Bioreaction Engineering Principles - Springer978-1-4419-9688-6/1.pdf · John Villadsen Department...
-
Upload
hoangkhanh -
Category
Documents
-
view
221 -
download
0
Transcript of Bioreaction Engineering Principles - Springer978-1-4419-9688-6/1.pdf · John Villadsen Department...
John VilladsenDepartment of Chemicaland Biochemical EngineeringTechnical University of Denmark (DTU)Lyngby, [email protected]
Gunnar LidenDepartment of Chemical EngineeringLund UniversityLund, Sweden
Jens NielsenSystems BiologyChalmers University of TechnologyGothenburg, [email protected]
ISBN 978-1-4419-9687-9 e-ISBN 978-1-4419-9688-6DOI 10.1007/978-1-4419-9688-6Springer New York Dordrecht Heidelberg London
Library of Congress Control Number: 2011931856
# Springer Science+Business Media, LLC 2011All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use inconnection with any form of information storage and retrieval, electronic adaptation, computer software,or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks, and similar terms, even if they arenot identified as such, is not to be taken as an expression of opinion as to whether or not they are subjectto proprietary rights.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Preface
In early 2009, we were approached by Springer Verlag, the company that had
absorbed Kluwer Academic/Plenum Publishers. The second edition of our textbook
“Bioreaction Engineering Principles” was now sold out, and we were asked to
prepare a third edition.
With very little hesitation we accepted the offer.
Since 2003 the book has been used as course-book, in European universities and
also in North and South America, in the Far East, and in Australia. We wished not
only to revise the text, but also to write a book that would appeal to students at the
best universities, at least until 2020. In short courses given at major Biotech
companies we have also found that some of the material in the previous editions
could be used right away to give the companies a better understanding of their
processes and to propose better design of their reactors. This acceptance of the book
by the industrial community prompted us to include even more examples relevant
for design of processes and equipment in the industry. The changes that have been
made since the second edition are outlined in the first, introductory chapter of the
present edition.
Our initial enthusiasm to embark on a complete revision of the text was mollified
by the duties imposed on two of us (J.N. and G.L.) in handling large research
groups and with the concomitant administration. One of us (J.V.) had much more
time available in his function as senior professor, and he became the main respon-
sible person for the work during the almost 2 years since the start of the project.
But we are all happy with the result of our common efforts – “Tous pour un, unpour tous.”
Some chapters have been read and commented by our colleagues. Special thanks
are owed to Prof. John Woodley for commenting on Chaps. 2 and 3, and to Prof.
Alvin Nienow for long discussions concerning the right way to present Chap. 11.
The former Ph.D. students, Drs. Mikkel Nordkvist and Thomas Grotkjær have
kindly given comments to many of the chapters.
v
We also thank Ph.D. student Saeed Sheykshoaie at Chalmers University who
redrew many of the figures in the last rush before finishing the manuscript. Ph.D.
student Jacob Brix at DTU has often assisted J.V. with his extensive knowledge of
“how to handle the many tricks of Word.”
Lyngby, Denmark John Villadsen
Gothenburg, Sweden Jens Nielsen
Lund, Sweden Gunnar Liden
vi Preface
Contents
1 What Is This Book About? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Note on Nomenclature .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Chemicals from Metabolic Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 The Biorefinery ... .. . . . .. . . . . .. . . . .. . . . . .. . . . .. . . . .. . . . . .. . . . .. . . . . .. . . . .. . . . 8
2.1.1 Ethanol Production ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Production of Platform Chemicals in the Biorefinery .. . . . . . . 14
2.2 The Chemistry of Metabolic Pathways. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 The Currencies of Gibbs Free Energy
and of Reducing Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Glycolysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.3 Fermentative Metabolism: Oxidation of NADH
in Anaerobic Processes .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.4 The TCA Cycle: Provider of Building Blocks
and NADH/FADH2... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.5 Production of ATP by Oxidative Phosphorylation .. . . . . . . . . . 33
2.2.6 The Pentose Phosphate Pathway:
A Multipurpose Metabolic Network ... . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.7 Summary of the Primary Metabolism of Glucose ... . . . . . . . . . 38
2.3 Examples of Industrial Production of Chemicals
by Bioprocesses .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3.1 Amino Acids .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.2 Antibiotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.3 Secreted Proteins .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.4 Design of Biotech Processes: Criteria for
Commercial Success. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.1 Strain Design and Selection... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4.2 Criteria for Design and Optimization
of a Fermentation Process .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.4.3 Strain Improvement .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
vii
2.5 The Prospects of the Biorefinery .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3 Elemental and Redox Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1 The Continuous, Stirred Tank Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.1 Mass Balances for an Ideal, Steady-State
Continuous Tank Reactor .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Yield Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3 Black Box Stoichiometries .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4 Degree of Reduction Balances .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4.1 Consistency Test of Experimental Data .. . . . . . . . . . . . . . . . . . . . . 86
3.4.2 Redox Balances Used in the Design
of Bioremediation Processes .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.5 Systematic Analysis of Black Box Stoichiometries .. . . . . . . . . . . . . . . . 96
3.6 Identification of Gross Measurement Errors .. . . . . . . . . . . . . . . . . . . . . . . . . 100
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4 Thermodynamics of Bioreactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.1 Chemical Equilibrium and Thermodynamic State Functions .. . . . . 120
4.1.1 Changes in Free Energy and Enthalpy ... . . . . . . . . . . . . . . . . . . . . 120
4.1.2 Free Energy Changes in Bioreactions .. . . . . . . . . . . . . . . . . . . . . . . 124
4.1.3 Combustion: A Change in Reference State .. . . . . . . . . . . . . . . . . 128
4.2 Heat of Reaction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.2.1 Nonequilibrium Thermodynamics .. . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.2.2 Free Energy Reclaimed by Oxidation
in the Electron Transfer Chain... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.2.3 Production of ATP Mediated
by F0 � F1 ATP Synthase.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5 Biochemical Reaction Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.1.1 Metabolic Network with Diverging Branches . . . . . . . . . . . . . . 157
5.1.2 A Formal, Matrix-Based Description
of Metabolic Networks .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.2 Growth Energetics .. . . . .. . . . . .. . . . .. . . . . .. . . . .. . . . .. . . . . .. . . . .. . . . . .. . . . .. . 172
5.2.1 Consumption of ATP for Cellular Maintenance .. . . . . . . . . . . 172
5.2.2 Energetics of Anaerobic Processes.. . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.2.3 Energetics of Aerobic Processes ... . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
viii Contents
5.3 Flux Analysis in Large Metabolic Networks .. . . . . . . . . . . . . . . . . . . . . . . . 184
5.3.1 Expressing the Rate of Biomass Formation ... . . . . . . . . . . . . . . 186
5.3.2 The Network Structure and the
Use of Measurable Rates ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.3.3 The Use of Labeled Substrates .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
6 Enzyme Kinetics and Metabolic Control Analysis. . . . . . . . . . . . . . . . . . . . 215
6.1 Enzyme Kinetics Derived from the Model
of Michaelis–Menten ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.2 More Complicated Enzyme Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
6.2.1 Variants of Michaelis–Menten Kinetics.. . . . . . . . . . . . . . . . . . . . . 222
6.2.2 Cooperativity and Allosteric Enzymes ... . . . . . . . . . . . . . . . . . . . . 227
6.3 Biocatalysis in Practice ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
6.3.1 Laboratory Studies in Preparation for an
Industrial Production Process .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
6.3.2 Immobilized Enzymes and Diffusion Resistance .. . . . . . . . . . 238
6.3.3 Choice of Reactor Type .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
6.4 Metabolic Control Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
6.4.1 Definition of Control Coefficients for Linear Pathways .. . 245
6.4.2 Using Connectivity Theorems to Calculate Control
Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
6.4.3 The Influence of Effectors.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
6.4.4 Approximate Methods for Determination of the CJi . . . . . . . . 258
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
7 Growth Kinetics of Cell Cultures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
7.1 Model Structure and Complexity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
7.2 A General Structure for Kinetic Models .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
7.2.1 Specification of Reaction Stoichiometries .. . . . . . . . . . . . . . . . . . 275
7.2.2 Reaction Rates .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
7.2.3 Dynamic Mass Balances.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
7.3 Unstructured Growth Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
7.3.1 The Monod Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
7.3.2 Multiple Reaction Models.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
7.3.3 The Influence of Temperature and pH.... . . . . . . . . . . . . . . . . . . . . 297
7.4 Simple Structured Models . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
7.4.1 Compartment Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
7.4.2 Cybernetic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
7.5 Derivation of Expression for Fraction of
Repressor-free Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
Contents ix
7.6 Morphologically Structured Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
7.6.1 Oscillating Yeast Cultures.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
7.6.2 Growth of Filamentous Microorganisms.. . . . . . . . . . . . . . . . . . . . 334
7.7 Transport Through the Cell Membrane.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
7.7.1 Facilitated Transport, Exemplified by Eukaryotic
Glucoside Permeases.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
7.7.2 Active Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
8 Population Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
9 Design of Fermentation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
9.1 Steady-State Operation of the STR ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
9.1.1 The Standard CSTR with vf ¼ ve ¼ v .. . . . . . . . . . . . . . . . . . . . 387
9.1.2 Productivity in the Standard CSTR .... . . . . . . . . . . . . . . . . . . . . . . . 390
9.1.3 Productivity in a Set of Coupled, Standard CSTR’s ... . . . . 394
9.1.4 Biomass Recirculation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
9.1.5 Steady-State CSTR with Substrates Extracted from
a Gas Phase ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
9.2 The STR Operated as a Batch or as a Fed-Batch Reactor .. . . . . . . . . 407
9.2.1 The Batch Reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
9.2.2 The Fed-Batch Reactor .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
9.3 Non-steady-State Operation of the CSTR... . . . . . . . . . . . . . . . . . . . . . . . . . . 419
9.3.1 Relations Between Cultivation Variables
During Transients.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
9.3.2 The State Vector [s, x, p] in a Transient
CSTR Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
9.3.3 Pulse Addition of Substrate to a CSTR. Stability
of the Steady State.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
9.3.4 Several Microorganisms Coinhabit the CSTR .... . . . . . . . . . . 429
9.3.5 The CSTR Used to Study Fast Transients .. . . . . . . . . . . . . . . . . . 436
9.4 The Plug Flow Reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
9.4.1 A CSTR Followed by a PFR... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
9.4.2 Loop Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
10 Gas–Liquid Mass Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
10.1 The Physical Processes Involved in Gas to Liquid
Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
10.1.1 Description of Mass Transfer Using kla...................... 462
x Contents
10.1.2 Models for kl ...................................................... 465
10.1.3 Models for the Interfacial Area, and for Bubble Size ... 466
10.2 Empirical Correlations for kla . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
10.3 Experimental Techniques for Measurement of O2 Transfer . . . . . . 482
10.3.1 The Direct Method.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
10.3.2 The Dynamic Method .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
10.3.3 The Sulfite Method .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
10.3.4 The Hydrogen Peroxide Method... . . . . . . . . . . . . . . . . . . . . . . . . . 486
10.3.5 kla Obtained by Comparison with the Mass
Transfer Coefficient of Other Gases.. . . . . . . . . . . . . . . . . . . . . . . 488
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
11 Scale-Up of Bioprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
11.1 Mixing in Bioreactors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
11.1.1 Characterization of Mixing Efficiency .. . . . . . . . . . . . . . . . . . . . 499
11.1.2 Experimental Determination of Mixing Time ... . . . . . . . . . 502
11.1.3 Mixing Systems and Their Power Consumption ... . . . . . . 505
11.1.4 Power Input and Mixing for High Viscosity Media .. . . . 514
11.1.5 Rotating Jet Heads: An Alternative
to Traditional Mixers . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
11.2 Scale-Up Issues for Large Industrial Bioreactors . . . . . . . . . . . . . . . . . . . 527
11.2.1 Modeling the Large Reactor Through Studies
in Small Scale .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
11.2.2 Scale-Up in Practice: The Desirable
and the Compromises... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
References ........................................................................... 545
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
Contents xi
List of Symbols
Symbols that are defined and used only within a particular Example, Note, or
Problem are not listed. It should be noted that a few symbols are used for different
purposes in different chapters. For this reason, more than one definition may apply
for a given symbol.
a Cell age (h)
a Specific interfacial area (m2 per m3 of medium)
ad Specific interfacial area (m2 per m3 of gas–liquid dispersion)
acell Specific cell surface area (m2 per gram dry weight)
A Matrix of stoichiometric coefficients for substrates, introduced in (7.2)
b(y) Breakage frequency (h�1)
B Matrix of stoichiometric coefficients for metabolic products,
introduced in (7.2)
ci Concentration of the ith chemical compound (kg m�3)
c�i Saturation concentration of the ith chemical compound (kg m�3)
c Vector of concentrations (kg m�3)
Cij Concentration control coefficient of the jth intermediate with respect to
the activity of the ith enzyme
CJi Flux control coefficient with respect to the activity of the ith enzyme
C* Matrix containing the control coefficients defined in (6.34)
db Bubble diameter (m)
df Thickness of liquid film (m)
dmean Mean bubble diameter (m)
dmem Lipid membrane thickness (m)
ds Stirrer diameter (m)
dSauter Mean Sauter bubble diameter (m), given by (10.18)
D Dilution rate (h�1), given by (3.1)
Dmax Maximum dilution rate (h�1)
Dmem Diffusion coefficient in a lipid membrane (m2 s�1)
Deff Effective diffusion coefficient (m2 s�1)
xiii
Di Diffusion coefficient of the ith chemical compound (m2 s�1)
e0 Enzyme concentration (g enzyme L�1)
Eg Activation energy of the growth process in (7.28)
E Mixing efficiency, defined in (11.1)
E Elemental matrix for all compounds
Ec Elemental matrix for calculated compounds
Em Elemental matrix for measured compounds
f(y,t) Distribution function for cells with property y in the population (8.1)
F Variance–covariance matrix
g Gravity (m s�2)
G Gibbs free energy (kJ mol�1)
G0 Gibbs free energy at standard conditions (kJ mol�1)
DGci Gibbs free energy of combustion of the ith reaction component
(kJ mol�1)
DGd Gibbs free energy of denaturation (kJ mol�1) (7.29)
DG0ci
Gibbs free energy of combustion of the ith reaction component at
standard conditions (kJ mol�1)
DG0f
Gibbs free energy of formation at standard conditions (kJ mol�1)
Gr Grashof number, defined in Table 10.6
h Test function, given by (3.54)
h(y) Net rate of formation of cells with property y upon cell division (cells
h�1)
h+(y) Rate of formation of cells with property y upon cell division (cells h�1)
h�(y) Rate of disappearance of cells with property y upon cell division (cells
h�1)
HA Henry’s constant for compound A (atm L mol�1)
DHci Enthalpy of combustion of the ith reaction component (kJ mol�1)
DH0f
Enthalpy of formation (kJ mol�1)
I Identity matrix (diagonal matrix with 1 in the diagonal)
J Jacobian matrix (9.102)
k0 Enzyme activity (g substrate [g enzyme]�1 h�1)
ki Rate constant (e.g., kg kg�1 h�1)
kg Mass transfer coefficient for gas film (e.g., mol atm�1 s�1 m�2)
kl Mass transfer coefficient for a liquid film surrounding a gas bubble
(m s�1)
kla Volumetric mass transfer coefficient (s�1)
ks Mass transfer coefficient for a liquid film surrounding a solid particle
(m s�1)
Ka Acid dissociation constant (mol L�1)
Kl Overall mass transfer coefficient for gas–liquid mass transfer (m s�1)
K Partition coefficient
Keq Equilibrium constant
Km Michaelis constant (g L�1) (6.1)
m Amount of biomass (kg)
xiv List of Symbols
mATP Maintenance-associated ATP consumption (moles ATP [kg DW]�1
h�1)
ms Maintenance-associated specific substrate consumption (kg [kg DW]�1
h�1)
Mn(t) The nth moment of a one-dimensional distribution function, given by
(8.9)
n Number of cells per unit volume (cells m�3) (8.1)
N Stirring speed (s�1)
NA Aeration number, defined in (11.14)
Nf Flow number, defined in (11.6)
Np Power number, defined in (11.10)
p Extracellular metabolic product concentration (kg m�3)
pA Partial pressure of compound A (e.g., atm.)
p(y,y*,t) Partitioning function (8.5)
P Dimensionless metabolic product concentration
P Permeability coefficient (m s�1)
P Power input to a bioreactor (W)
Pg Power input to a bioreactor at gassed conditions (W)
P Variance–covariance matrix for the residuals, given by (3.48)
Pe Peclet number, defined in Table 10.6
qtA Volumetric rate of transfer of A from gas to liquid (mol L�1 h�1)
qx Volumetric rate of formation of biomass (kg DW m�3 h�1)
q Volumetric rate vector (kg m�3 h�1)
qt Vector of volumetric mass transfer rates (kg m�3 h�1)
Q Number of morphological forms
Q Heat of reaction (kJ mol�1)
Qt Fraction of repressor-free operators, given by (7.47)
Q2 Fraction of promotors being activated, given by (7.53)
Q3 Fraction of promoters, which form complexes with RNA polymerase, in
(7.55)
ri Specific reaction rate for species i (kg [kg DW]�1 h�1)
r Enzymatic reaction rate (Chap. 6) (g substrate L�1 h�1)
rATP Specific ATP synthesis rate (moles of ATP [kg DW]�1 h�1)
r Specific reaction rate vector (kg [kg DW]�1 h�1)
rs Specific substrate formation rate vector (kg [kg DW]�1 h�1)
rp Specific product formation rate vector (kg [kg DW]�1 h�1)
rx Specific formation rate vector of biomass constituents (kg [kg DW]�1
h�1)
r(y,t) Vector containing the rates of change of properties, in (8.2)
R Gas constant (¼8.314 J K�1 mol�1)
R Recirculation factor (Sect. 9.1.4)
R Redundancy matrix, given by (3.41)
Rr Reduced redundancy matrix
List of Symbols xv
Re Reynolds number, defined in Table 10.6
s Extracellular substrate concentration (kg m�3)
s Extracellular substrate concentration vector (kg m�3)
sf Substrate concentration in the feed to the bioreactor (kg m�3)
S Dimensionless substrate concentration
DS Entropy change (kJ mol�1 K�1)
Sc Schmidt number, defined in Table 10.6
Sh Sherwood number, defined in Table 10.6
t Time (h)
tc Circulation time (s) (11.7)
tm Mixing time (s) (11.3)
T Temperature (K)
T Matrix in (5.11). TT, the transform of T, is the stoichiometric matrix
T1 Matrix corresponding to calculated fluxes (5.12)
T2 Matrix corresponding to measured rates (5.12)
ub Bubble rise velocity (m s�1)
ui Cybernetic variable, given by (7.36)
us Superficial gas velocity (m s�1)
u Vector containing the specific rates of the metamorphosis reaction
(kg kg�1 h�1)
v Liquid flow (m3 h�1)
ve Liquid effluent flow from the reactor (m3 h�1)
vf Liquid feed to the reactor (m3 h�1)
vg Gas flow (m3 h�1)
vi Flux of internal reaction i in metabolic network (kg [kg DW]�1 h�1)
vpump Impeller induced flow (m3 s�1) (11.6)
v Flux vector, i.e., vector of specific intracellular reaction rates (kg [kg
DW]�1 h�1)
V Volume (m3)
Vd Total volume of gas–liquid dispersion (m3) (10.16)
Vg Dispersed gas volume (m3) (10.16)
Vl Liquid volume (m3)
Vy Total property space (8.2)
wi Cybernetic variable, given by (7.47)
x Biomass concentration (kg m�3)
X Dimensionless biomass concentration
Xi Concentration of the ith intracellular component (kg [kg DW]�1)
X Vector of concentrations of intracellular biomass components (kg [kg
DW]�1)
y Property state vector
Yij Yield coefficient of j from i (kg j per kg of i or C-mol of j per kg of i)YxATP ATP consumption for biomass formation (moles of ATP [kg DW]�1)
Zi Concentration of the ith morphological form (kg [kg DW]-1)
xvi List of Symbols
Greek Letters
aji Stoichiometric coefficients for substrate i in intracellular reaction jbji Stoichiometric coefficient for metabolic product i in intracellular reaction j_g Shear rate (s�1)
gji Stoichiometric coefficient for intracellular component i in intracellular
reaction j_g Shear rate (s�1), defined in (11.24)
G Matrices containing the stoichiometric coefficients for intracellular biomass
components
d Vector of measurement errors in (3.43)
D Matrix for stoichiometric coefficients for morphological forms
e Gas holdup (m3 of gas per m3 of gas–liquid dispersion)
e Porosity of a pellet
eji Elasticity coefficients, defined in (6.27)
« Vector of residuals in (3.46)
Ε Matrix containing the elasticity coefficients
� Dynamic viscosity (kg m�1 s�1)
� Internal effectiveness factor, defined in (9) of Note 6.2
pi Partial pressure of compound i (atm)
y Dimensionless time
ki Degree of reduction of the ith compound
m Specific growth rate of biomass (h�1)
mmax Maximum specific growth rate (h�1)
mq Specific growth rate for the qth morphological form (kg DW [kg DW]�1 h-1)
rcell Cell density (kg wet biomass [m�3 cell])
rl Liquid density (kg m�3)
s Surface tension (N m�1)
s2 Variance
t Space time in reactor (h)
t Shear stress (N m�2), defined in (11.25)
tp Tortousity factor, used in (6.23)
Fn Thiele modulus for reaction of order n (2) and (5) in Note 6.2
Fgen Generalized Thiele modulus, Note 6.2
c(X) Distribution function of cells (8.8)
List of Symbols xvii
Abbreviations
AcCoA Acetyl co-enzyme A
ADP Adenosine diphosphate
AMP Adenosine monophosphate
ATP Adenosine triphosphate
CoA Coenzyme A
DHAP Dihydroxy acetone phosphate
DNA Deoxyribonucleic acid
Ec Energy charge
EMP Embden–Meyerhof–Parnas
FAD Flavin adenine dinucleotide (oxidized form)
FADH Flavin adenine dinucleotide (reduced form)
FDA Food and Drug Administration
F6P Fructose-6-phosphate
F1,6P Fructose 1,6 diphosphate
GAP Glyceraldehyde triphosphate
2 PG 2-phosphoglycerate
3 PG 3-phosphoglycerate
1,3 DPG 1,3 diphosphoglycerate
GTP Guanosine triphosphate
G6P Glucose-6-phosphate
HAc Acetic acid
HLac Lactic acid
LAB Lactic acid bacteria
MCA Metabolic control analysis
MFA Metabolic Flux Analysis
NAD+ Nicotinamide adenine dinucleotide (oxidized form)
NADH Nicotinamide adenine dinucleotide (reduced form)
NADP+ Nicotinamide adenine dinucleotide phosphate (oxidized form)
NADPH Nicotinamide adenine dinucleotide phosphate (reduced form)
PEP Phosphoenol pyruvate
PP Pentose phosphate
PSS Protein synthesizing system
PTS Phosphotransferase system
PYR Pyruvate
P/O ratio Number of molecules of ATP formed per atom of oxygen used in the
oxidative phosphorylation
RNA Ribonucleic acid
mRNA Messenger RNA
xviii List of Symbols
rRNA Ribosomal RNA
tRNA Transfer RNA
RQ Respiratory quotient
R5P Ribose-5-phosphate
TCA Tricarboxylic acid
UQ Ubiquinone
List of Symbols xix
List of Examples
Chapter 3
3.1 Anaerobic yeast fermentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2 Aerobic growth with ammonia as nitrogen source. . . . . . . . . . . . . . . . . . . . . 82
3.3 Anaerobic growth of yeast with NH3 as nitrogen source
and ethanol as the product. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4 Biomass production from natural gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.5 Consistency analysis of yeast fermentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.6 Citric acid produced by Aspergillus niger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.7 Design of an anaerobic waste water treatment unit . . . . . . . . . . . . . . . . . . . . 94
3.8 Anaerobic yeast fermentation with CO2, ethanol, and glycerol
as metabolic products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.9 Production of lysine from glucose with acetic acid as byproduct . . . . . 98
3.10 Calculation of best estimates for measured rates . . . . . . . . . . . . . . . . . . . . . . 103
3.11 Application of the least-squares estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.12 Calculation of the test function h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.13 Error diagnosis of yeast fermentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Chapter 4
4.1 Thermodynamic data for H2O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.2 Equilibrium constant for formation of H2O. . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.3 Free energy changes of reactions in the EMP pathway. . . . . . . . . . . . . . . . 125
4.4 Calculation of DGc for ethanol combustion at 25�C, 1 atm . . . . . . . . . . . 129
4.5 Heat of reaction for aerobic growth of yeast . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.6 Anaerobic growth on H2 and CO2 to produce CH4. . . . . . . . . . . . . . . . . . . . 134
Chapter 5
5.1 Analysis of the metabolism of lactic acid bacteria . . . . . . . . . . . . . . . . . . . . 159
5.2 Anaerobic growth of Saccharomyces cerevisiae. . . . . . . . . . . . . . . . . . . . . . . 161
5.3 Aerobic growth of Saccharomyces cerevisiae . . . . . . . . . . . . . . . . . . . . . . . . . 164
xxi
5.4 Production of butanol and acetone by fermentation . . . . . . . . . . . . . . . . . . . 170
5.5 Growth energetics for cultivation of Lactococcus lactis. . . . . . . . . . . . . . . 178
5.6 Energetics of Bacillus clausii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.7 Metabolic Flux Analysis of citric acid fermentation
by Candida lipolytica. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.8 Analysis of the metabolic network in S. cerevisiaeduring anaerobic growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.9 Identification of lysine biosynthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5.10 Analysis of a simple network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Chapter 6
6.1 Analysis of enzymatic reaction data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
6.2 Competition of two substrates for the same enzyme . . . . . . . . . . . . . . . . . . 230
6.3 Determination of NADH in cell extract using a
cyclic enzyme assay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
6.4 Lactobionic acid from lactose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
6.5 Kinetics for lactobionic acid synthesis applied to
an immobilized enzyme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
6.6 Illustration of Metabolic Control Analysis using
analytical expressions for ri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
6.7 Calculation of the flux control coefficient at a reference
state by large deviations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
6.8 Elasticities and flux control coefficients determined by
the lin-log method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
6.9 Determination of E and CJ from transients
in a steady-state chemostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Chapter 7
7.1 Steady-state chemostat described by the Monod model
with sterile feed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
7.2 Steady-state chemostat described by the Monod model
including maintenance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
7.3 An unstructured model describing the growth of
Saccharomyces cerevisiae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
7.4 Extension of the Sonnleitner and Kappeli model to
describe protein production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
7.5 Analysis of the model of Williams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
7.6 Two-compartment model for lactic acid bacteria . . . . . . . . . . . . . . . . . . . . . . 306
7.7 A model for diauxic growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
7.8 A simple morphologically structured model describing
plasmid instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
7.9 A simple morphologically structured model for the growth
of filamentous microorganisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
7.10 Transport of glucose to a yeast cell by facilitated diffusion . . . . . . . . . . . 343
7.11 Free diffusion of organic acids across the cell membrane . . . . . . . . . . . . . 346
xxii List of Examples
Chapter 8
8.1 Specification of the partitioning function
and the breakage frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
8.2 Population balance for recombinant Escherichia coli . . . . . . . . . . . . . . . . . 367
8.3 Age distribution model for Saccharomyces cerevisiae . . . . . . . . . . . . . . . . 369
8.4 Population model for hyphal elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
Chapter 9
9.1 Biomass and product concentrations for Monod kinetics
with maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
9.2 Design of a robust waste water treatment plant. . . . . . . . . . . . . . . . . . . . . . . . 395
9.3 Design of cell recirculation system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
9.4 Design of a recirculation system – with maintenance requirement. . . . 404
9.5 Design of an integrated lactic acid production unit . . . . . . . . . . . . . . . . . . . . 404
9.6 Optimal design of a single cell production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
9.7 Design of a fed-batch process for baker’s yeast production . . . . . . . . . . . 416
9.8 A step change of sf for constant D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
9.9 Transients obtained after a change of dilution rate
from D0 to D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
9.10 Competing microbial species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
9.11 Reversion of a desired mutant to the wild type . . . . . . . . . . . . . . . . . . . . . . . . 434
9.12 A steady-state CSTR followed by a PFR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
9.13 Design of a loop reactor for single cell production . . . . . . . . . . . . . . . . . . . . 444
Chapter 10
10.1 The oxygen requirement of a rapidly respiring yeast culture. . . . . . . . . . 460
10.2 Requirements for kla in a laboratory bioreactor . . . . . . . . . . . . . . . . . . . . . . . 462
10.3 Bubble size and specific interfacial area in an agitated vessel . . . . . . . . 472
10.4 Derivation of empirical correlations for klain a laboratory bioreactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
Chapter 11
11.1 Mixing time in a baffled tank reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
11.2 Macro- and micro-mixing of a liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
11.3 Measuring a pulse response using the pH rather than [H+] . . . . . . . . . . . . 505
11.4 Power required for liquid mixing and for gas
dispersion at the sparger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
11.5 Calculation of mixing time in Stirred Tank Reactors . . . . . . . . . . . . . . . . . . 514
11.6 Rheological characterization of xanthan solutions . . . . . . . . . . . . . . . . . . . . . 518
List of Examples xxiii
11.7 A two-compartment model for oxygen transfer
in a large bioreactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
11.8 Regimen analysis of penicillin fermentation . . . . . . . . . . . . . . . . . . . . . . . . . 533
11.9 Scale-up of a 600-L pilot plant reactor to 60 m3
for unaerated mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
11.10 Oxygen transfer to a 60 m3 industrial reactor . . . . . . . . . . . . . . . . . . . . . . . . 537
xxiv List of Examples
List of Tables
Chapter 2
2.1 Twelve sugar-based building blocks suggested
by Werpy and Petersen (2004) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Precursor metabolites and some of the building blocks
synthesized from the precursors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Composition of E. coli cells grown at 37 �C on a glucose
minimal medium at a specific growth rate rx ¼ m ¼ 1.04 g cell
formed per gram cell per hour and the corresponding
requirements for ATP and NADPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4 Measured concentrations of AMP, ADP, and ATP
in a continuous culture of Lactococcus lactis . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.5 Typical complex media used in the fermentation industry . . . . . . . . . . . . . 42
2.6 The 20 physiologically important (L-) amino acids
and their net-chemical formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.7 Four classes of antibiotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.8 Pros and cons of different production organisms for
recombinant proteins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Chapter 3
3.1 Average composition of S. cerevisiae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 Elemental composition of biomass for several microbial species . . . . . . 74
3.3 Values of the w2 distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Chapter 4
4.1 Concentrations (at pH ¼ 7) of intermediates and of cofactors
of the EMP pathway in the human erythrocyte . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.2 Approximate DGR values for the EMP pathway reactions
in the human erythrocyte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
xxv
4.3 Heat of combustion for various compounds
at standard conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.4 Single-electrode potential for electron acceptors . . . . . . . . . . . . . . . . . . . . . . 140
Chapter 5
5.1 Experimentally determined values of YxATP and ms for various
microorganisms grown under anaerobic conditions
with glucose as the energy source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
5.2 Calculated values of the requirements for NADPH for
biomass synthesis and the amount of NADH formed in
connection with biomass synthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.3 Fluxes through key reactions in the metabolic network during
anaerobic growth of S. cerevisiae and using different models . . . . . . . . 197
Chapter 6
6.1 Enzymatic rate data r at four levels of s and p . . . . . . . . . . . . . . . . . . . . . . . . 226
6.2 Reconstruction the reaction rates R1 and R2 using measurements
of (s1/s0, s/s0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Chapter 7
7.1 Compilation of Ks values for growth of different microbial cells
on different sugars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
7.2 Different unstructured kinetic models with one limiting substrate . . . . 284
7.3 “True” yield and maintenance coefficients for different
microbial species growing at aerobic growth conditions . . . . . . . . . . . . . . 290
7.4 Model parameters in the Sonnleitner and Kappeli model . . . . . . . . . . . . . 295
7.5 Model parameters in mmax (T), (7.29) for Klebsiella pneumoniaeand for Escherichia coli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
7.6 Characteristics of microbial growth on truly
substitutable substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Chapter 9
9.1 Advantages and disadvantages of different reactor types
and of different operating modes of the reactors . . . . . . . . . . . . . . . . . . . . . . 384
Chapter 10
10.1 Henry’s constant for some gases in water at 25�C. . . . . . . . . . . . . . . . . . . . . 463
10.2 Parameter values for power law correlation of specific
interfacial area a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
10.3 Data for a sparged, mechanically mixed pilot plant bioreactor . . . . . . . . 473
xxvi List of Tables
10.4 Parameter values for the empirical correlation . . . . . . . . . . . . . . . . . . . . . . . 475
10.5 Data for a standard laboratory bioreactor
with two Rushton turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
10.6 Some important dimensionless groups for mass
transfer correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
10.7 Literature correlations for the Sherwood number, Sh . . . . . . . . . . . . . . . . 480
10.8 Solubility of oxygen in pure water at an oxygenpressure pO ¼ 1 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
10.9 Solubility of oxygen at 25�C and pO ¼ 1 atm in various
aqueous solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
10.10 Molecular diffusivity DA of solutes in dilute
aqueous solution at 25�C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
Chapter 11
11.1 Viscosity of some Newtonian fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
11.2 Design data for the reactor modeled by Oosterhuis
and Kossen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
11.3 Characteristic times for important processes in fermentations . . . . . . . . 533
11.4 Characteristic times for a penicillin fermentation in a 41-L
pilot plant bioreactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
11.5 Scale-up by a factor 125 from pilot plant reactor
to industrial reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
List of Tables xxvii
List of Notes
Chapter 3
3.1 Time-dependent output with constant values of input variables . . . . . . . . 66
3.2 How to treat ions in the black box model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3 BOD as a unit of redox power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4 Variance–covariance matrix of the rate estimates. . . . . . . . . . . . . . . . . . . . . . . 103
3.5 Calculation of the variance–covariance matrix from the errors
in the primary variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Chapter 4
4.1 On the proper use of thermodynamic data from tables . . . . . . . . . . . . . . . . . 139
4.2 50 years of controversy about the chemiosmotic hypothesis
may now be resolved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Chapter 5
5.1 Comparison of the method based on the net fluxes V,and the method based on the total set
of internal fluxes v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.2 Calculation of the total ATP consumption for maintenance . . . . . . . . . . . . 175
5.3 Biomass equation in metabolic network models . . . . . . . . . . . . . . . . . . . . . . . . 186
5.4 Sensitivity analysis of the stoichiometric matrices. . . . . . . . . . . . . . . . . . . . . . 189
5.5 Linear dependency in reaction stoichiometries. . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.6 Measurement of 13C-enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Chapter 6
6.1 Assumptions in the mechanistic models for enzyme kinetics. . . . . . . . . . . 220
6.2 The steady-state substrate concentration profile for
a spherical particle. The effectiveness factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
xxix
Chapter 7
7.1 Model complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
7.2 The genesis of the Monod Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
7.3 Stable and unstable RNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
7.4 What should be positioned in the active compartment
of a simple structured model? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
7.5 Derivation of expression for fraction of repressor-free operators . . . . . 320
7.6 Mechanistic parameters in the protein synthesis model . . . . . . . . . . . . . . . 324
7.7 Relation between Tosc and the dilution rate in continuous culture . . . . 333
Chapter 8
8.1 Determination of the total number of cells from a
substrate balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
8.2 General form of the population balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
Chapter 9
9.1 Comparison of the productivity of a fed-batch and a continuous
baker’s yeast process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
9.2 Sampling in the Buziol et al. system and extraction of metabolites. . . 439
Chapter 10
10.1 Calculation of maximum stable bubble diameter using
the statistical theory of turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
10.2 Derivation of and use of the relation Sh = 2 for a sphere
in stagnant medium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
Chapter 11
11.1 Sheer stress as a tensor property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
11.2 In the design of RJH: Can power input Pbe scaled with medium volume V?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524
11.3 Mixing with stationary jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
xxx List of Notes