biothermodynamics : the role of thermodynamics in ... parti fundamentals 1...
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Biothermodynamics
With contributions by: John F. Carpenter, Eva Y. Chi, A. Espah Borujeni, M.T. Gude, W.M. van Gulik,
Charles Haynes, Sef J. J. Heijnen, Curtis B. Hughesman, Gunnar Karlstrom, Jiirgen U. Keller, E. Jamalzadeh,
Marcel L. Jansen, Hans-Olof Johansson, Karel Ch.A. M. Luyben, Thomas Maskow, Willem Norde,
John M. Prausnitz, Theodore W. Randolph, E.S.J. Rudolph, Urs von Stockar, Adrie Straathof, H. Taymaz-
Nikerel, Folke Tjerneld, Robin F. B. Turner, Patricia Vazquez Villegas, Voja Vojinic, P.J.T. Verheijen, and
Luukvan derWielen.
EPFL Press
A Swiss academic publisher distributed by CRC Press
CONTENTS
PARTI
FUNDAMENTALS
1 THE ROLE OF THERMODYNAMICS IN BIOCHEMICAL
ENGINEERING 3
1.0 Basic remarks on thermodynamics in biochemical engineering 3
1.1 Fundamental concepts in equilibrium thermodynamics 5
1.2 Charged species, gels and other soft systems 5
1.3 Stability and activity of biomacromolecules 8
1.4 Thermodynamics of live cells 9
1.5 Thermodynamic analysis of metabolism 10
1.6 Conclusions 11
1.7 References 12
2 PHASE EQUILIBRIUM IN NON-ELECTROLYTE SYSTEMS 13
2.1 Introduction 13
2.2 Essential formal relations 14
2.2.1 Criteria for equilibrium 14
2.3 Liquid-liquid equilibria 19
2.4 Solid-liquid equilibria 21
2.5 References 23
3 VIRIAL EXPANSION FOR CHEMICAL POTENTIALS IN A
DILUTE SOLUTION FOR CALCULATION OF LIQUID-LIQUID
EQUILIBRIA 25
3.1 Introduction 25
3.2 Example of protein separation 25
3.3 References 31
4 THE THERMODYNAMICS OF ELECTRICALLY CHARGED
MOLECULES IN SOLUTION 33
4.1 Why do electrically charged molecules call for a particular
thermodynamic treatment? 33
xii B iothermodynamics
4.2 The thermodynamics of electrolytes 35
4.2.1 The electrochemical potential 35
4.2.2 Equilibrium conditions 36
4.2.3 Appropriate concentration measures and non-ideality 37
4.3 Electrostatics 38
4.3.1 Coulombs law, force of interactions 38
4.3.2 Short and long range interactions 38
4.3.3 Simplifications within the Debye-Hiickel theory 40
4.3.4 Derivation of the simple Debye-Huckel (DH) model 42
4.4 Empirical and advanced ion activity coefficient models 48
4.4.1 Empirical extension of Debye-Huckel theory 48
4.4.2 The Bjerrum theory of ion association 49
4.4.3 Modern developments in electrolyte theory 51
4.4.4 Pitzer's Model 52
4.4.5 Guggenheims numerical integration 53
4.4.6 Integral theory of electrolyte solutions 54
4.4 Equations of state for strong electrolyte thermodynamics 56
4.5 References 60
5 WATER 63
5.1 Introduction 63
5.2 Phenomenological aspects of water 64
5.3 Molecular properties of water 67
5.4 Water as a solvent 70
5.4.1 Electrolytes 71
5.4.2 Uncharged components 72
5.5 Further reading 75
PART II
CHARGED SPECIES, GELS, AND OTHER SOFT SYSTEMS
6 POLYMERS, POLYELECTROLYTES AND GELS 79
6.1 Flory's Theory of polymer solutions 79
6.2 Electric Charge on a weak polyelectrolyte 86
6.3 Hydrogels: Elementary Equations for Idealized Networks and
Their Swelling Behavior 96
6.3.1 Affine Network Model'
97
6.3.2 Phantom Network Model 98
6.3.3 Swelling theory for hydrogels 98
6.3.4 Illustration for a perfect tetrafunctional network 100
6.3.5 Effect of chain entanglement on swelling 104
6.3.6 Polyelectrolyte hydrogels 107
6.3.7 Hydrogel collapse: phase transition 112
Contents xiii
6.4 Appendix: Entropy of mixing for polymer solutions 115
6.5 References 121
7 SELF-ASSEMBLY OF AMPHIPHILIC MOLECULES 123
7.1 Introduction 123
7.2 Self-assembly as phase separation 124
7.3 Different types of self-assembled structures 128
7.4 Aggregation as a "start-stop" process: size and shape of
self-assembled structures 130
7.5 Mass action model for micellization 132
7.6 Factors that influence the critical micelle concentration 135
7.7 Bilayer structures 138
7.8 Reverse micelles 141
7.9 Microemulsions 142
7.10 Self-assembled structures in applications 146
7.11 References 147
8 MOLECULAR THERMODYNAMICS OF PARTITIONING IN
AQUEOUS TWO-PHASE SYSTEMS 149 •
8.1 Introduction 149
8.2 Flory-Huggins theory applied to aqueous two-phase
partition systems 152
8.3 Dependence of partitioning on system variables 154
8.3.1 Entropic contribution to the partition coefficient 156
8.3.2 Enthalpic contribution to the partition coefficient 158
8.3.3 Relative magnitudes of enthalpic and entropic
contributions to partitioning 160
8.3.4 Effect of polymer molecular mass on partitioning 162
8.3.5 Effect of tie-line length on partitioning 163
8.4 Simple interpretation of the effects of added electrolyte 165
8.4.1 Ion partitioning in systems containing a single salt 166
8.4.2 Ion partitioning in systems containing a single salt of a
polyelectrolyte with monovalent counter ions 168
8.4.3 Protein (biologic solute) partitioning in systems
containing a dominant salt 169
8.5 Calculation of phase diagrams and partitioning 172
8.6 Conclusions 175
8.7 References 178
9 GENERALIZATION OF THERMODYNAMIC PROPERTIES FOR
SELECTION OF BIOSEPARATION PROCESSES: 181
9.1 Phase behavior in Bioseparation Processes 181
9.1.1 Phase behavior of 'Bio '-molecules 181
9.1.2 Intermolecular interactions and molecular structure 184
xiv Biothermodynamics
9.1.3 Physical interactions 184
9.1.4 Chemical interactions 187
9.1.5 Relative strength of molecular interactions 188
9.1.6 Effect of molecular structure 188
9.1.7 Pure 'bio'-molecules: crystalline and amorphoussolids 193
9.2 Generalized correlation 196
9.2.1 Basic model development 196
9.2.2 Solubilities in mixed solvents 198
9.2.3 Partitioning in mixed solvents and aqueous two
phase systems 202
9.2.4 Sorption in mixed solvents 210
9.2.5 Selectivity of ion exchange resins 212
9.3 Generalized polarity scales 213
9.4 Conclusions 215
9.A APPENDIX 215
9.A.1 An estimation of log P 215
9.A.2 Pure components and mixtures 221
9.5 References 228
10 PROTEIN PRECIPITATION WITH SALTS AND/OR POLYMERS....
231
10.1 Introduction 231
10.2 Equation of state 234
10.3 The potential of mean force 236
10.4 Precipitation calculations 238
10.5 Generalization to a multicomponent solution 239
10.6 Crystallization 241
10.7 References 243
11 MULTICOMPONENT ION EXCHANGE EQUILIBRIA OFWEAK
ELECTROLYTE BIOMOLECULES 245
11.1 Introduction 245
11.2 Multi-component ion exchange of weak electrolytes 247
11.2.1 Thermodynamic framework 247
11.2.2 The DIX-model for monovalent ions 249
11.3 Experimental case studies 250
11.3.1 Ion exchange of carboxylic and acetyl amino acids....
251
11.3.2 Anion exchange of B-lactam antibiotics 253
11.4 Conclusions 256
11.5 References 257
Contents xv
PART III
STABILITY AND ACTIVITY OF BIOMACROMOLECULES
12 PROTEINS 261
12.1 Introduction 261
12.2 The amino acids in proteins 262
12.3 The three-dimensional structure of protein molecules in
aqueous solution 266
12.4 Non-covalent interactions that determine the structure of a
protein molecule in water 271
12.4.1 Hydrophobic interaction 272
12.4.2 Electrostatic interactions 273
12.4.3 Dipolar interactions 276
12.4.4 Dispersion interactions 277
12.4.5 Hydrogen bonding 277
12.4.6 Bond lengths and angles 279
12.5 Stability of protein structure in aqueous solution 279
12.6 Thermodynamic analysis of protein structure stability 281
12.7 Reversibility of protein denaturation aggregation of
unfolded protein molecules 287
12.8 References 288
13 THERMODYNAMICS IN MULTIPHASE BIOCATALYSIS 289
13.1 Why multiphase biocatalysis? 289
13.2 Thermodynamics of enzymatic reactions in aqueous
systems 290
13.3 Non-aqueous media for biocatalysis 296
13.3.1 Fluid phase systems 297
13.3.2 Solid-fluid systems 298
13.4 Using enyzmes in organic solvents 299
13.4.1 Enzyme inactivation in organic solvents 299
13.4.2 Predicting solvent effects on enzyme stability 300
13.4.3 Water activity control 30
13.5 Phase equilibria in multiphase enyzmatic reactions 303
13.5.1 Partition coefficients 303
13.5.2 Aqueous solubilities 304
13.5.3 Calculation of reaction yields at equilibrium 305
13.5.4 Suspension-to-suspension reactions 308
13.6 Whole cells in organic solvents 31
13.7 List of symbols 31
13.8 References 31
xvi Biothermodynamics
14 THERMODYNAMICS OF THE PHYSICAL STABILITY OF
PROTEIN SOLUTIONS 315
14.1 Introduction 315
14.2 Factors influencing protein stability 316
14.2.1 Temperature 316
14.2.2 pH effects on protein stability 317
14.2.3 Ligands and co-solutes 318
14.2.4 Salt type and concentration 327
14.2.5 Antimicrobial agents 328
14.2.6 Surfactants 328
14.3 Mechanism of protein aggregation 329
14.3.1 Structural transitions accompanying aggregation 329
14.3.2 Characterization of the aggregation competent species ...
329
14.3.3 Aggregation models, energetics, and rates 330
14.3.4 Role of conformational stability 332
14.3.5 Role of colloidal stability 338
14.4 Summary and conclusions 344
14.5 References 345
15 MEASURING, INTERPRETING AND MODELING THE STABILITIES
AND MELTING TEMPERATURES OF B-FORM DNAS THAT
EXHIBIT A TWO-STATE HELIX-TO-COIL TRANSITION 355
15.1 Introduction 355
15.2 Methods for measuring duplex DNA melting thermodynamics... .
358
15.2.1 UV absorption spectroscopy 359
15.2.2 Calorimetry 365
15.3 Modeling dsDNA stability and the melting transition 370
15.3.1 Statistical mechanical models of the melting transition...
370
15.3.2 Linear nearest-neighbor thermodynamic models of
B-form DNA stability and melting 372
15.3.3 Non-linear NNT models of B-form DNA stability
and melting 375
15.4 Comparing and further improving the performance of
NNT models 377
15.4.1 Duplexes terminating in a 5'-TA group have statisticallysignificant ATm errors 381
15.4.2 Correcting Tm predictions for duplexes containing5'-TA type termini 382
15.4.3 The dependence of B-DNA melting temperatures on
ionic strength 384
15.4.4 Correcting Tm predictions for common features and
modifications of probes and primers 385
15.5 Final thoughts 387
15.6 References 389
Contents xvii
PART IV
THERMODYNAMICS IN LIVING SYSTEMS
16 LIVE CELLS AS OPEN NON-EQUILIBRIUM SYSTEMS 399
16.1 Introduction 399
16.2 Balances for open systems 400
16.2.1 General remarks 400
16.2.2 Molar balances 401
16.2.3 Energy balances 402
16.2.4 Entropy balance 404
16.2.5 Gibbs energy balance 404
16.3 Entropy production, forces and fluxes 405
16.3.1 Entropy production in closed systems 405
16.3.2 Entropy production in non-reactive and reactive
flow-systems 406
16.3.3 Entropy production in steady-state heat conduction....
407
16.3.4 Total entropy production 407
16.4 Flux-force relationships and coupled processes 408
16.5 The linear energy converter as a model for living systems 409
16.5.1 Reactions driven against their driving force
through coupling 409
16.5.2 Efficiency of energy converters 412
16.5.3 Driving output reactions up-hill and the principle of
minimum entropy production 415
16.5.4 Predicting growth kinetics from irreversible
thermodynamics 416
16.5.5 Maintenance as static head situation 417
16.6 Conclusions 419
16.7 References 421
17 MINIATURIZATION OF CALORIMETRY: STRENGTHS
AND WEAKNESSES FOR BIOPROCESS MONITORING
AND CONTROL 423
17.1 Why miniaturization of calorimeters? 423
17.2 Historical roots 425
17.3 Measurement principle 426
17.3.1 Assembly of chip-calorimeter 426
17.3.2 Miniaturization limits 427
17.3.3 Signal evaluation 430
17.4 Calorimetry versus off-gas analysis 432
17.5 Applications of chip-calorimetry 434
17.5.1 Monitoring of discontinuous bioprocesses 434
17.5.2 Monitoring and control of continuous bioprocesses 435
17.5.3 Application for biofilm analysis 436
xviii B iothermodynamics
17.6 Outlook 438
17.7 References 438
18 A THERMODYNAMIC APPROACH TO PREDICT BLACK BOX
MODEL PARAMETERS FOR MICROBIAL GROWTH 443
18.1 Introduction 443
18.2 Catabolic energy production 445
18.2.1 Catabolic Gibbs energy under standard conditions 445
18.2.2 Catabolic Gibbs energy under non-standard
conditions 447
18.2.3 Threshold inhibition concentrations of catabolic
reactants 452
18.3 Thermodynamic prediction of the parameters in the
Herbert-Pirt substrate distribution relation 453
18.3.1 The substrate consumption rate for organismmaintenance, ms 453
18.3.2 The biomass reaction substrate parameter, a 454
18.3.3 The anabolic product reaction substrate parameter b.... 458
18.3.4 Stoichiometry of the biomass, product and catabolic
reactions 460
18.4 Prediction of the qp{\i) relationship 461
18.5 Prediction of the process reaction 462
18.5.1 Catabolic products 462
18.5.2 Anabolic products 464
18.5.3 Conclusion 465
18.6 Prediction of the hyperbolic substrate uptake kinetic parameters ...465
18.6.1 The parameters «7smax (or |amax) 465
18.6.2 Affinity, Ks 467
18.6.3 Other mechanisms putting thermodynamically based
upper limits on qs and qp 467
18.7 Influence of temperature and pH on Black Box model parameters.. 468
18.7.1 Effect of temperature 468
18.7.2 Effect of pH 469
18.7.3 Conclusion on temperature and pH- related kinetic
effects 471
18.8 Heat production in biological systems 471
18.9 Conclusion 472
18.10 References 472
18.11 Further reading 472
19 BIOTHERMODYNAMICS OF LIVE CELLS: ENERGY DISSIPATION
AND HEAT GENERATION IN CELLULAR CULTURES 475
19.1 Why study heat generation and energy dissipation in
biotechnology? 475
Contents xix
19.2 The first law: measuring, interpreting and exploiting heat
generation in live cultures 477
19.2.1 Applying heat balances to bioreactors and calorimeters... 477
19.2.2 Calorimeters 479
19.2.3 Typical heat generation rates during microbial growth
and their interpretation 481
19.2.4 On-line monitoring and control of bioprocesses by
heat dissipation measurements 484
19.3 The second law: energy dissipation, driving force and growth ....486
19.3.1 Energy dissipation and the driving force for growth in
chemotrophes 486
19.3.2 The relationship between the driving force for growthand the biomass yield in chemotrophes 489
19.3.3 Summary of the thermodynamics of chemotrophic
growth 491
19.4 Predicting energy and heat dissipation by calculation 492
19.4.1 Problem statement 492
19.4.2 Standard states 493
19.4.3 Reference states 493
19.4.4 Stoichiometry of the growth reaction and split into
catabolic and biosynthetic reactions 498
19.5 Results: heat generation and Gibbs energy dissipation as a
function of biomass yield 501
19.5.1 Aerobic growth 501
19.5.2 Ethanol fermentation 502
19.5.3 Lactic acid fermentation 504
19.5.4 Acetotrophi£ mefhanogenesis 505
19.5.5 Autotrophic methanogenesis 506
19.5.6 The relationship between heat generation and free
energy dissipation for chemotrophic growth 507
19.5.6 Mixotrophic and phototrophic growth 508
19.6 Application: prediction of yield coefficients 512
19.6.1 Growth efficiency and irreversible thermodynamics.... 513
19.6.2 Gibbs energy correlations 514
19.6.3 Product and energy yields for biofuels and
biorefineries 517
19.7 Discussion and conclusions 519
19.A Appendix: Example calculation for prediction of growth
stoichiometry 523
19.A.1 Statement of the problem 523
19.A.2 Thermodynamic data 524
19.A.3 Solution 525
19.A.4 Discussion 528
19.8 References 531
XX Biothermodynamics
20 THERMODYNAMIC ANALYSIS OF PHOTOSYNTHESIS 535
20.1 Introduction 535
20.2 References 543
PART V
THERMODYNAMICS OF METABOLISM
21 A THERMODYNAMIC ANALYSIS OF DICARBOXYLIC ACID
PRODUCTION IN MICROORGANISMS 547
21.1 Introduction 547
21.2 Outline of the approach 548
21.2.1 Black Box thermodynamic analysis of the theoretical
dicarboxylic acid product reaction 548
21.2.2 Maximal theoretical product yield 549
21.2.3 Stoichiometry of the theoretical product reaction 549
21.2.4 Alkali consumption, osmotic stress and ionic
strength 552
21.2.5 Thermodynamics of product formation 555
21.3 Thermodynamics of dicarboxylic acid transport 556
21.3.1 Thermodynamically feasible transport mechanisms ....556
21.3.2 Metabolic energy required for dicarboxylicacid export 560
21.3.3 Converting Gibbs energy of the theoretical product
reaction into ATP for growth 561
21.3.4 Fumaric acid 561
21.3.5 Succinic acid 565
21.3.6 Acid back diffusion 566
21.4 Genetic engineering of target systems based upon thermodynamic
analysis results 569
21.5 Conclusion 569
21.A Appendices 571
21 .A. 1 Acid/alkali cost 571
21.A.2 Standard AfG values 571
21 .A.3 In vivo energy aspects of ATP, proton motive force,
and fumarate reductase ., 572
21 .A.4 Effect of acid back-diffusion on the product yield of
dicarboxylic acid 574
21.6 References 577
22 THERMODYNAMIC ANALYSIS OF METABOLIC PATHWAYS 581
22.1 Introduction 581
22.2 Thermodynamic feasibility analysis of individual
metabolic pathways 582
Contents xxi
22.3 Estimation of observable standard Gibbs energies of reaction 585
22.3.1 K vs. K' - accounting for the non-ideality of the
reaction medium 587
22.3.2 K vs. K" - accounting for the pH and pMg of the
reaction medium 588
22.4 Materials and methods [22] 594
22.4.1 Data for standard Gibbs energies of reaction 594
22.4.2 Data for physiological conditions in the cytosol 595
22.4.3 Computational software 596
22.5 Results and discussion 596
23.5.1 Influence of the metabolite concentration range 596
22.6 Conclusions 600
22.7 References 603
INDEX 605