Table Of ContentENZYME KINETICS AND MECHANISMS
Enzyme Kinetics
and Mechanisms
by
KENNETH B. TAYLOR
University of Alabama at Birmingham, U.S.A.
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To the colleagues who showed the way
and
to the students who taught me.
vii
TABLE OF CONTENTS
Dedication v
Table of Contents vii
Preface ix
Introduction xi
1.Introduction to Steady-State Kinetics 1
2. The Generation of Experimental Data 7
3.Methods for ModelEvaluation 14
4.Derivation of Mathematical Models 27
5.Effects of Substrate Concentration 44
6.Effects of Analog Inhibitors 66
7.Effects of Product Inhibitors 89
8.Effects of SubstrateInhibition 106
9. Slow and Tight Inhibition 122
10. The Thermodynamics of Initial Velocity 147
11. Effects of pH 164
12. Effects of Isotopic Substitution 184
13. Effects ofOther Reaction Conditions 206
Index 223
ix
PREFACE
It is said that necessity is the mother of invention. Although this seems to be true, I suspect
that indolence also has something to do with it and perhaps some paternity testing would
be in order. Such was the case with the present book. The necessity was provided by the
circumstance that I was to teach a course about a steady-state kinetics approach to the
elucidation of enzyme mechanisms, but in the apparent absence of a suitable textbook I was
forced to develop my own teaching materials. The putative father of this book was my
disinclination to burden myself and the students any more than necessary with long,
convoluted derivations and explanations as well as to attempt an exhaustive literature
review. Therefore, the approach taken was the shortest and simplest I could find. The
success or failure of this approach is to be determined by you the reader.
In addition the ancestry of this book includes the efforts and forbearance of several
other individuals. Dr. Tim Fritz, Staff Scientist at the National Institutes of Health,
NIDDK, read the manuscript and made many comments that improved the clarity of the
book very significantly. His efforts are greatly appreciated.
Dr. W. W. (Mo) Cleland was not only instrumental in the development of much
of the science described here but provided me, a number of years ago, with an introduction
to it and an opportunity to learn some of it. I am grateful.
Dr. Herb Cheung and Dr. Jeff Engler, both of the Department of Biochemistry and
Molecular Genetics at the University of Alabama at Birmingham, provided needed
encouragement.
Finally I am grateful to my wife, Carol, who exercised generous forbearance that
allowed me to develop the material and write the manuscript during time that otherwise
could have been devoted to joint activities and concerns.
Verona, Maine
Summer 2001
xi
INTRODUCTION
Although the rate of appearance in the scientific literature of rigorous
investigations of enzyme mechanisms by steady-state kinetics seems to have declined
somewhat in recent years, it remains rather steady. Nevertheless the usefulness of such
studies remains rather high, because the functions of enzymes are fundamentally kinetic
in nature. More specifically the possibilities for rate and mechanistic perturbation due to
the substitution of specific amino-acid residues by geneticengineering have enhanced the
need for rigorous kinetic studies to define the effects of these changes. With the present
availability of site-directed mutants, a plethora of structural information and the possibility
for comparison of very closely related enzymes, investigations of steady-state kinetics
assume even greater importance.
Two factors further enhance the relevance of investigations of enzyme
mechanisms by steady-state kinetics. First the experimental conditions are generally close
to physiological conditions. Specifically the enzyme concentration is much less than the
substrate concentration both physiologically and for steady-state experiments, as well as
necessary for the interpretation of the experimental results. In addition the temperature,
the pH, the pressure and the solvent are usually closer to the physiologicalthan is the case
with other experimental techniques. Second, the experiments generally require rather
simple equipment. As explained in a later chapter a good spectrophotometer and a
computer are generally the most sophisticated equipment necessary for most investigations.
However, additional analytical and control equipment may be required for some enzymes
and for some types of experiments.
The overall objective of the study of enzyme reaction mechanisms is the
description of the intermediates and transition states in the reaction. Since there are some
intermediates and transition states that are not accessible by these techniques,
investigations of steady-state enzyme kinetics have a focus on a subset of these objectives
that will be described later.
There are three major objectives of this book. The first is to describe the useful
experimental manipulations for the production of steady-state kinetic data as well as their
interpretation in order to give the reader an approximation of the magnitude of effort
required to complete a meaningful investigation. Second, this book purports to describe
the interpretation of data in sufficient detail to enable the reader to understand the principal
paths of logic associated with steady-state enzyme kinetics. Specifically the readershould
be able to understand the logic in the literature that connects hypothesis and data from
steady-state kinetic experiments, and the reader should be able to formulate and use steady-
state kinetics experiments and logic in the elucidation of the mechanism of enzymes.
xii
Although it is expected that the reader may want to consult some of the more detailed
descriptions of individual approaches that are cited in the text, the present book will be
invaluable in the understanding of these descriptions.
The third objective of this book is to expound several approaches to the theory of
steady-state enzyme kinetics in a context somewhat different from previous discussions in
an attempt to make them relatively easily understood while maintaining a standard of
rigorous logic.
This book is not meant to be a scholarly or an exhaustive treatise on enzyme
kinetics and mechanisms. Whereas examples from the literature will be presented, a
review of the literature is not a purpose of the book. There are a number of excellent and
comprehensive treatises on enzyme kinetics and mechanisms to which reference will be
made. The present book is intended to aid in the understanding of these treatises.
Furthermore, this is not meant to be a reference book, although it may serve that function.
There are other compendia of steady-state mechanisms, e.g. [1].
This book is for anyone who expends the funds in its purchase. More specifically
it is most appropriate for someone who has had an entry-level introduction to enzymes and
steady-state kinetics and would like to understand the subject in more detail. The material
herein was developed for a graduate level course in enzyme mechanisms and kinetics
taught by the author over a period of fifteen years. An understanding of the book will
require about an American secondary-school level of knowledge of algebra and analytical
geometry. The really necessary concepts will be reviewed very briefly. Some
understanding of calculus is necessary to understand the curve-fitting algorithms and the
slow inhibitors, but these are not essential for the understanding of steady-state enzyme
kinetics. An understanding of the material in this book does require the motivation to
indulge in the algebraic thought processes to derive the necessary equations. Equations are
central to the approach in this book and are basic for a conceptual understanding of the
theory of steady-state enzyme kinetics.
The book is divided into five general sections. In the first section the first three
chapters deal respectively with some important basic concepts of steady-state kinetics,
methods for the generation of data, and methods for the use of that data in the testing of
mathematical models for the mechanism. In the following chapter several methods for the
derivation of mathematical models are described. One of these methods will be employed
throughout the remainder of the book. Therefore, it is important to have an understanding
of this chapter in order to understand the remainder of the book. The third section consists
of four chapters in three of which models are described respectively to deal with initial-
velocity data from experiments in which the concentration of substrate, of analog
inhibitors, and of product inhibitors are varied respectively. The latter section also includes
a chapter about models for substrate inhibition. In a departure from strictly initial velocity
models the fourth section consists of a chapter containing a description of models for tight-
binding inhibitors, slow-binding inhibitors and slow-, tight-binding inhibitors, because of
their importance and because the models depend on many of the same concepts as initial-
velocity models. The final section contains Chapter 10 with a discussion of the
xiii
thermodynamics of initial velocity and general models for the description of the effects of
changes in environmental conditions, and other reaction conditions on the initial velocity.
An understanding of this chapter is important for the understanding of the final three
chapters, which present specific models for the description of the effects of pH, isotopic
substitution and other factors, such as temperature and pressure, on the initial velocity.
References
1. Segal, I.H. Enzyme Kinetics, Wiley Interscience, New York, 957pp (1975).
