Comprehensively introduces readers to modelling of rate of enzymatic reactions, including effects of physicochemical parameters
Analysis of Enzyme Reaction Kinetics is the second set in a unique eleven-volume collection on Enzyme Reactor Engineering. It describes rate expressions pertaining to enzymatic reactions, including modulation by physicochemical factors, as well as tools for prediction and control of how fast substrates are transformed to products. Volume 1 details rate expressions mathematically derived from mechanistic postulates, and is complemented by appropriate statistical approaches to fit them to experimental data. Volume 2 discusses the effects of physical and chemical parameters upon the rates of both enzyme-catalyzed and enzyme-deactivation reactions.
Starting with basic concepts and historical perspectives, the first volume introduces readers to the mathematics of rate expressions. It then goes on to cover kinetic features and the many forms of Michaelis & Menten’s-type rate expressions (single and multiple enzymes, autocatalysis, single and multiple substrates, multiphasic systems, etc.), and concludes with the statistical analysis of rate expressions – including the assessment of data, fitting of models to data, and generation of data themselves. The second volume introduces readers to physicochemical modulation of reaction rate – starting with basic concepts, and looking specifically at temperature-, mechanical force-, pH- and compound-driven effects: both unimodal and bimodal deactivation are considered.
Analysis of Enzyme Reaction Kinetics 2V Set is a comprehensive work for those studying or working with enzyme reactions, or practitioners involved in the control of reactors.
SERIES INFORMATION
Enzyme Reactor Engineering is organized into four major sets: Enzyme Reaction Kinetics and Reactor Performance; Analysis of Enzyme Reaction Kinetics; Analysis of Enzyme Reactor Performance; and Mathematics for Enzyme Reaction Kinetics and Reaction Performance.
Table of Contents
About the Author
Series Preface
Preface
Volume One
7. Mathematical Approach to Rate Expressions 2
7.1. Introduction 3
7.1.1. Basic concepts 3
7.1.2. Chemical mechanism and rate expression 4
7.1.3. Historical perspective 7
7.1.4. Further refinements 10
7.1.5. Multisubstrate approaches 12
7.1.6. Objective 15
7.1.7. Strategy 16
7.2. Rate expression 17
7.2.1. Kinetic features 17
7.2.2. Order of reaction 31
7.3. Michaelis & Menten’s rate expression with single enzyme 36
7.3.1. Michaelis & Menten’s rationale 37
7.3.2. Graphical interpretation 41
7.3.3. Semilogarithmic plot 47
7.3.4. Eisenthal, Cornish & Bowden’s plot 50
7.3.5. Dixon’s plot 54
7.3.6. Concentration of enzyme forms 57
7.3.7. Best reparameterization 60
7.3.8. van Slyke & Cullen’s rationale 62
7.3.9. Briggs & Haldane’s rationale 64
7.3.10. Absolute sensitivity to lumped parameters 70
7.3.11. Relative error of alternative derivations 74
7.3.12. Relative sensitivity to intrinsic parameters 77
7.3.13. Biochemical rationale 82
7.3.14. Derivatives of rate expression 92
7.4. Michaelis & Menten’s rate expression with multiple enzymes 94
7.4.1. Several isozymes 95
7.4.2. Two isozymes 100
7.4.3. Infinite isozymes 117
7.5. Michaelis & Menten’s rate expression with autocatalysis 94
7.6. Michaelis & Menten’s rate expression with multiphasic systems 137
7.7. Improved rate expression with single enzyme 151
7.7.1. Morrison’s rationale 152
7.7.2. Graphical interpretation 155
7.7.3. Low enzyme concentration 168
7.7.4. Best reparameterization 172
7.7.5. Kim’s rationale 175
7.7.6. Graphical interpretation 180
7.7.7. Specific kinetic features 200
7.7.8. Absolute sensitivity to intrinsic parameters 224
7.7.9. Improved simulation of initial transients 228
7.7.9.1. Batch stirred system 230
7.7.9.2. Flow stirred system 250
7.7.10. Improved simulation of final transients 285
7.8. Alternative forms of Michaelis & Menten’s rate expression 314
7.8.1. Integrated form 315
7.8.1.1. Lambert’s function 319
7.8.1.2. Taylor’s expansion 324
7.8.2. Linearized form 337
7.8.2.1. Differential expression 339
7.8.2.2. Integrated expression 350
7.9. Rate expressions for multisubstrate reactions 361
7.9.1. Shortcut approaches to pseudo steady state 362
7.9.1.1. King & Altman’s method 362
7.9.1.2. Cleland’s nomenclature 385
7.9.1.3. Supplementary simplifications 396
7.9.2. Uni Uni mechanism 410
7.9.2.1. Pseudo steady state 411
7.9.2.1.1. Classical approach 411
7.9.2.1.2. King & Altman’s approach 419
7.9.2.2. Rapid equilibrium 427
7.9.2.2.1. Classical approach 427
7.9.2.2.2. King & Altman’s approach with Cha’s aproximation 431
7.9.3. Ordered Bi Uni mechanism 439
7.9.3.1. Pseudo steady state 441
7.9.3.2. Rapid equilibrium 452
7.9.4. Other Uni/Bi and Bi/Bi mechanisms 462
7.9.5. Simplification of multisubstrate rate expressions 476
7.9.5.1. Uni Uni mechanism 483
7.9.5.2. Ordered Bi Uni mechanism 490
7.10. Further reading 497
8. Statistical Approach to Rate Expressions 1
8.1. Introduction 2
8.1.1. Basic concepts 2
8.1.2. Objective 27
8.1.3. Strategy 28
8.2. Assessment of data and models 29
8.2.1. Independence checks 30
8.2.2. Normality checks 33
8.2.3. Homoskedasticity checks 37
8.2.4. Linearity checks 41
8.2.5. Relationship checks 45
8.2.6. Adequacy checks 48
8.2.7. Sufficiency checks 54
8.3. Fitting of models to data 57
8.3.1. Linear regression analysis 60
8.3.1.1. Unipredictor/uniresponse 62
8.3.1.2. Multipredictor/uniresponse 96
8.3.1.3. Multipredictor/multiresponse 114
8.3.2. Improved regression analysis 130
8.3.2.1. Data transformation 131
8.3.2.2. Statistical tools 146
8.3.2.2.1. Weighed least squares 147
8.3.2.2.2. Nonparametric techniques 154
8.3.3. Nonlinear regression analysis 155
8.3.3.1. General form 155
8.3.3.2. Enzymatic reaction 157
8.3.3.2.1. Estimation 157
8.3.3.2.2. Stationarity 168
8.3.3.2.3. Inference 186
8.4. Generation of data 201
8.4.1. Empirical designs 202
8.4.2. Mechanistic designs 214
8.4.2.1. Starting designs 214
8.4.2.2. Sequential designs 220
8.4.2.3. Subset designs 222
8.4.2.4. Conditional linearity 226
8.4.2.5. Enzymatic reaction 229
8.4.2.6. Enzymatic reaction with enzyme decay 234
8.5. Further reading 246
Volume 2
9. Physical Modulation of Reaction Rate 1
9.1. Introduction 2
9.1.1. Basic concepts 2
9.1.2. Thermodynamic approach 5
9.1.3. Kinetic approach 29
9.1.4. Physical deactivation of enzymes 38
9.1.5. Objective 33
9.1.6. Strategy 44
9.2. Unimodal deactivation 45
9.2.1. Simple reversible deactivation 46
9.2.2. Simple irreversible deactivation 53
9.2.3. General deactivation 59
9.2.3.1. Series reversible deactivation 65
9.2.3.2. Series irreversible deactivation 77
9.2.3.2.1. Stirred batch reactor 79
9.2.3.2.2. Stirred flow reactor 109
9.2.3.2.3. Model discrimination 120
9.2.3.2.4. Infinite isozymes 142
9.2.3.3. Series reversible and parallel irreversible deactivation 151
9.2.3.4. Series irreversible and parallel reversible deactivation 172
9.3. Bimodal deactivation 208
9.3.1. Simple reversible deactivation 209
9.3.2. Simple irreversible deactivation 222
9.4. Effects upon nonelementary reactions 242
9.5. Temperature-driven modulation 245
9.5.1. Thermodynamic formulation of temperature-dependence of elementary steps 248
9.5.1.1. Reversible reaction 248
9.5.1.2. Reversible deactivation 252
9.5.2. Kinetic formulation of temperature-dependence of elementary steps 258
9.5.2.1. Collision theory 258
9.5.2.2. Transition state theory 293
9.5.3. Improvement of parameter fitting 300
9.6. Mechanical force-driven modulation 307
9.6.1. Normal elastic forces 310
9.6.1.1. Effect of pressure 311
9.6.1.2. Combined effect of pressure and temperature 316
9.6.2. Tangential elastic forces 336
9.6.2.1. Gibbs’ adsorption isotherm 338
9.6.2.2. Langmuir’s adsorption isotherm 346
9.6.3. Tangential plastic forces 363
9.6.3.1. Effect of shear 364
9.7. Response of enzyme deactivation 383
9.8. Response of enzyme reaction 389
9.9. Further reading 393
10. Chemical Modulation of Reaction Rate 1
10.1. Introduction 2
10.1.1. Basic concepts 2
10.1.2. Thermodynamic approach 4
10.1.3. Kinetic approach 29
10.1.4. Chemical deactivation 44
10.1.4.1. Denaturation 45
10.1.4.2. Condensation 52
10.1.4.3. Stabilization 56
10.1.4.4. Inhibition 68
10.1.4.4.1. Reversible inhibitors 71
10.1.4.4.2. Irreversible inhibitors 78
10.1.5. Chemical modulation 82
10.1.5.1. Effects of pH 83
10.1.5.2. Self-control 94
10.1.6. Objective 96
10.1.7. Strategy 97
10.2. pH-driven modulation 99
10.2.1. Protolysis of enzyme only 100
10.2.2. Protolysis of enzyme and substrate 127
10.3. Ionic strength-driven modulation 147
10.4. pH-driven deactivation 175
10.4.1. Reversible decay 176
10.4.2. Irreversible decay 184
10.5. Self-deactivation 197
10.6. Microbial deactivation 206
10.7. Heterologous bimodal deactivation 217
10.7.1. Reversible deactivation 218
10.7.1.1. Mixed inhibition 218
10.7.1.1.1. Michaelis & Menten’s plot 222
10.7.1.1.2. Lineweaver & Burk’s plot 230
10.7.1.1.3. Hanes & Woolf’s plot 237
10.7.1.1.4. Woolf, Augustinsson & Hofstee’s plot 245
10.7.1.1.5. Eadie & Scatchard’s plot 254
10.7.1.1.6. Dixon’s plot 263
10.7.1.1.7. Cornish-Bowden’s plot 269
10.7.1.1.8. Hunter & Downs’ plot 275
10.7.1.2. General mixed inhibition 280
10.7.1.3. Competitive inhibition 311
10.7.1.4. Uncompetitive inhibition 326
10.7.2. Irreversible deactivation 350
10.8. Heterologous unimodal deactivation 363
10.8.1. Reversible deactivation 364
10.8.1.1. Noncompetitive inhibition 364
10.8.2. Irreversible deactivation 382
10.9. Mechanism discrimination 389
10.9.1. Sequential random Bi Bi 392
10.9.2. Sequential ordered Bi Bi 400
10.9.3. Ping pong Bi Bi 405
10.9.4. Graphical comparison 414
10.10. Homologous modulation 423
10.10.1. Independent sites 434
10.10.1.1. Two-sited enzyme 434
10.10.1.2. N-sited enzyme 437
10.10.2. Sequential transition 441
10.10.2.1. Equivalent sites 442
10.10.2.1.1. Three-sited enzyme 442
10.10.2.1.2. N-sited enzyme 454
10.10.2.2. Nonequivalent sites 471
10.10.2.2.1. Three-sited enzyme 471
10.10.2.2.2. N-sited enzyme 483
10.10.3. Concerted transition 516
10.10.3.1. Equivalent sites 517
10.10.3.1.1. Two-sited enzyme 517
10.10.3.1.2. N-sited enzyme 541
10.10.3.2. Hybrid behaviors 563
10.10.4. Asymptotic patterns 571
10.11. Further reading 597
INDEX
