Bioreaction Engineering Principles

John Villadsen l Jens Nielsen l Gunnar Liden

Bioreaction EngineeringPrinciples

Third Edition

John VilladsenDepartment of Chemicaland Biochemical EngineeringTechnical University of Denmark (DTU)Lyngby, Denmarkjv@kt.dtu.dk

Gunnar LidenDepartment of Chemical EngineeringLund UniversityLund, Sweden

Jens NielsenSystems BiologyChalmers University of TechnologyGothenburg, Swedennielsenj@chalmers.se

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.

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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