Table Of ContentEnzymeKinetics
Enzyme Kinetics
PrinciplesandMethods
HansBisswanger
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v
Contents
Preface xi
SymbolsandAbbreviations xiii
IntroductionandDefinitions xv
1 MultipleEquilibria,Principles,andDerivations 1
1.1 GeneralConsiderations 1
1.2 Diffusion 2
1.3 ModesofLigandBinding 4
1.4 InteractionbetweenMacromoleculesandLigands 6
1.4.1 BindingConstants 6
1.4.2 BindingtoaSingleSite 7
1.5 BindingtoIdenticalIndependentSites 7
1.5.1 GeneralBindingEquation 7
1.5.2 GraphicRepresentationsoftheBindingEquation 13
1.5.2.1 DirectandLinearDiagrams 13
1.5.2.2 AnalysisofBindingDatafromSpectroscopicTitrations 15
1.5.3 BindingofDifferentLigands,Competition 18
1.5.4 NoncompetitiveBinding 21
1.6 BindingtoNonidentical,IndependentSites 23
References 25
2 CooperativityandAllostericEnzymes 27
2.1 BindingtoInteractingSites 27
2.1.1 TheHillEquation 27
2.1.2 TheAdairEquation 29
2.1.3 ThePaulingModel 32
2.2 AllostericEnzymes 32
2.2.1 TheSymmetryorConcertedModel 33
2.2.2 TheSequentialModelandNegativeCooperativity 38
2.2.3 AnalysisofCooperativity 42
2.2.4 PhysiologicalAspectsofCooperativity 44
vi Contents
2.2.5 ExamplesofAllostericEnzymes 46
2.2.5.1 Hemoglobin 46
2.2.5.2 AspartateTranscarbamoylase 48
2.2.5.3 Aspartokinase 49
2.2.5.4 Phosphofructokinase 50
2.2.5.5 AllostericRegulationoftheGlycogenMetabolism 50
2.2.5.6 Membrane-BoundEnzymesandReceptors 50
2.3 BindingtoNonidentical,InteractingSites 51
References 52
3 FromReactionOrdertotheMichaelis–MentenLaw:
FundamentalRelationshipsofEnzymeKinetics 55
3.1 ReactionOrder 55
3.1.1 First-OrderReactions 56
3.1.2 Second-OrderReactions 57
3.1.3 Zero-OrderReactions 58
3.2 Steady-StateKineticsandtheMichaelis–MentenEquation 58
3.2.1 DerivationoftheMichaelis–MentenEquation 58
3.3 AnalysisofEnzymeKineticData 62
3.3.1 GraphicRepresentationsoftheMichaelis–MentenEquation 62
3.3.1.1 DirectandSemilogarithmicRepresentations 62
3.3.1.2 DirectLinearPlots 68
3.3.1.3 LinearizationMethods 70
3.3.2 AnalysisofProgressCurves 72
3.3.2.1 IntegratedMichaelis–MentenEquation 73
3.3.2.2 DeterminationofReactionRates 75
3.3.2.3 GraphicMethodsforRateDetermination 77
3.3.2.4 GraphicDeterminationofTrueInitialRates 79
3.4 ReversibleEnzymeReactions 80
3.4.1 RateEquationforReversibleEnzymeReactions 80
3.4.2 ProductInhibition 82
3.4.3 TheHaldaneRelationship 84
References 85
4 EnzymeInhibitionandRelatedMechanisms 87
4.1 UnspecificandIrreversibleInhibition 87
4.1.1 UnspecificInhibition 87
4.1.2 IrreversibleInhibition 88
4.1.2.1 GeneralFeaturesofIrreversibleInhibition 88
4.1.2.2 SuicideSubstrates 90
4.1.2.3 Transition-StateAnalogs 91
4.1.2.4 AnalysisofIrreversibleInhibition 92
4.2 ReversibleInhibition 94
4.2.1 GeneralRateEquation 94
Contents vii
4.2.1.1 NoncompetitiveInhibitionandGraphicRepresentationofInhibition
Data 97
4.2.1.2 CompetitiveInhibition 102
4.2.1.3 UncompetitiveInhibition 106
4.2.2 PartialInhibitions 108
4.2.2.1 PartiallyNoncompetitiveInhibition 108
4.2.2.2 PartiallyUncompetitiveInhibition 110
4.2.2.3 PartiallyCompetitiveInhibition 111
4.2.3 NoncompetitiveandUncompetitiveProductInhibition 113
4.2.4 SubstrateInhibition 114
4.3 EnzymeReactionswithTwoCompetingSubstrates 116
4.4 DifferentEnzymesCatalyzingtheSameReaction 118
References 119
5 Multi-SubstrateReactions 121
5.1 Nomenclature 121
5.2 Multi-SubstrateMechanisms 122
5.2.1 RandomMechanism 122
5.2.2 OrderedMechanism 127
5.2.3 Ping-PongMechanism 129
5.2.4 ProductInhibitioninMulti-SubstrateReactions 131
5.2.5 HaldaneRelationshipsinMulti-SubstrateReactions 132
5.2.6 MechanismswithMoreThanTwoSubstrates 133
5.2.7 OtherNomenclaturesforMulti-SubstrateReactions 134
5.3 DerivationofRateEquationsofComplexEnzyme
Mechanisms 135
5.3.1 King–AltmannMethod 135
5.3.2 SimplifiedDerivationsApplyingGraphTheory 140
5.3.3 CombinationofEquilibriumandSteady-StateApproach 141
References 143
6 pHandTemperatureDependenceofEnzymes 145
6.1 pHOptimumandDeterminationofpK Values 145
6.2 pHStability 147
6.3 TemperatureDependence 148
References 152
7 SpecialEnzymeMechanisms 153
7.1 KineticTreatmentofAllostericEnzymes 153
7.2 HystereticEnzymes 154
7.3 KineticCooperativity,theSlowTransitionModel 155
7.4 Ribozymes 156
7.5 EnzymesReactingwithPolymericSubstrates 159
References 160
viii Contents
8 EnzymesBoundtoArtificialMatricesandtoMembranes 163
8.1 ImmobilizedEnzymes 163
8.1.1 KineticsofImmobilizedEnzymes 163
8.1.2 ExternalDiffusionLimitation 165
8.1.3 InternalDiffusionLimitation 166
8.1.4 InhibitionofImmobilizedEnzymes 168
8.1.5 pHandTemperatureBehaviorofImmobilizedEnzymes 169
8.2 EnzymeReactionsattheMembrane 169
8.2.1 TransportProcesses 169
8.2.2 EnzymeReactionsatMembraneInterfaces 172
References 175
9 IsotopeExchangeandIsotopeEffects 177
9.1 IsotopeExchange 177
9.1.1 IsotopeExchangeKinetics 177
9.2 IsotopeEffects 181
9.2.1 PrimaryKineticIsotopeEffect 181
9.2.2 InfluenceoftheKineticIsotopeEffectonV andK 182
m
9.2.3 OtherIsotopeEffects 183
References 184
10 RelatedSubjectAreas 185
10.1 RelationshipbetweenEnzymeKineticsandPharmacokinetics 185
10.2 ApplicationofStatisticalMethodsinEnzymeKinetics 189
10.2.1 GeneralRemarks 189
10.2.2 StatisticalTermsUsedinEnzymeKinetics 191
References 193
11 MethodsfortheStudyofMultipleEquilibria 195
11.1 GeneralAspects 195
11.2 EquilibriumDialysisasanExampleforthePerformanceofBinding
Measurements 197
11.2.1 PrincipleofEquilibriumDialysis 197
11.2.2 ControlExperimentsandSourcesofError 200
11.2.2.1 DialysisTime 200
11.2.2.2 ConcentrationandActivityoftheMacromolecule 200
11.2.2.3 ConcentrationoftheLigand 201
11.2.2.4 DonnanEffect 202
11.2.3 ContinuousEquilibriumDialysis 203
11.3 Ultrafiltration 206
11.4 GelFiltration 208
11.4.1 BatchMethod 208
11.4.2 TheMethodofHummelandDreyer 209
11.4.3 OtherGelFiltrationMethods 210
11.5 Ultracentrifugation 212
11.5.1 Fixed-AngleUltracentrifugationMethods 212
Contents ix
11.5.2 Sucrose-GradientCentrifugation 215
11.6 SurfacePlasmonResonance 218
References 220
12 Manometric,Electrochemical,andCalorimetricMethods 223
12.1 Warburg’sManometricApparatus 223
12.2 ElectrochemicalMethods 224
12.2.1 TheOxygenElectrode 224
12.2.2 TheCO Electrode 226
2
12.2.3 Potentiometry,RedoxPotentials 227
12.2.4 ThepH-Stat 227
12.2.5 Polarography 229
12.3 Calorimetry 230
References 232
13 AbsorptionandFluorescenceSpectroscopy 235
13.1 GeneralAspects 235
13.2 AbsorptionSpectroscopy 237
13.2.1 TheLambert–BeerLaw 237
13.2.2 SpectralPropertiesofEnzymesandLigands 238
13.2.3 StructureofSpectrophotometers 241
13.2.4 Double-BeamSpectrophotometer 245
13.2.5 DifferenceSpectroscopy 246
13.2.6 TheDual-WavelengthSpectrophotometer 249
13.3 PhotochemicalActionSpectra 250
13.4 Bioluminescence 251
13.5 FluorescenceSpectroscopy 251
13.5.1 QuantumYield 251
13.5.2 StructureofSpectrofluorometers 252
13.5.3 PerturbationsofFluorescenceMeasurements 254
13.5.4 FluorescentCompounds(Fluorophores) 255
13.5.5 RadiationlessEnergyTransfer 260
13.5.6 FluorescencePolarization 262
13.5.7 PulseFluorometry 263
13.5.8 FluorescenceCorrelationSpectroscopy 265
References 265
14 OtherSpectroscopicMethods 269
14.1 CircularDichroismandOpticalRotationDispersion 269
14.2 InfraredandRamanSpectroscopy 274
14.2.1 IRSpectroscopy 274
14.2.2 RamanSpectroscopy 275
14.2.3 Applications 275
14.3 NuclearMagneticResonanceSpectroscopy 276
14.4 ElectronParamagneticResonanceSpectroscopy 279
References 281
