

s

0 . 0 2 5 ppm ELEMENT!

0.02

0.01

Figure 9. Predicted influence of temperature on the rate of metabolite excretion with substrate concentration as a parameter. Solid lines, curves generated from Equations lib and 17 with the parameter values given in Figures 3 and 4. Dashed line, locus of thermal rate maxima (O).

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

QUINLAN

Thermochemical

Optimization

483

Figure 10. Predicted influence of substrate concentration and dilution rate on the temperature that maximizes the rates of net biomass production and metabolite excretion in batch (a = 0) and continuous (a > 0) culture.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

484

BIOCHEMICAL

ENGINEERING

becomes v e r y l o w , t h e optimum t e m p e r a t u r e a s y m p t o t i c a l l y a p p r o a c h ­ es a minimum v a l u e c h a r a c t e r i s t i c o f e a c h d i l u t i o n r a t e . The minimum optimum t e m p e r a t u r e i s t h e t e m p e r a t u r e a t w h i c h t h e s l o p e o f t h e h a l f - s a t u r a t i o n c o e f f i c i e n t ( F i g u r e 4) e q u a l s t h a t o f t h e maximum-velocity c o e f f i c i e n t , namely, the m i c r o s c o p i c e x c r e t i o n r a t e c o e f f i c i e n t e. As s u b s t r a t e c o n c e n t r a t i o n i n c r e a s e s , t h e i n f l u e n c e o f t h e d i l u t i o n r a t e p r o g r e s s i v e l y d i m i n i s h e s , and t h e optimum t e m p e r a t u r e c u r v e s c o n v e r g e . A t h i g h s u b s t r a t e c o n ­ c e n t r a t i o n s , t h e optimum t e m p e r a t u r e i n c r e a s e s a l m o s t l i n e a r l y w i t h the logarithm of substrate concentration. Thermo-Chemical O p t i m i z a t i o n o f P r o c e s s Rates A t t h i s p o i n t , t h e g o a l o f t h i s p a p e r has b e e n a c h i e v e d . The two f a m i l i e s o f c u r v e s shown i n F i g u r e 10 c o n s t i t u t e t h e r m o chemical rate-optimizatio ture, substrate concentration o f t h e s e t h r e e v a r i a b l e s a r e f i x e d , e a c h f a m i l y s p e c i f i e s what v a l u e t h e t h i r d must h a v e t o m a x i m i z e i t s r a t e . The s e p a r a t i o n o f t h e two f a m i l i e s means t h a t b o t h r a t e s c a n n o t be s i m u l t a n e ­ o u s l y maximized. As a r e s u l t , an o p t i m i z a t i o n s t r a t e g y may be n e e d e d , s u c h a s o p e r a t i n g a t t h e optimum t e m p e r a t u r e o f t h e p r o c e s s whose r a t e i s most s e n s i t i v e t o t e m p e r a t u r e . Summary and C o n c l u s i o n s T h i s p a p e r showed how c h a n g e s i n s u b s t r a t e c o n c e n t r a t i o n and d i l u t i o n r a t e may s h i f t t h e optimum t e m p e r a t u r e o f m i c r o b i a l p r o c e s s e s whose r a t e s s a t u r a t e i n s u b s t r a t e c o n c e n t r a t i o n a c c o r d ­ i n g t o Monod r a t e l a w s . The optimum t e m p e r a t u r e s h i f t was a t t r i b u ­ t e d t o t h e e f f e c t s o f t e m p e r a t u r e and d i l u t i o n r a t e on t h e m a c r o c o e f f i c i e n t s i n t h e Monod r a t e l a w s . E q u a t i o n s d e s c r i b i n g t h e s e e f f e c t s were d e r i v e d from a s u i t a b l y m o d i f i e d M i c h a e l i s - M e n t e n r e a c t i o n mechanism. W i t h o n l y a few e x c e p t i o n s , t h e s e e q u a t i o n s a g r e e d w i t h p u b l i s h e d d a t a when A r r h e n i u s t e m p e r a t u r e d e p e n d e n c i e s were assumed f o r t h e m i c r o - c o e f f i c i e n t s i n t h e r e a c t i o n mechanism. As a c o n s e q u e n c e , t h e s e e q u a t i o n s and t h e optimum t e m p e r a t u r e c u r v e s may be c o n s i d e r e d a s p l a u s i b l e , e x p e r i m e n t a l l y t e s t a b l e hypotheses. They d e s e r v e c a r e f u l q u a n t i t a t i v e t e s t i n g b e c a u s e t h e y p r o m i s e t o u n i f y h e r e t o f o r e f r a g m e n t a r y and s e e m i n g l y c o n ­ t r a d i c t o r y b a t c h and c o n t i n u o u s c u l t u r e d a t a . S u c h u n i f i c a t i o n i s needed t o d e v e l o p a r a t i o n a l m e t h o d o l o g y f o r o p t i m i z i n g t h e d e s i g n and o p e r a t i o n o f b i o l o g i c a l r e a c t o r s i n w h i c h s u b s t r a t e c o n c e n t r a t i o n , t e m p e r a t u r e , and d i l u t i o n r a t e a r e e c o n o m i c a l l y important v a r i a b l e s .

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

22.

QUiNLAN

Thermochemical

Optimization

485

Legend o f Symbols A

=

pre-exponential f a c t o r i n Arrhenius temperature law; same u n i t s a s k.

Β

Ξ

t o t a l b i o m a s s c o n c e n t r a t i o n i n r e a c t o r ; e q u a l s sum o f B p l u s B ; mg d r y w e i g h t p e r l i t e r . c

n

B

c

=

biomass c o n c e n t r a t i o n a s s o c i a t e d w i t h s u b s t r a t e con­ s u m p t i o n s i t e s c a p a b l e o f c o n s u m i n g s u b s t r a t e ; mg dry weight per l i t e r .

B

n

=

biomass c o n c e n t r a t i o n a s s o c i a t e d w i t h s u b s t r a t e con­ sumption s i t e s n o t c a p a b l e o f consuming s u b s t r a t e ; mg d r y w e i g h t p e liter

Ξ

t o t a l concentratio consumptio i n m i c r o b i a l p o p u l a t i o n ; e q u a l s sum o f C p l u s C^; number o f s i t e s p e r l i t e r .

C

c

C

c

=

c o n c e n t r a t i o n o f s u b s t r a t e consumption s i t e s capable o f consuming s u b s t r a t e ; number o f s i t e s p e r l i t e r .

C

n

=

c o n c e n t r a t i o n o f s u b s t r a t e consumption s i t e s n o t c a p a b l e o f c o n s u m i n g s u b s t r a t e ; number o f s i t e s per l i t e r .

=

c o n c e n t r a t i o n o f f r e e enzyme.

=

apparent a c t i v a t i o n

Ε

energy;

cal./mol.

ES =

concentration o f enzyme-substrate

Κ

half-saturation coefficient;

=

complex.

same u n i t s a s S.

KJJJ Ξ

the Michaelis-Menten half-saturation

Μ

Ξ

concentration of metabolite of interest;

Ν

Ξ

c o n c e n t r a t i o n o f m i c r o o r g a n i s m s i n r e a c t o r ; number o f organisms per l i t e r .

Ρ

=

concentration of product(s).

R

Ξ

g a s c o n s t a n t = 1.987 c a l . m o l "

S

=

s u b s t r a t e c o n c e n t r a t i o n i n r e a c t o r ; ppm o f a n e l e m e n t .

=

i n l e t s u b s t r a t e c o n c e n t r a t i o n ; same u n i t s a s S.

S

Q

1

coefficient. same u n i t s a s S.

1

Κ" .

C o n t i n u e d on n e x t page

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

ENGINEERING

threshold c o e f f i c i e n t ; steady-state substrate concentra­ t i o n t h a t must be e x c e e d e d f o r a p o s i t i v e n e t b i o m a s s p r o d u c t i o n r a t e ; same u n i t s a s S. t e m p e r a t u r e ; °C. t e m p e r a t u r e ; °K. maximum p o s s i b l e s p e c i f i c r a t e o f n e t b i o m a s s p r o d u c t i o n i n the reactor; time" (e.g., K h r " ) . 1

1

maximum p o s s i b l e r a t e o f g r o s s m e t a b o l i t e time" (e.g., K h r " ) . 1

formation;

1

y i e l d c o e f f i c i e n t ; ppm d r y w e i g h t p r o d u c e d p e r ppm e l e m e n t consumed microscopic substrate-consumption (ppm e l e m e n t ) " time" . 1

rate

coefficient;

1

d i l u t i o n r a t e (flow/volume); r a t e a t which s u b s t r a t e , b i o m a s s , and m e t a b o l i t e d i s p l a c e d f r o m c u l t u r e v e s s e l ; time" . 1

microscopic metabolite-excretion rate c o e f f i c i e n t ;

g e n e r i c m i c r o s c o p i c r a t e c o e f f i c i e n t , e.g., c,f,s,u,w. microscopic rate coefficient s u b s t r a t e complex.

f o r f o r m a t i o n o f enzyme-

microscopic rate coefficient enzyme-substrate complex.

f o r d i s a s s o c i a t i o n of

microscopic rate coefficient

f o r formation of product.

number o f s u b s t r a t e m o l e c u l e s needed t o f i l l consumption s i t e .

a substrate

microscopic substrate-saturation rate coefficient; (ppm e l e m e n t ) " time" . 1

1

m i c r o s c o p i c u n s a t u r a t i o n r a t e c o e f f i c i e n t ; t i m e *. m i c r o s c o p i c wastage r a t e c o e f f i c i e n t ;

1

time" .

value of generic microscopic rate c o e f f i c i e n t same u n i t s a s k.

a t 0°C;

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

1

time" .

22.

QUiNLAN

Thermochemical

Optimization

487

3

=

a v e r a g e b i o m a s s p e r m i c r o o r g a n i s m ; mg d r y w e i g h t p e r organism.

Ύ

=

a v e r a g e number o f s u b s t r a t e c o n s u m p t i o n s i t e s p e r o r g a n i s m ; number o f s i t e s p e r o r g a n i s m .

PJJJ =

maximum s p e c i f i c g r o w t h r a t e c o e f f i c i e n t ; t i m e " " .

θ

r e t a r d a t i o n t e m p e r a t u r e ; °C.

=

1

Acknowledgments The r e s e a r c h r e p o r t e d i n t h i s p a p e r was s u p p o r t e d i n p a r t by t h e D e p a r t m e n t o f M e c h a n i c a a g r a n t f r o m t h e Therm The f i g u r e s w e r e drawn b y Michèle H a l v e r s o n , a n d t h e t e x t was p r e p a r e d f o r p u b l i c a t i o n by Anna M. P i c c o l o . The a u t h o r greatly appreciates their efforts i nher behalf. Literature Cited 1. 2.

3.

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

Dorn, F.L.; Rahn, O. Arch. M i k r o b i o l . 1939, 10, 6-12. Aiba, S.; Humphrey, A.E.; Millis, N.F. "Biochemical Engineering;" 2nd ed.; Academic: New York, 1973; pp. 93-94, 103-110, 115-117. Johnson, F.H.; E y r i n g , H.; Steblay, R.; Chaplin, H.; Huber, C.; Gherardi, G. J . Gen. P h y s i o l . 1945, 28, 463-537. K o f f l e r , H.; Johnson, F.H.; Wilson, P.W. J . Am. Chem. Soc. 1947, 69, 1113-1117. Hromatka, O.; Kastner, G.; Ebner, H. Enzymologia 1953, 15, 337-350. Deppe, K.; Engel, H. Z e n t r a l b l . B a k t e r i o l . P a r a s i t e n k d . Infek. Hyg. Abt. I I 1960, 113, 561-568. McCombie, A.M. J . F i s h . Res. Bd. Canada 1960, 17, 871-894. Quinlan, A.V. Water Res. 1980, 14, 1501-1507. Quinlan, A.V. J. F r a n k l i n I n s t . 1980, 310, 325-342. Quinlan, A.V. J . Thermal Biol. 1981, 6, 103-114. Knowles, G.; Downing, A.L.; B a r r e t t , M.J. J . Gen. M i c r o b i o l . 1965, 38, 263-278. Laudelout, H.; van T i c h e l e n , L. J. Bact. 1960, 79, 39-42. S t r a t t o n , F.E.; McCarty, P.L. Environ. S c i . Technol. 1967, 1, 405-410. Novak, J.T. J. Water Poll. C o n t r o l Fed. 1974, 46, 1984-1994. Lawrence, A.W.; McCarty, P.L. J . Water Poll. C o n t r o l Fed. 1969, 41, R1-R17.

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

BIOCHEMICAL

488

16.

17. 18. 19. 20. 21. 22. 23. 24.

25. 26. 27. 28.

29. 30.

31. 32. 33. 34.

ENGINEERING

Lawrence, A.W. "Anaerobic B i o l o g i c a l Treatment Processes;" Adv. Chem. Ser. 105; American Chemical S o c i e t y : Washington, DC, 1971; pp. 163-189. Topiwala, H.; S i n c l a i r , C.G. B i o t e c h n o l . Bioeng. 1971, 13, 795-813. Muck, R.E.; Grady, C.P.L., Jr. ASCE J. Environ. Eng. D i v . 1974, 100, 1147-1163. Charley, R.C.; Hooper, D.G.; McLee, A.G. Water Res. 1980 14, 1387-1396. Caperon, J . ; Meyer, J. Deep-Sea Res.1972, 19, 619-632. Eppley, R.W.; Renger, E.H. J. Phycol. 1974, 10, 15-23. M i c h a e l i s , L.; Menten, M.L. Biochem.Z. 1913, 49, 333-369. B r i g g s , G.E.; Haldane, J.B.S. J. Biol. Chem. 1925, 19, 338-339. B a i l e y , J.E.; Ollis, "Biochemical Engineerin Funda mentals;" McGraw-Hill 345-347. Monod, J. Ann. Rev. M i c r o b i o l . 1949, 3, 371-394. H o l l i n g , C.S. Mem. Ent. Soc. Can. 1965, 5-60. Caperon, J. Ecology 1967, 48, 715-722. Smith, F.E. " E u t r o p h i c a t i o n : Causes, Consequences, C o r r e c t i v e s ; " R o h l i c h , G.A., Ed.; N a t i o n a l Academy of Sciences: Washington, DC, 1969; pp. 631-645. Odum, H.T. "Modelling o f Marine Systems;" N i h o u l , J.C.J., Ed.; E l s e v i e r : Amsterdam, 1975; pp. 133-135. Quinlan, A.V. "Energy and E c o l o g i c a l M o d e l l i n g ; " Mitsch, W.J., Bosserman, R.W., Klopatek, J.M., Eds.; E l s e v i e r : Amsterdam, 1981; pp. 635-640. Eadie, G.S. J. B i o l . Chem. 1942, 146, 85-93. Augustinsson, K.-B. Acta P h y s i o l . Scand. 1948, 15 (suppl. 52), 99-100. Dowd, J.E.; Riggs, D.S. J. Biol. Chem. 1965, 240, 863-869. Arrhenius, S. " Q u a n t i t a t i v e Laws in B i o l o g i c a l Chemistry;" Bell: London, 1915; pp. 49-60.

R E C E I V E D July 7, 1 9 8 2

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

23 Kinetics of Yeast Growth and Metabolism in Beer Fermentation IVAN MARC and JEAN-MARC ENGASSER Institut National Polytechnique de Lorraine, Laboratoire des Sciences du Génie Chimque, CNRS-ENSIC, Nancy 54042 France MANFRED M O L L and BRUNO DUTEURTRE Centre de Recherche TEPRAL, Champigneulles 54250 France An experimental and t h e o r e t i c a l k i n e t i c study o f yeast growth and uptake, ethanol, during beer fermentation is presented. C e l l u l a r growth, and consequently amino a c i d s uptake and some metabolites production, stops a f t e r about 100 hours o f f e r mentation. Yeast f l o c c u l a t i o n , which s t a r t s when glucose is totally removed from the medium, then becomes a predominant phenomenon. Fermentable sugars are sequentially taken up, maltose and m a l t o t r i o s e being repressed by glucose. Ethanol and CO production r a t e remain e s s e n t i a l l y p r o p o r t i o n a l to the t o t a l r a t e o f sugar uptake both during the growth and f l o c c u l a t i o n phase. The increase with temperature o f s u b s t r a t e uptake, yeast growth and f l o c c u l a t i o n , and metabolite product i o n r a t e is simply described by Arrhenius type o f relationships. 2

The conversion by yeast o f sugars and amino a c i d s i n t o aromatic compounds represents a c e n t r a l process i n brewing. A q u a n t i t a t i v e understanding o f the m i c r o b i a l events t a k i n g p l a c e during the t r a n s f o r m a t i o n o f wort i n t o beer i s e s s e n t i a l when c o n s i d e r i n g the automatic c o n t r o l o f t h i s fermentation. A f i r s t k i n e t i c modeling o f yeast growth, sugar and amino a c i d uptake and aromatic m e t a b o l i t e p r o d u c t i o n was p r e v i o u s l y proposed (1,2). On the b a s i s o f recent experimental r e s u l t s we propose a new model which takes i n t o account the e v o l u t i o n o f the yeast v i a b i l i t y during the f e r m e n t a t i o n , and d e s c r i b e s i n g r e a t e r d e t a i l the f l o c c u l a t i o n phase and the p r o d u c t i o n o f CO2. The k i n e t i c study i s s p e c i a l l y aimed a t e s t a b l i s h i n g r e l a t i o n s p h i p s between the wort i n i t i a l composition, the f i n a l beer q u a l i t y and v a r i o u s process parameters, such as temperature, pressure and i n o cculum s i z e .

0097-6156/83/0207Ό489$06.00/0 ©

1983 American Chemical Society

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

490

BIOCHEMICAL

ENGINEERING

EXPERIMENTAL The experimental p a r t of t h i s work was performed at the TEPRAL Beer Research Center i n Champigneulles, France. Beer pro­ d u c t i o n was c a r r i e d out e i t h e r i n l a b o r a t o r y t u b u l a r fermentors, 1,80 m h e i g h t and 4,5 cm inner diameter, c o n t a i n i n g 2 l i t e r s of medium, or i n 1000 l i t e r s c y l i n d r o - c o n i c a l p i l o t p l a n t fermentors without mechanical a g i t a t i o n . Standart i n d u s t r i a l wort and yeast Saccharomyces uvarum 0019 were used. The i n i t i a l d i s s o l v e d oxygen c o n c e n t r a t i o n i n the wort was f i x e d at 8 ppm. The temperature was maintained constant at e i t h e r 10° C or 14° C during the whole f e r ­ mentation. The overhead pressure was 1 atm w i t h the l a b o r a t o r y fermentor and 2,2 atm w i t h the p i l o t p l a n t . Samples of 80 cm^ and 4 l i t e r s were p e r i o d i c a l l y withdrawn from the l a b o r a t o r y and p i l o t v e s s e l r e s p e c t i v e l y Yeast t r a t i o n was determined e i t h e ter counter. The v a r i o u sugars, glucose, , , charose, m a l t o t r i o s e were analyzed by high pressure l i q u i d chroma­ tography. The c o n c e n t r a t i o n o f the twenty amino a c i d s were d e t e r ­ mined by i o n exchange chromatography. Ethanol was assayed by microc a l o r i m e t r y and other m e t a b o l i t e s by gas chromatography.(3) THE KINETIC MODEL In c o n v e n t i o n a l fermentation models the c e n t r a l equation u s u a l l y expresses c e l l u l a r growth as a f u n c t i o n o f s u b s t r a t e , pro­ duct and c e l l u l a r c o n c e n t r a t i o n i n the medium. Product formation i s then r e l a t e d to c e l l growth or c e l l u l a r c o n c e n t r a t i o n , whereas s u b s t r a t e uptake r a t e may i n c l u d e s e v e r a l c o n t r i b u t i o n s from c e l l u ­ l a r growth, maintenance and product formation. Moreover, these mo­ d e l s most o f t e n are based on constant y i e l d s . In view of the experimental r e s u l t s (4) i t i s c l e a r t h a t the c o n v e n t i o n a l approach cannot be used to model beer fermentation. F i r s t , the fermentation medium c o n t a i n s s e v e r a l sugars which are a s s i m i l a t e d at d i f f e r e n t r a t e s . The uptake of each sugar may be l i ­ mited by i t s own c o n c e n t r a t i o n and i n h i b i t e d by the presence of others. Second, the i n v e s t i g a t e d beer fermentation from a k i n e t i c p o i n t of view i s complicated by yeast f l o c c u l a t i o n which becomes predominant during the second stage of the process, and which i s a f f e c t e d by one of the fermentable sugars, namely glucose. T h i r d , the v a r i o u s y i e l d s between fermentable sugars uptake, yeast growth, ethanol and CÛ2 formation are not constant during the course of the fermentation. F i n a l l y , the r a t e o f aromas production i s r e l a t e d to e i t h e r yeast growth r a t e or sugars uptake r a t e . In order to d e s c r i b e the i n f l u e n c e of the i n i t i a l wort compo­ s i t i o n on the fermentation process the proposed model i s based on separate r a t e equations f o r the v a r i o u s sugars uptake. Production of y e a s t , ethanol and carbon d i o x i d e i s then r e l a t e d to the t o t a l uptake of fermentable sugars w i t h v a r i a b l e y i e l d s . The r a t e of amino a c i d s uptake and other m e t a b o l i t e s production i s expressed as a f u n c t i o n of growth r a t e or sugars uptake r a t e w i t h constant or v a r i a b l e y i e l d s .

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

23.

MARC ET AL.

Kinetics

in Beer

491

Fermentation

Y e a s t g r o w t h and f l o c c u l a t i o n . D i s t i n c t i o n i s made between t h e t o t a l y e a s t p r o d u c e d d u r i n g t h e g r o w t h p h a s e and t h e s u s p e n d e d y e a s t c o n c e n t r a t i o n i n t h e f e r m e n t a t i o n medium. The i n c r e a s e i n t o t a l yeast c o n c e n t r a t i o n i n the fermentor i s d i r e c t l y r e l a t e d t o the t o t a l r a t e o f fermentable sugar consumption. d(X ) T

= - R

dt

X/S

d(TFS) dt

(1)

(Xy)

being the t o t a l yeast concentration

(TFS) R X/S

t h e t o t a l fermentable sugar c o n c e n t r a t i o n the yeast t o sugar y i e l d

The e x p e r i m e n t a l l y o b s e r v e d d e c r e a s e o f R x / s d u r i n g t h e f e r ­ mentation has p r e v i o u s l c e l l u l a r sterol concentratio a b s e n c e o f o x y g e n . We f o u n d i t most c o n v e n i e n t t o m a t h e m a t i c a l l y r e l a t e t h e d e c r e a s e o f Rx/s t o t h e i n c r e a s e o f t h e e t h a n o l c o n c e n ­ t r a t i o n i n t h e medium, ( E t h ) , a s : R

X/S

=

Y

(2)

X/S 1 +

with Y ^ g

(Eth)

4

t h e i n i t i a l yeast t o sugar the ethanol i n h i b i t i o n

yield

constant.

Y e a s t f l o c c u l a t i o n , an e s s e n t i a l phenomenon i n b e e r f e r m e n t a ­ t i o n , i s i n f l u e n c e d by t h e medium c o m p o s i t i o n , e s p e c i a l l y by t h e g l u c o s e c o n c e n t r a t i o n , and i s d e l a y e d by t h e m i x i n g e f f e c t o f CO2 p r o d u c t i o n . The t i m e v a r i a t i o n o f t h e s u s p e n d e d y e a s t c o n c e n t r a ­ t i o n i s t h u s t a k e n a s t h e d i f f e r e n c e between t h e g r o w t h and f l o c ­ c u l a t i o n r a t e as : d(X ) T

dt

- k

dt K

CO,

(x )

(3)

s

G1

w i t h ( X ) t h e suspended y e a s t c o n c e n t r a t i o n 5

k

the yeast f l o c c u l a t i o n

f

constant

(Gl)

the glucose c o n c e n t r a t i o n

K

the i n h i b i t i o n constant o f f l o c c u l a t i o n

G1 k m d r

co

by g l u c o s e

t h e m i x i n g c o n s t a n t by CO^ t h e r a t e o f CO^ d e s o r p t i o n 2

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

492

BIOCHEMICAL

ENGINEERING

Sugars consumption. Saccharose i s f i r s t hydrolysed i n t o g l u ­ cose and f r u c t o s e a t the c e l l s u r f a c e , then the four fermentable sugars, glucose, f r u c t o s e , maltose and m a l t o t r i o s e are a s s i m i l a t e d at d i f f e r e n t r a t e s depending on the medium composition. Glucose i s taken up the f a s t e s t as the maltose, m a l t o t r i o s e and f r u c t o s e i n t r a ­ c e l l u l a r t r a n s p o r t s are i n h i b i t e d by glucose. Assuming that the s u b s t r a t e s are mainly consumed by the suspended y e a s t s , the f o l l o ­ wing r a t e expressions are proposed t o describe the time v a r i a t i o n of fermentable sugars : d(Gl) _ dt " " G1 K

(Gl) + (Gl)

V

G 1

U

, S

γ ;

χ 180 d(Sac) " 342 d t

d(Mal) _ (Mal) dt " " Mal K + (Mal

1

,

m K

J

χ

, n

V

M a l

K

d(Sac) dt " * sac k

(

S

d(Mlt) .

c

)

(

V

(

(Mit)

1

KMit Z T W- I

v

"dt

a

- - Mit

G1

V , , J

W

,

: 1— + (cry K G1

(

γ

6

)

χ

v

m (

7

)

1

K

d(Fr) _

~dF~~ " * F r K V

(Fr) 1 , . 180 d(Sac) + (Fr) ~ (GÎT V " 342 "dt Fr 1 + -prY

(

W

r

K

G1

with ( G l ) , (Mal), (Sac), ( M i t ) , ( F r ) the glucose, maltose, saccha­ rose, m a l t o t r i o s e and f r u c t o s e c o n c e n t r a t i o n . ^ G l ' ^Mal* ^ M l t ' V r ^ ^ ^ ^ °^ glucose, maltose, malto­ t r i o s e and f r u c t o s e consumption. i i i " ^Gl' ^ G l ' ^Gl 9 ^ i n h i b i t i o n constants n e m a x

m a

r a

e

f

u c o s e

k

K

K

K

K

k i n e t i c

c o n s t a n t s

s a c ' G1' M a l ' M l t ' F r The time v a r i a t i o n o f the t o t a l fermentable sugar concentra­ t i o n i s c a l c u l a t e d by adding the p r e v i o u s l y defined r a t e s o f v a r i a ­ t i o n o f the c o n c e n t r a t i o n o f the i n d i v i d u a l sugars.

Amino a c i d s consumption. Two r a t e expressions were used. For threonine, s e r i n e , methionine, i s o l e u c i n e , l e u c i n e , l y s i n e , the r a t e o f consumption i s p r o p o r t i o n a l t o the r a t e o f yeast growth, but can be l i m i t e d by the amino a c i d c o n c e n t r a t i o n

In Foundations of Biochemical Engineering; Blanch, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

23.

MARC

ET

Kinetics

AL.

in Beer

493

Fermentation

(AA) being the amino a c i d c o n c e n t r a t i o n i n the medium the maximal r a t e of amino a c i d consumption a k i n e t i c constant. For other amino a c i d s , such as a s p a r t i c a c i d , glutamic a c i d , a l a n i n e , v a l i n e , t y r o s i n e , p h e n y l a l a n i n e , h i s t i d i n e , a r g i n i n e , an a d d i t i o n n a i i n h i b i t o r y e f f e c t of threonine demonstrated by expe­ riments w i t h threonine enriched wort, i s considered (AA)

d(AA)

dt

AA Κ

TThrT

+ (AA) ~

Δ

V

d (

1

n n ) v

dt

J

Thr w i t h K.^

the i n h i b i t i o n constant by threonine

Ethanol p r o d u c t i o n r e l a t e d to the t o t a l r a t e of fermentable sugar consumption

Φ*

- - Vs