Preface xi
Symbols and Abbreviations xiii
Introduction and Definitions xv
1 Multiple Equilibria, Principles, and Derivations 1
1.1 General Considerations 1
1.2 Diffusion 2
1.3 Modes of Ligand Binding 4
1.4 Interaction between Macromolecules and Ligands 6
1.4.1 Binding Constants 6
1.4.2 Binding to a Single Site 7
1.5 Binding to Identical Independent Sites 7
1.5.1 General Binding Equation 7
1.5.2 Graphic Representations of the Binding Equation 13
1.5.2.1 Direct and Linear Diagrams 13
1.5.2.2 Analysis of Binding Data from Spectroscopic Titrations 15
1.5.3 Binding of Different Ligands, Competition 18
1.5.4 Noncompetitive Binding 21
1.6 Binding to Nonidentical, Independent Sites 23
References 25
2 Cooperativity and Allosteric Enzymes 27
2.1 Binding to Interacting Sites 27
2.1.1 The Hill Equation 27
2.1.2 The Adair Equation 29
2.1.3 The Pauling Model 32
2.2 Allosteric Enzymes 32
2.2.1 The Symmetry or Concerted Model 33
2.2.2 The SequentialModel and Negative Cooperativity 38
2.2.3 Analysis of Cooperativity 42
2.2.4 Physiological Aspects of Cooperativity 44
2.2.5 Examples of Allosteric Enzymes 46
2.2.5.1 Hemoglobin 46
2.2.5.2 Aspartate Transcarbamoylase 48
2.2.5.3 Aspartokinase 49
2.2.5.4 Phosphofructokinase 50
2.2.5.5 Allosteric Regulation of the Glycogen Metabolism 50
2.2.5.6 Membrane-Bound Enzymes and Receptors 50
2.3 Binding to Nonidentical, Interacting Sites 51
References 52
3 FromReaction Order to the Michaelis-Menten Law: Fundamental Relationships of Enzyme Kinetics 55
3.1 Reaction Order 55
3.1.1 First-Order Reactions 56
3.1.2 Second-Order Reactions 57
3.1.3 Zero-Order Reactions 58
3.2 Steady-State Kinetics and the Michaelis-Menten Equation 58
3.2.1 Derivation of the Michaelis-Menten Equation 58
3.3 Analysis of Enzyme Kinetic Data 62
3.3.1 Graphic Representations of the Michaelis-Menten Equation 62
3.3.1.1 Direct and Semilogarithmic Representations 62
3.3.1.2 Direct Linear Plots 68
3.3.1.3 LinearizationMethods 70
3.3.2 Analysis of Progress Curves 72
3.3.2.1 Integrated Michaelis-Menten Equation 73
3.3.2.2 Determination of Reaction Rates 75
3.3.2.3 Graphic Methods for Rate Determination 77
3.3.2.4 Graphic Determination of True Initial Rates 79
3.4 Reversible Enzyme Reactions 80
3.4.1 Rate Equation for Reversible Enzyme Reactions 80
3.4.2 Product Inhibition 82
3.4.3 The Haldane Relationship 84
References 85
4 Enzyme Inhibition and RelatedMechanisms 87
4.1 Unspecific and Irreversible Inhibition 87
4.1.1 Unspecific Inhibition 87
4.1.2 Irreversible Inhibition 88
4.1.2.1 General Features of Irreversible Inhibition 88
4.1.2.2 Suicide Substrates 90
4.1.2.3 Transition-State Analogs 91
4.1.2.4 Analysis of Irreversible Inhibition 92
4.2 Reversible Inhibition 94
4.2.1 General Rate Equation 94
4.2.1.1 Noncompetitive Inhibition and Graphic Representation of Inhibition Data 97
4.2.1.2 Competitive Inhibition 102
4.2.1.3 Uncompetitive Inhibition 106
4.2.2 Partial Inhibitions 108
4.2.2.1 Partially Noncompetitive Inhibition 108
4.2.2.2 Partially Uncompetitive Inhibition 110
4.2.2.3 Partially Competitive Inhibition 111
4.2.3 Noncompetitive and Uncompetitive Product Inhibition 113
4.2.4 Substrate Inhibition 114
4.3 Enzyme Reactions with Two Competing Substrates 116
4.4 Different Enzymes Catalyzing the Same Reaction 118
References 119
5 Multi-Substrate Reactions 121
5.1 Nomenclature 121
5.2 Multi-Substrate Mechanisms 122
5.2.1 Random Mechanism 122
5.2.2 Ordered Mechanism 127
5.2.3 Ping-Pong Mechanism 129
5.2.4 Product Inhibition in Multi-Substrate Reactions 131
5.2.5 Haldane Relationships in Multi-Substrate Reactions 132
5.2.6 Mechanisms with MoreThan Two Substrates 133
5.2.7 Other Nomenclatures for Multi-Substrate Reactions 134
5.3 Derivation of Rate Equations of Complex Enzyme Mechanisms 135
5.3.1 King-Altmann Method 135
5.3.2 Simplified Derivations Applying GraphTheory 140
5.3.3 Combination of Equilibrium and Steady-State Approach 141
References 143
6 pH and Temperature Dependence of Enzymes 145
6.1 pH Optimum and Determination of pK Values 145
6.2 pH Stability 147
6.3 Temperature Dependence 148
References 152
7 Special EnzymeMechanisms 153
7.1 Kinetic Treatment of Allosteric Enzymes 153
7.2 Hysteretic Enzymes 154
7.3 Kinetic Cooperativity, the Slow Transition Model 155
7.4 Ribozymes 156
7.5 Enzymes Reacting with Polymeric Substrates 159
References 160
8 Enzymes Bound to Artificial Matrices and to Membranes 163
8.1 Immobilized Enzymes 163
8.1.1 Kinetics of Immobilized Enzymes 163
8.1.2 External Diffusion Limitation 165
8.1.3 Internal Diffusion Limitation 166
8.1.4 Inhibition of Immobilized Enzymes 168
8.1.5 pH and Temperature Behavior of Immobilized Enzymes 169
8.2 Enzyme Reactions at the Membrane 169
8.2.1 Transport Processes 169
8.2.2 Enzyme Reactions at Membrane Interfaces 172
References 175
9 Isotope Exchange and Isotope Effects 177
9.1 Isotope Exchange 177
9.1.1 Isotope Exchange Kinetics 177
9.2 Isotope Effects 181
9.2.1 Primary Kinetic Isotope Effect 181
9.2.2 Influence of the Kinetic Isotope Effect on V and Km 182
9.2.3 Other Isotope Effects 183
References 184
10 Related Subject Areas 185
10.1 Relationship between Enzyme Kinetics and Pharmacokinetics 185
10.2 Application of StatisticalMethods in Enzyme Kinetics 189
10.2.1 General Remarks 189
10.2.2 Statistical Terms Used in Enzyme Kinetics 191
References 193
11 Methods for the Study of Multiple Equilibria 195
11.1 General Aspects 195
11.2 Equilibrium Dialysis as an Example for the Performance of Binding Measurements 197
11.2.1 Principle of Equilibrium Dialysis 197
11.2.2 Control Experiments and Sources of Error 200
11.2.2.1 Dialysis Time 200
11.2.2.2 Concentration and Activity of the Macromolecule 200
11.2.2.3 Concentration of the Ligand 201
11.2.2.4 Donnan Effect 202
11.2.3 Continuous Equilibrium Dialysis 203
11.3 Ultrafiltration 206
11.4 Gel Filtration 208
11.4.1 Batch Method 208
11.4.2 The Method of Hummel and Dreyer 209
11.4.3 Other Gel FiltrationMethods 210
11.5 Ultracentrifugation 212
11.5.1 Fixed-Angle UltracentrifugationMethods 212
11.5.2 Sucrose-Gradient Centrifugation 215
11.6 Surface Plasmon Resonance 218
References 220
12 Manometric, Electrochemical, and Calorimetric Methods 223
12.1 Warburg's Manometric Apparatus 223
12.2 Electrochemical Methods 224
12.2.1 The Oxygen Electrode 224
12.2.2 The CO2 Electrode 226
12.2.3 Potentiometry, Redox Potentials 227
12.2.4 The pH-Stat 227
12.2.5 Polarography 229
12.3 Calorimetry 230
References 232
13 Absorption and Fluorescence Spectroscopy 235
13.1 General Aspects 235
13.2 Absorption Spectroscopy 237
13.2.1 The Lambert-Beer Law 237
13.2.2 Spectral Properties of Enzymes and Ligands 238
13.2.3 Structure of Spectrophotometers 241
13.2.4 Double-Beam Spectrophotometer 245
13.2.5 Difference Spectroscopy 246
13.2.6 The Dual-Wavelength Spectrophotometer 249
13.3 Photochemical Action Spectra 250
13.4 Bioluminescence 251
13.5 Fluorescence Spectroscopy 251
13.5.1 Quantum Yield 251
13.5.2 Structure of Spectrofluorometers 252
13.5.3 Perturbations of Fluorescence Measurements 254
13.5.4 Fluorescent Compounds (Fluorophores) 255
13.5.5 Radiationless Energy Transfer 260
13.5.6 Fluorescence Polarization 262
13.5.7 Pulse Fluorometry 263
13.5.8 Fluorescence Correlation Spectroscopy 265
References 265
14 Other Spectroscopic Methods 269
14.1 Circular Dichroism and Optical Rotation Dispersion 269
14.2 Infrared and Raman Spectroscopy 274
14.2.1 IR Spectroscopy 274
14.2.2 Raman Spectroscopy 275
14.2.3 Applications 275
14.3 Nuclear Magnetic Resonance Spectroscopy 276
14.4 Electron Paramagnetic Resonance Spectroscopy 279
References 281
15 Methods to Measure Fast Reactions 283
15.1 General Aspects 283
15.2 Flow Methods 284
15.2.1 The Continuous-Flow Method 284
15.2.2 The Stopped-Flow Method 287
15.2.3 Measurement of Enzyme Reactions by Flow Methods 291
15.2.4 Determination of the Dead Time 293
15.3 Relaxation Methods 294
15.3.1 The Temperature-Jump Method 294
15.3.2 The Pressure-Jump Method 297
15.3.3 The Electric Field Method 299
15.4 Flash Photolysis, Pico- and Femtosecond Spectroscopy 300
15.5 Evaluation of Rapid Kinetic Reactions (Transient Kinetics) 302
References 305
Index 307
