Fundamentals of
Enzyme Kinetics
Third edition
by Athel Cornish-Bowden
Universitats-und Landesbibliothek
Bibliothek Biologie
Schnittspahnstr. 10, 64287 Darmstadt
lnv,Nr.
PORTLAND PRESS
Contents
Preface to the Third Edition
xv
Basic Principles of Chemical Kinetics
1.1
Abbreviations and symbols
1
1.2
Order of a reaction
2
1.2.1
Order and molecularity
2
1.2.2
Determination of the order of a reaction
6
1.3
Dimensions of rate constants
8
1.4
Reversible reactions
1.5
Determination of first-order rate constants
10
1.6
Catalysis
12
1.7
The influence of temperature and pressure on rate
9
.
constants
13
1.7.1
The Arrhenius equation
13
1.7.2
Elementary collision theory
15
1.7.3
Transition-state theory
16
1.7.4
Effects of hydrostatic pressure on rate constants
Problems
20
21
Introduction to Enzyme Kinetics
2.1
The idea of an enzyme-substrate complex
23
2.2
The Michaelis-Menten equation
25
2.3
The steady state of an enzyme-catalysed reaction
29
2.3.1
The Briggs-Haldane treatment
29
2.3.2
The Michaelis-Menten equation
30
2.3.3
Units of enzyme activity
31
2.3.4 The curve defined by the Michaelis-Menten
equation
2.4
32
2.3.5
Mutual depletion kinetics
34
2.3.6
Ways of writing the Michaelis-Menten equation
35
Specificity
36
Contents
2.5
Validity of the steady-state assumption
39
2.6
Graphs of the Michaelis-Menten equation
41
2.6.1
Plotting v against a
41
2.6.2
The double-reciprocal plot
42
2.6.3
The plot of a/v against a
44
2.6.4
The plot of v against via
45
2.6.5
The direct linear plot
2.7
2.8
2.9
The reversible Michaelis-Menten mechanism
2.7.1
The reversible rate equation
48
2.7.2
The Haldane relationship
52
2.7.3
"One-way enzymes"
53
Product inhibition
55
Integration of enzyme rate equations
57
2.9.1
2.9.2
2.10
46
48
Michaelis-Menten equation without product
inhibition
57
Effect of product inhibition on the progress curve
58
2.9.3
Accurate estimation of initial rates
60
2.9.4
Time courses for other mechanisms
63
Artificial enzymes, RNA enzymes and catalytic
antibodies
64
2.10.1 "Alternative enzymes"
64
2.10.2 Artificial enzymes
65
2.10.3 Catalytic RNA
66
2.10.4 Catalytic antibodies
67
Problems
68
Practical Aspects,of Kinetic Studies
3.1
Enzyme assays
71
3.1.1
Discontinuous and continuous assays
71
3.1.2
Estimating the initial rate
72
3.1.3
Increasing the straightness of the progress curve
73
3.1.4
Coupled assays
75
3.2
Detecting enzyme inactivation
78
3.3
Experimental design
81
3.4
3.3.1
Choice of substrate concentrations
81
3.3.2
Choice of pH, temperature and other conditions
83
3.3.3
Use of replicate observations
84
Treatment of ionic equilibria ,
Problems
86
89
Contents
Deriving Steady-State Rate Equations
4.1
Introduction
4.2
The principle of the King-Altman method
4.3
The method of King and Altman
4.4
The method of Wong and Hanes
4.5
Modifications to the King-Altman method
4.6
Reactions containing steps at equilibrium
4.7
Analysing mechanisms by inspection
4.8
4.7.1
Topological reasoning
4.7.2
Mechanisms with alternative routes
4.7.3
Dead-end steps
91
91
95
99
100
103
106
106
107
107
108
111
Derivation of rate equations by computer
Problems
Reversible Inhibition and Activation
5.1
5.2
Introduction
Linear inhibition
114
5.2.1
Competitive inhibition
114
5.2.2
Mixed inhibition
116
5.2.3
Uncompetitive inhibition
119
' 5.2.4
5.3
113
Summary of linear inhibition types
120
Plotting inhibition results
121
5.3.1
Simple plots
121
5.3.2
Combination plots
124
5.4
Multiple inhibitors
5.5
Relationship between inhibition constants and the
5.6
5.7
5.8
5.9
125
concentration for half-inhibition
126
Inhibition by a competing substrate
127
5.6.1
Competition between substrates
127
5.6.2
Testing if two reactions occur at the same site
128
Enzyme activation
130
5.7.1
Miscellaneous uses of the term activation
130
5.7.2
Essential activation
131
5.7.3
Hyperbolic activation and inhibition
133
Design of inhibition experiments
135
Inhibitory effects of substrates
5.9.1
Non-productive binding
5.9.2
Substrate inhibition
Problems
137
'
137
140
141
Contents
Tight-binding and Irreversible Inhibitors
6.1
Tight-binding inhibitors
145
6.2
Irreversible inhibitors
148
6.2.1
Non-specific irreversible inhibition
148
6.2.2
Specific irreversible inhibition
6.3
6.4
Substrate protection experiments
148
150
Chemical modification as a means of identifying
essential groups
151
6.4.1
Kinetic analysis of chemical modification
151
6.4.2
Remaining activity as a function of degree of
modification
Problems
153
155
Reactions of More than One Substrate
7.1
Introduction
157
7.2
Classification of mechanisms
158
7.2.1
Ternary-complex mechanisms
158
7.2.2
Substituted-enzyme mechanisms
161
7.2.3
Comparison between chemical and kinetic
7.2.4
7.3
classifications
163
Schematic representation of mechanisms
165
Rate equations
166
7.3.1
Compulsory-order ternary-complex mechanism
166
7.3.2
Random-order ternary-complex mechanism
169
7.3.3
Substituted-enzyme mechanism
169
7.3.4
Calculation of rate constants from kinetic
parameters
7.4
7.5
Initial-rate measurements in the absence of products
170
171
7.4.1
Meanings of the parameters
171
7.4.2
Apparent Michaelis-Menten parameters
173
7.4.3
Primary plots for ternary-complex mechanisms
174
7.4.4
Secondary plots
175
7.4.5
Plots for the substituted-enzyme mechanism
177
Substrate inhibition
178
7.5.1
Why substrate inhibition occurs
178
7.5.2
Compulsory-order ternary-complex mechanism
179
7.5.3
Random-order ternary-complex mechanism
179
7.5.4
Substituted-enzyme mechanism
180
7.5.5
Diagnostic value of substrate inhibition
180
Contents
7.6
Product inhibition
181
7.7
Design of experiments
184
7.8
Reactions with three or more substrates
185
Problems
8
188
Use of Isotopes for Studying Enzyme Mechanisms
8.1
Isotope exchange and isotope effects
191
8.2
Principles of isotope exchange
192
8.3
Isotope exchange at equilibrium
194
8.4
Isotope exchange in substituted-enzyme mechanisms
196
Non-equilibrium isotope exchange
197
8.5.1
197
8.5
8.6
Chemiflux ratios
8.5.2
Isomerase kinetics
200
8.5.3
Tracer perturbation
203
Theory of kinetic isotope effects
204
8.6.1
Primary isotope effects
204
8.6.2
Secondary isotope effects
206
8.6.3
Equilibrium isotope effects
207
8.7
Primary isotope effects in enzyme kinetics
207
8.8
Solvent isotope effects
209
Problems
9
211
Effect of pH on Enzyme Activity
9.1
Enzymes and pH
213
9.2
Acid-base properties of proteins
214
lonization of a dibasic acid
216
9.3
9.3.1
Expression in terms of group dissociation
constants
9.4
9.5
216
9.3.2
Molecular dissociation constants
217
9.3.3
Bell-shaped curves
219
Effect of pH on enzyme kinetic constants
221
9.4.1
Underlying assumptions
221
9.4.2
pH dependence of V and V/Km
222
9.4.3
pH-independent parameters and their
relationship to "apparent" parameters
223
9.4.4
pH dependence of Km
224
9.4.5
Experimental design
225
lonization of the substrate
226
Contents
9.6
More complicated pH effects
Problems
1_0
228
Temperature Effects on Enzyme Activity
10.1
Temperature denaturation
231
10.2
Temperature optimum
233
10.3
Application of the Arrhenius equation to enzymes
234
10.4
Entropy-enthalpy compensation
235
Problems
11
228
237
Control of Enzyme Activity
11.1
Function of cooperative and allosteric interactions
239
11.1.1 Futile cycles
239
'11.1.2 Inadequacy of Michaelis-Menten kinetics for
regulation
11.2
240
11.1.3 Cooperativity
241
11.1.4 Allosteric interactions
242
The development of models to explain cooperativity
243
11.2.1 The Hill equation
243
11.2.2 An alternative index of cooperativity
245
11.2.3 Assumption of equilibrium binding in cooperative
kinetics
11.2.4 The Adair equation
246
247
11.2.5 Mechanistic and operational definitions of
cooperativity
11.3
Analysis of binding experiments
252
254
11.3.1 Equilibrium dialysis
254
11.3.2 The Scatchard plot
255
11.4
Induced fit
257
11.5
The symmetry model of Monod, Wyman and Changeux
260
11.6
11.5.1 Basic postulates of the symmetry model
260
11.5.2 Algebraic analysis
261
11.5.3 Properties implied by the binding equation
262
11.5.4 Heterotropic effects
265
The sequential model of Koshland, Nemethy and Filmer
266
11.6.1 Postulates
266
11.6.2 Algebraic analysis
268
11.6.3 Properties implied by the binding equation
270
Contents
11.7
Association-dissociation models of cooperativity
272
11.8
Kinetic cooperativity
273
Problems
12
275
Kinetics of Multi-Enzyme Systems
12.1
Enzymes in their physiological context
277
12.1.1 Enzymes as components of systems
277
12.1.2 Moiety conservation
278
12.1.3 Characterization of enzymes in permeabilized
cells
279
12.2
Metabolic control analysis
280
12.3
Elasticities
282
12.3.1 Definition of elasticity
282
12.3.2 Common properties of elasticities
285
12.3.3 Enzyme kinetics viewed from control analysis
286
12.3.4 Rates and concentrations as effects, not
causes
12.4
Control coefficients
287
290
12.4.1 Definitions
290
12.4.2 The perturbing parameter
292
12.5
Summation relationships
293
12.6
Relationships between elasticities and control
coefficients
295
12.6.1 Connectivity properties
295
12.6.2 Control coefficients in a three-step pathway
297
12.6.3 Expression of summation and connectivity
relationships in matrix form
298
12.6.4 Connectivity relationship for a metabolite not
involved in feedback
299
12.6.5 The flux control coefficient of an enzyme for the
flux through its own reaction
300
12.7
Response coefficients: the partitioned response
301
12.8
Control and regulation
302
12.9
Mechanisms of regulation
305
12.9.1 Metabolite channelling
306
12.9.2 Interconvertible enzyme cascades
308
12.9.3 The metabolic role of adenylate kinase
310
12.10 Computer modelling of metabolic systems
312
Problems
315
Contents
13
Fast Reactions
13.1
Limitations of steady-state measurements
317
13.1.1 The transient state
317
13.1.2 The relaxation time
318
13.1.3 "Slow" and "fast" steps in mechanisms
318
13.1.4 Ambiguities in the steady-state analysis of systems
with intermediate isomerization
13.2
320
13.1.5 Ill-conditioning
321
Product release before completion of the catalytic cycle
323
13.2.1 "Burst" kinetics
323
13.2.2 Active site titration
13.3
13.4
Experimental techniques
325
-
13.3.1 Classes of method
326
13.3.2 Continuous flow
328
13.3.3 Stopped flow
329
13.3.4 Quenched flow
330
13.3.5 Flash photolysis
332
13.3.6 Magnetic resonance methods
334
13.3.7 Relaxation methods
334
Transient-state,kinetics
336
13.4.1 Systems far from equilibrium
336
13.4.2 Simplification of complicated mechanisms
340
13.4.3 Systems close to equilibrium
343
Problems
14
326
345
Estimation of Kinetic Constants
14.1
The effect of experimental error on kinetic analysis
347
14.2
Least-squares fit to the Michaelis-Menten equation
350
14.2.1 Introduction of error in the Michaelis-Menten
equation
14.2.2 Estimation of the-Michaelis-Menten parameters
350
352
14.2.3 Corresponding results for a uniform standard
deviation in the rates
14.3
Statistical aspects of the direct linear plot
354
355
14.3.1 Comparison between classical and
distribution-free statistics
355
14.3.2 Application to the direct linear plot
357
14.3.3 Lack of need for weighting
358
Contents
14.3.4 Insensitivity to outliers
'
359
14.3.5 Handling of negative parameter estimates
359
14.4
Precision of estimated kinetic parameters
361
14.5
Residual plots and their uses
Problems
References
367
372
,
375
Solutions and Notes to Problems
399
Index
407