New comprehensive biochemistry vol 06 the chemistry of enzyme action

THE CHEMISTRY OF ENZYME ACTION


New Comprehensive Biochemistry

Volume 6

General Editors

A. NEUBERGER
London

L.L.M. van DEENEN
Utrecht

ELSEVIER
AMSTERDAM *NEWYORK-OXFORD


The Chemistry of Enzyme Action
Editor

Michael I. PAGE
Department of Chemical Sciences, The Polytechnic, Huddersfield (Great Britain)

1984

ELSEVIER
AMSTERDAM-NEW YORK. OXFORD

0 Elsevier Science Publishers B.V., 1984

All rights reserved. N o part of this publication may be reproduced, stored
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ISBN for the volume: 0444 80504 4

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Preface
Recognition is of fundamental importance to living systems. How do proteins and
other macromolecules distinguish between molecules of similar shape or ions of
similar size? Recognition is controlled by the intermolecular forces between the
‘host’ and ‘guest’. The binding energy resulting from the mutual satisfying of these
forces are ultimately responsible for the catalysis and specificity of enzyme-catalysed
reactions. Understanding how enzymes efficiently transform their substrates is not
only a question of reaction mechanisms, describing the routes of bond making and

breaking processes, but also one of recognising that the interactions between the
‘non-reacting’ parts of the substrate and enzyme play a crucial role in the activation
step. The forces responsible for the chemical mechanism adopted by the enzyme are
closely related to those which account for recognition of the ‘non-reacting’ parts.
The interplay of these forces is fundamental to an appreciation of enzymic catalysis.
This volume describes the physical and organic basis of enzyme action. The
background knowledge required to understand the chemistry of enzyme action is
presented by major scientists in their own field. The borderline area between
disciplines are stimulating and rewarding and this is reflected by the high calibre of
the contributors to this volume. The level of understanding enzyme-catalysed
reactions is dependent upon the techniques employed. Determining reaction mechanisms requires a detailed knowledge of kinetic techniques and discussions of these
topics are followed by examples of their applications. The level of understanding
enzyme catalysis that has been reached by using physical organic methods is
illustrated by some biologically important examples. Finally the important contribution that biomimetic studies have made to understanding the recognition and
catalysis exhibited by enzymes is emphasised by leading exponents in the field.
Michael I. Page
Huddersfield, October 1983


This Page Intentionally Left Blank


vii

Contents
Preface

.........

................

f

.

.

.

Chapter I
The energetics and specificity of enzyme - substrate interactions
Michael I. Page (Huddersfield) . . . . . . . . . . . . . . . . . . . .

......

V

...... . . . .

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enzyme structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Michaelis - Menten kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...................................
Intra- and extra-cellular enzymes
Regulation and thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specificity and k , , , / K ,
. . . . .. . . . . .. . . . ..... . . . . . . . ... ... . ... . . . . . . . . . . . .
Rate enhancement and specificity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specificity, induced fit and non-productive binding
Approximation, entropy and intramolecular reactio

Decreasing the activation energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Utilisation of binding energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Intramolecular force fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bond stretching, 35 - Bond angle bending, 35 - Torsion, 35 - Disulphide links, 36 Non-bonded interaction, 37 13. Intermolecular force fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hydrogen bonding, 39 - Electrostatic interactions, 40 - Hydrophobicity, 44 - Dispersion
forces, 45 14. Stress and strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15. Estimation of binding energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47
50
53

Chapter 2
Non-covalent forces of importance in biochemistry
Peter Kollman (San Francisco) . . . . . . . . . . . . . . . . . . . .

..........

55

Introduction
................................
1.1. The basis
.......................................
2. The thermodynamics of non-covalent interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1. Gas phase interactions
...............................
2.2. Solution phase association . . . . . . . . . . . .
3. Examples of biological

3.1. Electrostatic forces
....................................
3.2. Dispersion forces
..................................
3.3. Hydrophobic interactions . . . .
..............................
............................
4. Summary.. . . . . . . . . . . . . . . . . .
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

1.

1
2

6
7
9
11
12
14
16
22
27
34

38

55
57
57
59
62
62
. 65
66
69
70
70


...

Vlll

Chapter 3
Enzyme kinetics
Paul C. Engel (Sheffield) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction: aims and approaches in enzyme kinetics
...............
.....
................................
2. Steady-statekinetics . . . .
2.1. Michaelis-Menten equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Relationship between K , and dissociation constant . . . . . . . . . . . . . . . . . . . .
2.3. Experimental determination of kinetic constants
.............
(a) Experimental design, 78 - (b) Lineweaver-Burk plot, 79 - (c) Eadie-Hofstee plot, 79 (d) Hanes plot, 79 - (e) Eisenthal and Cornish-Bowden plot, 82 - (f) Does the choice of
plotting method matter? 82 2.4. Non-linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5. Inhibition.. . . . . . . . . . . . . . . . . . . . . .
(a) Definition, 86 - (b) Competitive inhibit
Non-competitive inhibition, 89 - (e) Mixed inhibition, 90 2.6. Multi-substrate kinetics . . . . . . . . . . . . . .
............
(a) Types of mechanism, 91 - (b) Overall strategy, 93 - (c) Deriving a rate equation, 93 (d) Experimental determination of the rate equation for an individual enzyme, 97 - (e)
Drawing conclusions from the experimentally determined rate equation, 99 - (f) Inhibition
experiments, 104 - (g) Isotope exchange at equilibrium, 106 - (h) Whole time-course
studies, 106 3. Rapid reaction kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
....
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73
73
76
76
78

78

82
86

91

107
109

Chapter 4
Aspects of kinetic techniques in enzymology
Kenneth T. Douglas and Michael T. Wilson (Colchester) . . . . . . . . . . . 111
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
..........
2. Use of steady-state techniques . . . . . . . . . . . . .
..............
2.1. Note on measurement of initial velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Experimental treatment of transients . . . . . . . . . . .
3.1. Determination of k,,
........__.....
4. Stopped-flow methods .
................................
4.1. Binding reactions
......................................
4.2. Burst kinetics . . . . . . . . . . . . . . . . . . . . . . . .
............
.........

5.1. Ligand binding . . . . . . . . . . . . . . . . . .

........._....._
5.2. Coupled reactions, linked redox reactions and structural rearrangements . . . . . . . . . . . . .
6. Conclusion . . . . . . . . . .
References . . . . . .
...................................................

111
113
114
115
116
119
119
121

123
123
124
125
125

Chapter 5
Free-energy correlations and reaction mechanisms
Andrew Williams (Canterbury) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Brensted relationships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

127
128

ix
Simple proton transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Molecular basis of the Bransted relationship and interpretation of the exponents . . . . . . .
Statistical treatments
.....
The extended Brcanste
Meaning of the Brans
(a) Effective charges in transition states, 134 - (b) Additivity of ‘effective’ charge, 135 - (c)
Transition state index (a),136 2.6. Curvature in Bransted correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Eigen curvature, 137 - (b) Marcus curvature, 139 -

128
129
130

...
..............
................................................

141
142
143

2.1.
2.2
2.3.
2.4.
2.5.

3. Indices of el

(a) Additivity of sigma values, 147 - (b) Resonance and inductive effects, 148 - (c)
Sigma-minus parameters, 148 - (d) Sigma-plus parameters, 149 - (e) More than one
transmission path for u , 151 - (f) The Yukawa-Tsuno equation, 155 3.2. Separation of inductive, steric and resonance effects . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Taft’s polar ( 0 *) and steric ( E , ) parameters, 158 - (b) Taft’s steric parameter ( E s ) , 161
- (c) Relationship between u * and u,, 162 - (d) Meaning and use of E, and 6, 163 - (e)
Other steric parameters, 164 - ( f ) Values of u * for alkyl groups, 166 4. Hydrophobic interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1. Other hydrophobic parameters
4.2. Non-linear hydrophobic relation
4.3. Molar refractivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4. Additivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5. Ambiguities arising from interrelationships between parameters . . . . . . . . . . . . . . . . . . .
4.6. Application to n
5. Solvent effects . . . .
..................................
..................................
5.1. Reporter groups
..............................................
6. General equations of
6.1. Swain-Scott and Edwards relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7. Cross-correlation and selectivity-reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1. Cross-correlation
.......................................
7.2. Reactivity-selecti
8. Estimation of ionisation constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9. Elucidation of mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.1. Mechanistic identity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Correlations with model reactions, 187 9.2. Changes in mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3. Change in rate-limiting step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9.4. Dependece on concentration as a free energy correlation
9.5. Distinction between kinetic ambiguities . . . . .
9.6. Proton transfer . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 6
Isotopes in the diagnosis of mechanism
Andrew Williams (Canterbury)

.............................

1. Theoretical background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Measurement of isotope effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

137

156

166

170
171
172
172
173
175
177
177
179

179
183
183
186
186
189
191

197
200

203
203
205


X

3. Equilibrium isotope effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Primary isotope effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.................
4.1. Variation in primary isotope effects . . .
4.2. Solvent isotope effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Nucleophilic versus general base catalysis, 213 - (b) Fractionation factors, 214 4.3. Heavy atom isotope effects
...
.......................
5. Secondary isotope effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. Labelling techniques . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.......................
6.1. Position of bond cleavage

6.2. Proton transfer . . . . . . .
..
6.3. Detection of intermediates by isotope exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4. Isoracemisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5. Double-labelling experiments
....
6.6. Isotopic enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General references . . . .
................................................

Chapter 7
The mechanisms of chemical catalysis used by enzymes
Michael I. Page (Huddersfield) . . . . . . . . . . . . . . .

....

1. Introduction . . .
2. General acid base
2.1. Catalysis by stepwise proton tra
2.3. Catalysis by preassociation . . .
2.4. Concerted catalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Metal-ion catalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . .
5. Catalysis by coenzymes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1. Pyridoxal phosphate coenzyme
................
5.2. Thiamine pyrophosphate coenzy
5.3. Adenosine triphosphate (ATP)

6.2. Nicotinamidecoenzymes . . . .

6.3. Flavin coenzymes . . . . . . . . . .
(a) Oxidation of amino and hy
thiols, 261 - (c) Reductive activation of oxygen by dihydroflavins, 261 - (d) Flavomonooxygenase, 262 ....
6.4. Electron transfer with metals . . . . . . . . . . . . . . . . . . . . .
edox
(a) Thermodynamic stability of metal complexes, 263 - (b)
metalloproteins and oxygen, 264 - (d) Iron-containing proteins and enzymes, 265 - (e)
Copper-containing oxidases and monooxygenases, 261 References . .
..........................................

207
209
21 1
213
218
219
220
220
222
222
223
225
226
226
227

229
229
230
23 1

235
236
236
231
240
243
246
246
249
252
253
256
256
251
259

262

269


xi
Chapter 8
Enzyme reactions involving imine formation
Donald J. Hupe (Rahway) . . . . . . . . . . .

. . ... . . . ... . . . . . . . ....

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . ......

....
2. Iminium ion formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4. Aldolases . . . .
..................
5. Transaldolase .
6. Acetoacetate decarboxylase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I . Pyruvate-containing enzymes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8. Dehydratases . . . . . . . . . . . . . . . . . . . . . . . . . .
....
9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgement
...................................
.......
References . . . . . . . . . . . . .

27 1
27 1
272
216
279
286
288
29 1
294
298
298
299

Chapter 9

Pyridoxal phosphate-dependent enzymic reactions: mechanism and stereochemistry
Muhammad Akhtar, Vincent C . Emery and John A. Robinson (Southampton) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Historic background: Braunstein-Snell hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Pyridoxal phosphate-dependent reactions involving C,-CO, H bond cleavage . . . . . . . . . . . . .
3. Pyridoxal phosphate-dependent enzymic reactions involving C,-H bond cleavage . . . . . . . . . .
.....
...................
3.1. Aminotransferases . . . . . . . . . . . . . . . . .
(a) Metabolic background, 314 - (b) Transaminations at the C, of amino acid, 315 - (c)
Mechanistic studies on miscellaneous transaminations, 3 15 -

...............................
..................
................
3.4. 5-Aminolevulinate synthetase (ALA synthetase
..............
4.1. General introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
...........
4.2. P-Replacement reactions . . . . . . . . . . . . . . . . . . . . .
(a) Tryptophan synthetase, 331 ..............................
4.3. 8-Elimination-deamination reactions . . .
) Tryptophanase, 338 - (c) Miscellaneous
(a) Tryptophan synthetase-/3, protein, 33
enzymes, 339 5. Pyridoxal phosphate-dependent reactions occurring at C, . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1. Enzymic aspects . . . .
.................................
...
..................
5.2. Stereochemical aspects . . . . . . . . . . . . . .
rnary complexes . . . . . . . . . . . . . .

6. Structure and molecular dyn
6. 1. Electronic spectrum of the coenzyme chromophore . . . . . . . . . . . . .
6.2. Chemical studies on binary (coenzyme-enzyme) complexes . . . . . . . . . . . . . . . . . . . . . .
6.3. Stereochemical aspects of the reduction of Schiff base at C-4' with NaBH, . . . . . . . . . . .
6.4. Structure and stereochemistry of the substrate-coenzyme bond in ternary complexes . . . .
6.5. Stereochemical and mechanistic events at C, of the substrates and at C-4' of the coenzyme
..............
during catalysis . . . . . . . . . . . . . . . . . . . . . .
rnarycomplexes . .
6.6. Orientation of the pyridinium ring of the coenzy
...............................

..............

303
306
314
314

319
320
327
33 1
33 1
331
336

343
343
344

349
349
353
354
355
359
366
367


xii
Chapter 10
Transformations involving folate and biopterin cofactors
S.J. Benkovic and R.A. Lazarus (University Park) . . . . . . . . . . . . . . . . 373
I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Reduction
..
.....
.......

............................
5. Formyltransfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. Methyl transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.....

...

......

..

Chapter 1 1
Glycosyl transfer - The Physicochemical Background
Michael L. Sinnott (Bristol) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
...................................
2. Effects of the
gen in space . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1. The anomeric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Geometrical changes in oxocarbonium ion formation
......
.......
2.3. Stereoelectronic control of reactions of acetals? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. The chemistry of processes occurring with electrophiles or acids . . . . . . . . . . . . . . . . . . . . . .
3.1. Lifetimes of oxocarbonium ions
..
...................
3.2. Preassociation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3. Chemical synthesis of glycosides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4. Effect of oxocarbonium ion structure . . . . .
3.5. Intramolecular nucleophilic assistance . . . . . .
3.6. Electrostatic stabilisation? . . . . . . . . . . . . .
4. Processes occurring via the application of acidic
oxygen-leavinggroups . . . . . .
4.1. Specific acid catalysis of acetals,
..........................
4.2. Intramolecular nucleophilic assistance in specific acid-catalysed processes . . . . . . . . . . . .
4.3. Intermolecular general acid catalysis of the hydrolysis of acetals and ketals . . . .
4.4. Intramolecular general acid catalysis of the hydrolysis of acetals, ketals and glycosides

4.5. Intramolecular general acid catalysis concerted with intramolecular nucleophilic (or elec-

4.6. Electrophilic catal
5. Acid- and electrophi
sulphur and fluorine
5.1. Hydrolysis of gl

373
373
375
376
379
38 1
381
385

389
389
390
39 1
395
396
398
398
399
402
403
406
407
408

408
413
413
417
419
420

......................

5.3. Hydrolysis of hemithioacetals, hemithioketals, and thio- and thia-glycosides . . . . . . . . . . .
5.4. Hydrolysis of glycosyl fluorides . . . . . . . . . . . . . . . . . . . . .
6. Envoi . . . . . . . . . . . . . . . . . . . . .
.....
References . . . . . . . . . . . . . . . . . . . .
.....

42 1
422
423
425
426
421
427


Chapter 12
Vitamin B12
Kenneth L. Brown (Arlington)

.. . . .. . . . . . .. . . . . ... . . . . . . . . ..

,

1. Introduction and scope of this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Structure.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Oxidation states
..........................................

..........................................

5. Chemical reactivity of organocobalt complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. I . Reactions in which carbon-cobalt bonds are formed
(a) Synthesis of organocobalt complexes via cobalt(1) reagents, 439 - (b) Synthesis of
organocobalt complexes via cobalt(I1) reagents, 441 - (c) Synthesis of organocobalt
complexes via cobalt(II1) reagents, 443 5.2. Reactions in which carbon-cobalt bonds are cleaved . . .
....
(a) Mode I cleavage of carbon-cobalt bonds, 445 - (b) M
cobalt
bonds, 447 - (c) Mode 111 cleavages of carbon-cobalt bonds, 450 5.3. Axial ligand substitution reactions . . . . . . . . . . . . . . . . .
...........
5.4. Reactions of cobalt-bound organic ligands . . . . . . . .
6. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . .
.........

Chapter 13
Reactions in micelles and similar self-organized aggregates
Clifford A. Bunton (Santa Barbara) . . . . . . . . . . . . . . .

433
433

435
437
438
439

444

452
455
457
457

. . . . . . . . . . . 46 1

Introduction . . . . . . . . . . . . . . . .
Formation of normal micelles . . . .
Micellar structure in water . . . . . .
Kinetic and thermodynamic effects . . . . . . . .
.........................
4.1. Micellar effects upon reaction rates and e
...........................
4.2. Quantitative treatments of micellar effects in aqueous solution . . . . . . . . . . . . . . . . . .
4.3. Quantitative treatment of bimolecular reactions . . . . . .
...............
4.4. Second-order rate constants in the micellar pseudophase . . .
....
5. Reactive counterion micelles
............
.......................
6. Reactions in functional micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7. Stereochemical recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8. Submicellar and non-micellar aggregates
9. Micelles in non-aqueous systems . . . . . . . . . .
.............
9.1. Normal micelles in non-aqueous media
9.2. Reverse micelles in aprotic solvents . . . . . . . .
.......................
10 Related systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1. Reactions in microemulsions
.....,.......
10.2. Reactions in vesicles
............
.......................
11. Photochemical reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12. Isotopic enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13. Preparative and practical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Noteaddedinproof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.
2.
3.
4.

433

46 1
462
464
468

468
47 1
472
475
479
482
487
487
490
490
49 1
493
493
495
496
497
498
499
500
500


XiV

Chapter 14
Cyclodextrins as enzyme models
Makoto Komiyama and Myron L. Bender (Tokyo and Evanston)

. . . . . 505

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Formation of an inclusion complex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Catalysis by cyclodextrins
3.1. Catalysis by the hydro
3.2. Effect of reaction field
4. Specificity in cyclodextrin
4.1. Substrate specificity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Product specificity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Models of hydrolytic enzymes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model of carbonic anhydrase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model of metalloenzymes . . , . . . . . . . . . . . . . . . . . . . . .
Introduction of a coenzyme moiety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements
..
...
...
...
...
...
5.1.
5.2.
5.3.
5.4.

......................................

Chapter I5
Crown ethers as enzyme models

J. Fraser Stoddart (Sheffield) . . . . . . . . . . . . . . . . . . . . . . . .

.

. . . . . . . 529

1. Introduction . . . . . . . . . . .
2. Ground-state binding and reco
2.1. Binding forces . . . . . . . .
2.2. Complexation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3. Enantiomeric differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,
2.4. Substrate recognition
...
2.5. Allosteric effects . . .
.........................
.................
3. Binding and recognition at
3.1. Enzyme mimics: hydrogen-transfer reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Enzyme mimics: acyl transfer reactions . . .
3.3. Enzyme analogues: Michael addition reactio
4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...
..
References . . . . . . . .

.

505
506
511

511
513
514
514
517
519
520
520
524
525
525
526
526
526

529
530
530
538
540
542
544
546
546
550
556
558
559

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563

CHAPTER

The energetics and specificity of enzyme-substrate
interactions
MICHAEL I. PAGE
Department of Chemical and Physical Sciences, The Polytechnic, Queensgate, Huddersfield HD1 3HD, Great Britain

1. Introduction
Life is a dynamic process which depends upon the recognition (interaction) between
inanimate molecules. Living organisms have the capacity to utilize external energy
and matter to maintain and propagate themselves. The interactions between substrate and enzyme that account for the catalysis and specificity of the reactions of
intermediary metabolism also account for the energy-coupling processes which
enable the exchange of chemical energy and allow the system to do work.
Because of their relative masses the electron density distribution controls the
movement of nuclei. Electronic interactions and distortions of electron density
distributions are responsible not only for the formation of structures and complexes
but also for chemical reactions themselves. It is thus logical to examine the forces
that hold enzymes in their unique 3-dimensional structure, then the energetics of
enzyme-substrate interactions and finally the forces or mechanism by which the
bond-making and -breaking processes occur during the reaction catalysed by the
enzyme.
Enzymes are usually globular proteins and are distinguished from fibrous proteins
by the ability of the pieces of secondary structure to associate and give a stable
3-dimensional structure. The forces responsible for protein folding are similar to
those used in the formation of antibody-antigen or hormone-receptor complexes
and to those giving rise to enzymic catalysis. The problem with protein folding is
how does the system gain enough energy from hydrophobicity, hydrogen bonds and
all the various electrostatic interactions to overcome the loss of conformational

entropy and steric strain that occurs in the folded state? The problem with complex
formation is how does the system gain enough energy to overcome the loss of
translational, rotational and vibrational entropy that occurs upon complexation?
The problem with enzymic catalysis is how are these interactions expressed in the
transition state but not in the ground state of the enzyme-substrate complex?
It is necessary to understand the structures of folded proteins so that we are
aware of the environment or force field generated by the enzyme which in turn
controls the interaction between substrate and enzyme. This chapter will briefly
Michael I. Page (Ed.), The Chemistry of Enzyme Action
0 1984 Elsevier Science Publishers B. V .


2
review the problems associated with understanding the energetics of enzymic catalysis, the strength and geometrical requirements of the various forces available to
molecular systems (which is dealt with in detail in Chapter 2) and how these forces
stabilise transition states.

2. Enzyme structure
Proteins, with a specific function and isolated from a single source, usually have a
homogeneous population of molecules all with the same unique amino acid sequence. Yet with 20 different amino acids possible at each position in a polypeptide
chain of n residues, 20" different primary structures are theoretically possible.
Furthermore, the great majority of all molecules of a natural protein may exist in a
unique conformation despite the degrees of freedom formally permitted by rotation
about the peptide backbone (motility) and side chains (mobility). For example, with
only 3 conformations defined per residue, a polypeptide chain of 210 residues would
have a theoretical possibility of existing in 1 O 1 O0 different conformations.
Reversible unfolding of proteins has been known for some time. The folding of
several proteins occurs spontaneously showing that the required information for
folding is present in the protein's primary structure [ 11.
The forces stabilising the folded state are presumably similar to those that bind

the substrate to enzymes. The conventional stress with protein structures is on (i) the
primary structure of the peptide sequence, i.e. the linear covalent linkage, (ii) the
secondary structure of the hydrogen bonds between the peptide links, (iii) the
tertiary structure formed by hydrophobic interaction which is largely responsible for
many protein folds, together with charge-charge interactions and disulphide linkages.
The production of a disordered polypeptide chain by removing just a few of the
interactions which normally contribute to the stability of the folded state is well
illustrated by breaking the 4 disulphide bonds in ribonuclease A - even in the
absence of a denaturant, the reduced protein is fully unfolded despite all other
favourable interactions, such as hydrogen bonds and hydrophobic forces, still being
possible [2].
Detailed models of the folded states of proteins depend almost entirely on X-ray
diffraction analysis of the protein crystal. Although side chains and flexible loops on
the surface may be mobile in solution, protein conformation in solution is essentially
that determined in the solid crystal. The atoms of folded proteins are generally well
fixed in space.
The overall structure-of a folded protein is remarkably compact. The extended
chain of carboxypeptidase, with 307 residues, would be 1114 A long but the
maximum dimension of the folded molecule is only about 50 A. However, the
polypeptide topology in roughly spherical, globular proteins has never been observed
to form knots [3].
The non-polar side chains tend to be on the inside, shielded from the solvent, and


3
generate globular structures. The ionised hydrophilic side chains are nearly always
on the outside and help maintain solubility. Many polar groups are buried in the
hydrophobic interior but these tend to be “neutralised” by hydrogen bonding [3].
However, internal hydrogen bonds probably provide no substantial net stabilisation
energy to the folded state because similar hydrogen bonds would be formed with

water in the unfolded state. Hydrogen bonds are probably important in limiting
conformational fluctuations in the folded protein. The major difference between
folded and unfolded molecules is probably the decreased exposure of the non-polar
groups to water.
Upon folding, there is a large decrease, amounting to several thousand A2, in the
surface area of the protein exposed to water. Even choosing the transfer of amino
acids from water to a non-polar solvent as an estimation of these changes (which, as
we shall see later, underestimates the change) yields hundreds of kJ/mole. The free
energy of folding amounts to only 15-60 kJ/mole which shows the large unfavourable entropic contribution which accompanies folding as a result of the loss of
internal rotations.
The polar external surface of a protein which is in contact with water is usually
much more mobile than the interior. Generally, the higher the proportion of charged
amino acids in a protein the greater is its flexibility. Most enzymes have a high
proportion of hydrophobic amino acids relative to charged ones. Together with
disulphide bridges this makes proteins have low motility and mobility. An exception
is the kinases whch are not globular, have a high content of charged amino acids,
are not cross-linked, and are relatively flexible [6].
Charge-charge interactions between two opposite charges in a buried hydrophobic region of low dielectric constant could be important in strengthening the
fold.
Proteins found in membranes can experience very different solvation environments. In the membrane the environment may be similar to a hydrocarbon solvent
while at its surface the medium slowly changes to an aqueous region. Proteins or
parts of proteins located in the non-polar region of the membrane are expected to
have very few exposed charged groups.
The atoms within a protein molecule are very closely packed with few holes about 75% of the volume of the interior is filled with atoms [4]. However, the
packing density does appear to vary somewhat which may be important for the
flexibility of the molecule. Any holes present within the molecule tend to be
occupied by solvent molecules as in chymotrypsin and carboxypeptidase. In micelles,
by contrast, the packing density is low with the volume occupied by the surfactant
atoms being large. Enzymes are not like micelles and the “oil drop” model of protein
structure is incorrect. The low packing density of micelles accounts for the much

lower efficiency of micellar catalysis (Chapter 13) compared with enzymic catalysis;
the surface area of contact between micelle and substrate is much less than that
between enzyme and substrate. The close packing of protein interiors prevents water
molecules being trapped in non-polar cavities and maximises the packing energy.
Most of the larger protein structures are composed of 2 or 3 globular units, each


4

of 40- 150 residues. However, disulphide bonds always link cysteine residues within
the same domain. Each domain is closely packed with flexibility between the
domains.
Proteins from different species are often functionally indistinguishable; even
though their primary sequences may be different their folded conformations are
often very similar. Even more surprising is the observation that functionally unrelated proteins sometimes have similar folded conformations, e.g. superoxide dismutase and immunoglobulin domain [5]. Structural homology between proteins of
different amino acid sequence may be a packing phenomenon.
Although the high degree of time-averaged order of the individual atoms of
folded proteins in the crystalline state permits their location in space many protein
molecules exhibit varying degrees of flexibility. The motions have very different
activation energies ranging from 5 to over 100 kJ/mole, but their importance, if any,
is often unknown. For example, in most proteins aromatic rings of tyrosine and
phenylalanine residues flip by 180’ rotations at a rate greater than 104/s. In general,
experimental techniques such as fluorescence quenching and relaxation, phosphorescence and NMR indicate a rather fluid, dynamic structure for globular proteins [ 6 ] .
It is of interest to note that the smaller the substrate, apparently, the greater is the
requirement for a rigid enzyme. Cytochrome c transfers electrons and is very
immobile, the solution structure is almost identical to that found in the solid state
[6 ] .The flavodoxins, transferring hydride ion; catalase, of molecular weight 284 000
with hydrogen peroxide as substrate and carbonic anhydrase, of molecular weight
31000 with carbon dioxide as substrate show a slight increase in mobility. Lysozyme, of molecular weight 14000 with a polysaccharide as substrate has the same
outline fold in solution and in the solid state but many aromatic rings and aliphatic

groups are mobile. Kinases, molecular weight 45 000, transfer phosphate from ATP
and show even greater mobility but like all enzymes still have well defined structures.
NMR relaxation parameters, by virtue of their sensitivity to both the frequencies
and the amplitudes of motions, are potentially the best source of experimental
information on macromolecular dynamics, largely for motions in the frequency
range lo6- 10’’/sec. However, it is difficult to find a unique model and often several
models, differing largely in the formulation of amplitude factors, account equally
well for the experimental data. Physically non-existent motions may erroneously be
assumed to exist or motions which actually do contribute to relaxation may be
suppressed in the analysis [7]. Succinctly, some techniques indicate a rigid inflexible
system whereas others suggest that enzymes are fluid and flexible. The apparent
dichotomy may be attributable to the application of concepts derived from macroscopic observations (density, elasticity, heat capacity, etc.) of an assembly of a large
number of molecules or atoms to one molecule of an enzyme. There is no clear-cut or
sharp boundary between statistical mechanics and thermodynamics. A macroscopic
system undergoes incessant and rapid transitions among its microstates. Extensive
parameters, such as energy and volume, have average values equal to the sum of the
values in each of the subsystems and undergo macroscopic fluctuations. Statistical


5
distribution functions give the probability that any specified value of a fluctuating
extensive parameter will be realised at a given moment. The distribution function for
macroscopic systems is so sharply peaked that average values and most probable
values are nearly identical. The most probable values are those that maximise the
distribution function. The average value of the deviation from the average parameter
is clearly zero, but the average square of the deviation is non-zero and is called the
mean square deviation, a convenient measure of the magnitude of the fluctuations,
although it is only a partial specification of the distribution. The distribution
becomes increasingly sharp as the size of the system increases [8].
Familiar macroscopic systems consist of many discrete particles, e.g. 6 x

molecules per mole, and their thermodynamic properties are very sharp. In contrast
the. individual molecules of proteins are very small systems consisting of relatively
few particles, a few thousand atoms, and statistical fluctuations will cause the
thermodynamic parameters to be blurred (Fig. 1).
A typical globular protein may have a molecular weight of 25000 and each
molecule a mass of 4.2 X
g and a volume of 3.2 X
cm3. The root mean
square volume fluctuation is about 0.2%per molecule. A system with similar gross
thermal properties but one hundredth of the size of the protein molecule, i.e.
3.2 X
cm3 would show a volume fluctuation of about 28, whereas a system of
volume 3.2 cm3 would show a volume fluctuation of only 2 X lo-"%.
Although globular proteins appear to be only marginally stable in the folded state
this does not imply conformational flexibility. Indeed environmental changes do not
easily induce changes in the folded state. Crystallisation under different conditions
does not produce large changes in conformation and even the binding of ligands
tends only to alter the relative orientations of sub-units or domains. In no instance
has a substantial change of conformation of a globular protein been observed even

Thermodynamic value

Fig. 1. The distribution function for thermodynamic values showing the difference between the most
probable and average value of the thermodynamic function.


6
when the binding energies of the ligands are comparable to the net stability of the
folded conformation [9]. Substantial energy barriers must therefore separate alternative conformations of globular proteins. Of course, proteins have considerable
thermal energy and consequently their structures, like all molecules, fluctuate but the

atoms within the molecule do not appear to deviate far from their positions
determined crystallographically. Of course this is not true of all proteins, surfaces
and structural units, for example, may show high mobility and motility [6].

3. Michaelis-Menten kinetics
Experimentally, the initial rate, v, of enzyme catalysed reactions is found to show
saturation kinetics with respect to the concentration of the substrate, S. At low
concentrations of substrate the initial rate increases with increasing concentration of
S but becomes independent of [S] at high or saturating concentrations of S (Fig. 2).
This observation was interpreted by Michaelis and Menten in terms of the rapid and
reversible formation of a non-covalent complex (ES), from the substrate (S) and
enzyme (E), which then decomposes into products (P) (Eqn. 1).

This scheme led to the familiar Michaelis-Menten equation.

where K , is the Michaelis constant which is the concentration of substrate at which
the initial rate is hay the maximal rate at saturation, V,,,. The first-order rate
constant for the decomposition of ES is k,,, (the turnover number). At low
concentration of substrate, where [S] << K,, v is given by Eqn. 3, with k , , , / K ,
being an apparent second-order rate constant.

At high concentrations of S, where [S] >> K,, v is given by Eqn. 4 and becomes
independent of S.
~ = k c a t [ E o l =‘ma,

(4)

Although the Michaelis-Menten equation (Eqn. 2 ) is valid for several enzymecatalysed reactions the mechanism (Eqn. 1) is not always followed. The measured
K , and k,,, values are not always equal to the dissociation constant, K , , for the

7

c
TI

151

Fig. 2. Reaction rate-substrate concentration profile for a reaction obeying Michaelis-Menten (or
saturation) kinetics.

enzyme-substrate complex and the rate constant for decomposition of ES, respectively. The apparent dissociation constant K , can be less than K , , i.e. apparent
tighter binding of substrate, if additional intermediates, covalently or non-covalently
bound, are formed during the reaction pathway and the rate-limiting step is the
reaction of one of these intermediates. Similarly, K , > K , if the rate of dissociation
of ES to E and S is comparable or slower than the forward rate of reaction of ES
(Briggs-Haldane kinetics). The measured value of k,,, may also be a function of
various and several microscopic rate constants (see Chapter 3).
When the activation energies for the catalytic steps have been sufficiently lowered,
the binding of the substrate or the desorption of the product may become at least
partially rate-limiting.

4. Intra- and extra-cellular enzymes
Extracellular enzymes show little motility and are not very sensitive to the ionic
strength of the solutions in which they are dissolved. They are synthesised in one
environment but are then placed in another outside the cell. In particular, salt
concentrations vary between the two environments; for example, calcium concentration outside the cell is lo4 times greater than in the cell. Furthermore many
extracellular enzymes are produced as zymogens and are activated by removing a
section of the protein. Insensitivity to the environment is an essential requirement of

8

these enzymes if activity is to be maintained in extracellular fluids of uncertain
composition. Extracellular enzymes are usually cross-linked several times by disulphide bridges. The more oxidising environments generally encountered outside
cells make the disulphide bonds correspondingly more stable. Stability depends
upon the thiol redox potential of the environment but, of course, the disulphide
bond could be formed inside the cell.
Intracellular enzymes exist in a more controlled medium and as the requirement
for rigidity is less very few intracellular enzymes have disulphide cross-links. Some
enzymes, particularly those involved in electron transfer, have a very fixed fold.
Intracellular enzymes, in distinction to most extracellular ones, have a quaternary
structure.
Individual enzymes in vivo have different constraints and requirements. Generally, intracellular enzymes are required to maintain a constant concentration of the
various metabolites and this may be achieved by having a wide variation in the
reaction flux of the material through the various metabolic pathways. The reaction
rate will vary with [S] if the enzyme is working below saturation, K , >> [S], and the
rate is given by Eqn. 3. However, extracellular enzymes are often faced with
dramatic changes in the concentration of their substrates and yet are required to
maintain a steady flow of material for absorption and use by the cell. The reaction
rate will be independent of [S] if the enzyme is working under saturation conditions,
[S] >> K,, and the rate is given by Eqn. 4.
Given the obedience to Michaelis-Menten kinetics one may obtain information

Fig. 3. A reaction rate showing saturation kinetics has different rates, u , . and u2, at different substrate
concentrations, S, and S,, respectively.


9
about the optimal physiological concentration for the substrate [ 101. Obviously, the

maximal change in rate for a change in substrate concentration is when S and v are
minimal (dv/dS is maximal at S = 0, v = 0). If there is an optimal physiological
concentration for the substrate, enzymes could have evolved to bind the substrate
more or less tightly to maximise the changes in rate with respect to changes in
substrate concentration. The problem is illustrated in Fig. 3, with two substrate
concentrations S , and S, with respective rates v I and v,. The minimal fractional
change in substrate concentration (S,/S,) to obtain a given change in velocity x,
occurs at the K , for the reaction.
From Eqn. 2 the substrate concentration is given by

If v,

= v,

+ x, the concentration of S, is given by

The derivative of S2/S, is zero when v l + v,
reaction.

V,

=x

=

V
,

(Eqns. 7-9), i.e. at the K , of the

+ 28, = v, + v2

(9)

The optimal physiological concentration of the substrate is at its K , [10,1I].

5. Regulation and thermodynamics
Biochemical reactions exist to bring about the net formation of a compound which
may be required either of itself or as the starting material of a further process. A
metabolic pathway could involve the conversion of a large, or constantly maintained,
concentration of substrate S into an equally well maintained pool of product P (Eqn.
10).


10
The sequence may involve the formation of several intermediates, B, C, D and
require the conversion of coenzymes w and y into x and z , respectively. The chemical
flux out of S and P may be controlled by: (i) changing the concentrations of S or P,
(ii) changing the concentrations of the coenzymes, (iii) changing the activities of the
enzymes involved in the pathway.
Although the thermodynamics of the step S -+ B may be unfavourable, net
synthesis can occur from left to right if the overaN equilibrium constant is favourable. Thermodynamically, Eqn. 10 may be described by Eqn. 11 where AG is the
Gibbs free energy change for the reaction under the given conditions and AGO is the
change in Gibbs energy for the reaction with reactants and products at the standard
state concentrations.

At thermodynamic equilibrium there can be no net flow. Enzymes do not alter the
position of equilibrium between unbound substrates and products. If B, C or D are
removed rapidly their concentration will not correspond to their equilibrium value
but rather to their steady state concentrations. The total chemical flux out of C is

given by the sum of the fluxes out of C into B and D. The total chemical flux into C
is given by the sum of the flux of B into C and that of D into C. The rate of
appearance of C is then given by the difference of these two sums (Eqn. 12).

The flux through a sequence of reactions cannot generally be controlled by suppressing the activity of the enzyme catalysing any one of the reactions. The positions of
the reaction with respect to its equilibrium value and with respect to the degree of
enzyme saturation are important. If any of the steps in Eqn. 10 are near equilibrium
the rate of the reverse reaction will be similar to that of the forward reaction and this
step cannot, therefore, limit the rate of production of P. It is often suggested that
control of metabolism through alteration of enzyme activity should be exerted at
reactions which are far from thermodynamic equilibrium. If the substrate concentration is not in excess and if the dissociation constants for substrate and product, K ,
and Kp, respectively, are very different it is conceivable that the overall equilibrium
constant K (Eqn. 14) is not a good guide to the value of the equilibrium constant, K ,
(Eqn. 13).