Initial Rate Enzyme Kinetics

332 Pages·1975·9.618 MB·English

by  Herbert J. Fromm

Molecular Biology
Biochemistry and Biophysics
22
Editors:
A. Kleinzeller, Philadelphia· G. F. Springer, Evanston
H. G. Wittmann, Berlin
Advisory Editors:
C. R. Cantor, New York· F. Cramer, Gattingen . F. Egami, Tokyo
M. Eigen, Gattingen . F. Gros, Paris· H. Gutfreund, Bristol
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E. Katzir, Rehovot . B. Keil, Gif-sur-Yvette· M. Klingenberg, Munich
I. M. Klotz, Evanston· F. Lynen, Martinsried/Munich
W T. J. Morgan, London· K. Muhlethaler, Zurich· S. Ochoa, New York
G. Palmer, Houston· I. Pecht, Rehovot . R. R. Porter, Oxford
W Reichardt, Tiibingen . H. Tuppy, Vienna
J. Waldenstram, M alma
Herbert J. Fromm
Initial Rate
Enzyme Kinetics
With 88 Figures
Springer-Verlag Berlin· Heidelberg· New York 1975
Professor HERBERT 1. FROMM, Ph. D.
Iowa State University
Biochemistry and Biophysics Department
Ames, IA 500lOjUSA
Distributed in the British Commonwealth Market
by Chapman and Hall, London
ISBN-13: 978-3-642-80968-2 e-ISBN-13: 978-3-642-80966-8
001: 10.1007/978-3-642-80966-8
Library of Congress Cataloging in Publication Data. Fromm, Herbert 1. 1929-. Initial rate enzyme kinetics.
(Molecular biology, biochemistry, and biophysics; v. 22). Bibliography: p. Includes indexes. i. Enzymes. 2. Chemical
reaction, Rate of. I. Title. II. Series. [DNLM: 1. Enzymes-Metabolism. WI MOl95T no. 22/QU135 F932]
QP601.F76. 574.1'925. 75-20206
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© by Springer-Verlag Berlin Heidelberg 1975
Softcover reprint of the hardcover 1st edition 1975
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Preface
Enzyme kinetics has undergone very rapid growth and development
during the past fifteen years and has been well received by the
biochemical community. A cursory glance at the current biochem
ical literature reveals the increasing popularity of enzyme ki
netics1 yet, there are very few books available to guide the
enzymologist who wishes to conduct kinetic experiments.
This monograph was undertaken to provide the fledgling kineticist
with an outline of contemporary initial rate enzyme kinetics. A
large portion of the material contained in this book is presented
in a second-year, graduate-level course in biochemistry at Iowa
State University. I have found that the presentation in this
course has enabled students without a strong background in math
ematics to undertake initial rate studies at the research bench.
The monograph obviously is more comprehensive than any course
could be, and should permit similar accomplishment.
As the title implies, the major emphasis of this monograph is on
initial rate enzyme kinetics. I considered at length the advis
ability of including chapters on integrated rate equations and
on the theory and application of rapid reaction kinetics, such
as rapid-mixing stopped-flow, and temperature-jump kinetics.
These, however, are topics that would require a good deal of
space to develop if they were to be helpful to the beginner.
Some deviation from initial rate kinetics was required when the
topics of cooperativity and allostery were broached. A very large
fraction of the research in this area of biochemistry has in
volved static binding measurements, and the current literature
clearly reflects this. It was necessary, therefore, to intro
duce these topics within the framework of the simpler equilib
rium binding models before the kinetics of allostery and coop
erativity were considered.
It will become quite obvious that a number of topics are omitted
that might have been included inChapter IX. In an area of research
such as allostery, which is in a state of flux at this writing,
concepts that are not widely accepted or clearly defined are
either treated superficially or not included.
Books on kinetics usually cover theory and interpretation of
data in the literature, but rarely present the experimental pro
tocol. Chapters III and VI are devoted in large measure to instruc
tion on setting up and carrying out initial rate and isotope
exchange experiments. Although these sections may not provide
enlightenment for the advanced student, they may serve to lower
VI
the energy barrier to potential experimentalists who wish to
use their theoretical knowledge for practical ends.
Acknowledgement
Thanks are in order to the faculty members of the Department of
Biochemistry and Biophysics, Iowa State University, and to my
graduate students and post-doctoral fellows for their help and
encouragement both before and during the writing of the book.
The critical reading of sections of the manuscript by Drs. JON
APPLEQUIST, JAMES ESPENSON, JAMES LUECK, DAVID METZLER, and
GREGORIO WEBER is gratefully acknowledged. Special and sincere
thanks to go Drs. DANIEL PURICH and DONALD SIANO whose help
made writing sections of the book an educational experience
for me. Finally, I wish to acknowledge the consideration and
encouragement I received from my wife, KATHY, who in seeking
her own liberation, did not impede my work.
Ames, January 1975 HERBERT J. FROMM
Contents
Chapter I Nomenclature, Definitions, and Evolution of
the Kinetic Mechanism •.....•.•••.........•...
A. Nomenclature.............................. 3
B. Evolution of Initial Rate Kinetics........ 6
References. . . . . . . . • . . . . . • . . • . . . . . . . . . . . . . . 20
Chapter II Derivation of Initial Velocity Rate Equations 22
A. Definitions and Derivations .......•....... 22
1. Steady-State........................... 22
2. Initial Velocity ...•.....•..•.......... 29
3. The Maximal Velocity and Michaelis
Constant. . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . 30
4. Reverse Reaction Parameters and Rate
Constants. . . . . . . . • . • • . . . . . . . . . . . . . . . . . . 31
B. The Equilibrium Assumption................ 31
C. Derivation of Complex Steady-State Rate
Equations................................. 33
D. Derivation of the Rate Equation Using the
Rapid Equilibrium Assumption.............. 36
1. The Random Bi Bi Mechani sm. . . . . . . . . . . . . 36
2. The Ordered Bi Bi Mechanism............ 37
E. Derivation of Initial Rate Equations Using
a Combination of Equilibrium and Steady-
State Assumptions......................... 38
F. Derivation of Steady-State Rate Equations
by Using the Digital Computer ............. 40
References. . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter III Experimental Protocol and Plotting of
Kinetic Data................................. 41
A. General Considerations.................... 41
B. Analysis of Radioactive Substrates and De-
termination of Radiopurity................ 45
C. pH Effects................................ 46
D. Substrate Concentration................... 47
E. Studies of Forward and Reverse Reactions.. 49
F. Studies of Nucleotide Dependent Enzymic Re-
actions. . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
G. The Kinetic Assay ................•..•....•. 56
VIII
1. The Continuous Assay •••..........•.•... 56
2. The Stop-Time Assay •.••..•••.•.....•..• 60
H. Plotting Methods. .• . . . • . . . • . . •. . .• . • . . . • . . 62
1. Graphical Procedures...................... 69
J. The Point of Convergence of Sequential
Double Reciprocal Plots as a Criterion of
Kinetic Mechanism......................... 73
K. Protocol and Data Plotting for Three Sub-
strate Systems............................ 75
L. Graphical Methods for Differentiating be
tween Steady-State and Equilibrium Ordered
Bi Bi Mechanisms.......................... 81
References................................ 81
Chapter IV Use of Competitive Substrate Analogs and
Alternative Substrates for Studying Kinetic
Mechani sms. . . . • • • • . . . . . • . . . . . . . . . . . . . • . . • . . • . 83
A. Competitive Inhibition.................... 83
B. Partial Competitive Inhibition ........••.• 86
C. Noncompetitive Inhibition ................. 88
D. Uncompetitive Inhibition .................. 91
E. Nonlinear Enzyme Inhibition ....•.••..•.... 92
F. The Use of Substrate Analogs for Studying
Kinetic Mechanisms........................ 94
1. Bireactant Enzymic Systems ..•.......... 94
2. Terreactant Systems.................... 101
3. Kinetic Studies of AdenylosuccinateSyn-
thetase Using Dead End Inhibitors ...... 108
G. Cleland's Rules for Dead End Inhibition ... 110
H. The Stereochemical Nature of Enzyme and
Substrate Interaction ................•.... 112
1. Kinetics of Enzyme Specificity ..........•. 115
J. The Kinetics of Transition State Analogs .. 116
References ......•..•.....•.•.............. 119
Chapter V Product, Substrate, and Alternative Substrate
Inhibition. • . . . • . • • • . . . • . . . • . . . . • . . . . . . . . . . .. 121
A. Product Inhibition Experiments ......•.•..• 121
1. Experimental ProtocoL................. 121
2. One Substrate Systems •................. 122
3. Two Substrate Systems .................. 125
4. Abortive Ternary Complex Formation •.... 127
5. Calculation of Rate Constants from
Product Inhibition Experiments ......... 138
6. Noncompetitive Product Effects ••••.••.• 139
B. Substrate Inhibition •••••••••.•••.•.•••••. 144
1. A Simple Model for Substrate Inhibition. 144
2. Two Substrate Systems ••••••••.••••••••• 146
IX
C. Alternative Substrate Inhibition .•.•...... 152
1. Alternative Substrates Acting as Inhi-
bi tors Only............................ 152
2. Bireactant Systems .......•.•...•......• 153
3. Terreactant Systems.................... 156
D. Alternative Product Inhibition ••..•...•.•. 158
E. Multisite Ping Pong Mechanisms .....•..••.. 158
F. Enzymes with Identical Substrate-Product
Pairs. • . . . . . • . . . • . . • . . . . . . . • . . . • . . . • . • . . •. 159
References •.....•....................•.... 160
Chapter VI I sotope Exchange............................. 1 61
A. Abortive Complex Formation ..........•.•... 163
B. Derivation of Rate Equations .•....•....... 165
1. The Equilibrium Case: Ping Pong Bi Bi .. 165
2. The Steady-State Case: Ordered Bi Bi
(Theorell-Chance) ..•................... 167
3. Random Bi Bi........................... 1 72
4. Theorell-Chance Mechanism ........•.•... 172
C. Substrate Synergism ....••....•.•.....•.... 172
D. Calculation of Kinetic Parameters .....•.•. 174
1. The Ping Pong Bi Bi Meehanism .......... 174
2. The Random Bi Bi Mechanism (Rapid
Equilibrium) ............•.•.......•.... 175
E. Exper imental ProtocoL.................... 175
F. Isotope-Trapping •...•...•.•.•..•.......•.. 183
References. . . . . . • . . . . . . . . . . . . . . . . . . . . . . . •. 184
Chapter VII Isomerization Mechanisms and the p and Haldane
Relationships ......•..•...................... 186
A. The ~ Relationships ....................... 186
B. The Haldane Relationships ..•••..•......•.. 189
1. Ordered Bi Bi.......................... 190
2. Rapid Equilibrium Random Bi Bi ......... 190
3. Steady-State Random Bi Bi ......•.•..... 191
C. Isomerization Mechanisms ..........•....... 193
References ..........................•..... 199
Chapter VIII The Effect of Temperature and pH on Enzyme
Activity .•..••..•......•.•................... 201
A. Effect of pH on Enzyme Kinetics ........•.• 201
1. pH Functions........................... 202
2. The Effect of pH on Unireactant Models. 204
3. Evaluation of Ionization Constants ..... 208
4. Bisubstrate Systems .......•..•..•.•.•.. 213
5. Cooperative Proton Binding ......•.•...• 214
6. Identification of Amino Acid Residues
from Studies of pH Kinetics ...•........ 215
x
7. Some Limitations in the Study of pH
Kinetics. • . . . • . . . . . • • • . • • . • . • • . . . . . . . .. 21 7
8. Choosing a Buffer for Kinetic Experi-
ments ..•...••••.....•.•.••...." . . . . . . . .. 220
9. The pH Kinetics of the Fumarase
Reaction •......•.•..•.•.•••..•......•.. 221
B. The Effect of Temperature on Enzyme Catal-
yzed Reactions •..•..••.•••.•..........•••. 224
1. Collision Theory and the Arrhenius
Equation ........................•...... 225
2. Transition-State Theory ...•....•...•... 227
3. Significance of Activation Enthalpy and
Activation Entropy •.••••......•....•... 230
4. Application of Transition-State Theory
to the a-Chymotrypsin Reaction ..•....•. 233
References .•....•...•.••...•....•...•..... 234
Chapter IX Cooperativity and Allostery •.......•....•.••• 236
A. Cooperativity ..•........•..•......•....•.. 237
1. The Hill Equation ........•......•..•... 237
2. The Adair Equation..................... 241
3. The Scatchard Plot ••.••••...•...••..... 244
B. Molecular Models .•..•....•..•......•....•. 244
1. The Monod Model .•........•....••..••.•. 245
2. The Adair-Koshland Model ..•.......•.... 248
3. Subunit-Subunit Polymerization •..•..... 250
4. Protein Isomerization .•.••.........••.. 252
C. Kinetic Models .......••.••.••..........•.• 254
1. Kinetic Models Involving Subunit-Sub-
unit Interaction ......•.•.......•.•.... 254
2. Kinetic Models Involving Alternative
Path~ays of Substrate Addition and
Enzyme Isomerization .•.........•....... 256
D. Allostery ...•.........•.•.••.............• 266
1. Nonsigmoidal Systems................... 267
2. The Monod ModeL....................... 269
3. The Adair-Koshland Model .........••.•.. 273
4. Enzyme Isomerization Mechanisms .•...•.. 274
5. Kinetic Models....... . . • • . • . . . • . . • • • . •• 275
E. Product Effects •.•.••..•••.•.•.•.•••••.••. 276
References .•...•.•.•.••..•.•••••.••..•..•. 278
Appendix I Rate Equations, Determinants, and Haldane Ex
pressions for Some Common Kinetic Mechanisms. 281
Appendix II A Computer Program for Deriving Enzyme Rate
Equations. • • . • • . . • • • . . • • • • . • • • . . . . . . • • . . . • . .. 295
Appendix III Plotting and Statistical Analysis of Kinetic
Data Using the OMNITAB Program .....•.••..•.•. 307
Subj ect Index............................................. 31 3