ENZYME KINETICS A Modern Approach ALEJANDRO G. MARANGONI Department of Food Science University of Guelph A JOHN WILEY & SONS, INC., PUBLICATION This book is printed on acid-free paper. Copyright 2003 by John Wiley & Sons, Inc. All rights reserved.
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Library of Congress Cataloging-in-Publication Data: Marangoni, Alejandro G., 1965- Enzyme kinetics : a modern approach / Alejandro G.7—dc21 2002014042 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 To Dianne, Isaac, and Joshua CONTENTS PREFACE xiii 1 TOOLS AND TECHNIQUES OF KINETIC ANALYSIS 1 1.2 Elementary Rate Laws / 2 1.2 Order of a Reaction / 3 1.4 Integrated Rate Equations / 4 1.1 Zero-Order Integrated Rate Equation / 4 1.2 First-Order Integrated Rate Equation / 5 1.3 Second-Order Integrated Rate Equation / 7 1.4 Third-Order Integrated Rate Equation / 8 1.5 Higher-Order Reactions / 9 1.7 Reaction Half-Life / 11 vii viii CONTENTS 1.5 Experimental Determination of Reaction Order and Rate Constants / 12 1.3 Dependence of Reaction Rates on Temperature / 14 1.2 Energy of Activation / 18 1.4 Acid–Base Chemical Catalysis / 20 1.5 Theory of Reaction Rates / 23 1.6 Complex Reaction Pathways / 26 1.1 Numerical Integration and Regression / 28 1.2 Least-Squares Minimization (Regression Analysis) / 29 1.2 Exact Analytical Solution (Non-Steady-State Approximation) / 39 1.3 Exact Analytical Solution (Steady-State Approximation) / 40 2 HOW DO ENZYMES WORK? 41 3 CHARACTERIZATION OF ENZYME ACTIVITY 44 3.1 Progress Curve and Determination of Reaction Velocity / 44 3.2 Catalysis Models: Equilibrium and Steady State / 48 3.2 Steady-State Model / 49 3.3 Plot of v versus [S] / 50 3.3 General Strategy for Determination of the Catalytic Constants Km and Vmax / 52 3.5 Determination of Enzyme Catalytic Parameters from the Progress Curve / 58 CONTENTS ix 4 REVERSIBLE ENZYME INHIBITION 61 4.3 Linear Mixed Inhibition / 63 4.1 Inhibition of Fumarase by Succinate / 65 4.2 Inhibition of Pancreatic Carboxypeptidase A by β-Phenylpropionate / 67 4.3 Alternative Strategies / 69 5 IRREVERSIBLE ENZYME INHIBITION 70 5.1 Simple Irreversible Inhibition / 72 5.2 Simple Irreversible Inhibition in the Presence of Substrate / 73 5.3 Time-Dependent Simple Irreversible Inhibition / 75 5.4 Time-Dependent Simple Irreversible Inhibition in the Presence of Substrate / 76 5.5 Differentiation Between Time-Dependent and Time-Independent Inhibition / 78 6 pH DEPENDENCE OF ENZYME-CATALYZED REACTIONS 79 6.2 pH Dependence of the Catalytic Parameters / 82 6.3 New Method of Determining pK Values of Catalytically Relevant Functional Groups / 84 7 TWO-SUBSTRATE REACTIONS 90 7.1 Random-Sequential Bi Bi Mechanism / 91 7.2 Ordered-Sequential Bi Bi Mechanism / 95 7.3 Order of Substrate Binding / 97 7.3 Ping-Pong Bi Bi Mechanism / 98 7.4 Differentiation Between Mechanisms / 100 8 MULTISITE AND COOPERATIVE ENZYMES 102 8.1 Sequential Interaction Model / 103 8.3 Microscopic versus Macroscopic Dissociation Constants / 106 8.4 Generalization of the Model / 107 8.2 Concerted Transition or Symmetry Model / 109 8.4 Reality Check / 115 9 IMMOBILIZED ENZYMES 116 9.2 Plug-Flow Reactors / 118 9.3 Continuous-Stirred Reactors / 119 10 INTERFACIAL ENZYMES 121 10.2 Determination of Interfacial Area per Unit Volume / 125 10.3 Determination of Saturation Interfacial Enzyme Coverage / 127 11 TRANSIENT PHASES OF ENZYMATIC REACTIONS 129 11.1 Rapid Reaction Techniques / 130 11.2 Reaction Mechanisms / 132 CONTENTS xi 11.1 Early Stages of the Reaction / 134 11.2 Late Stages of the Reaction / 135 11.3 Relaxation Techniques / 135 12 CHARACTERIZATION OF ENZYME STABILITY 140 12.3 Decimal Reduction Time / 143 12.4 Energy of Activation / 144 12.1 Thermodynamic Characterization of Stability / 151 12.2 Kinetic Characterization of Stability / 156 13 MECHANISM-BASED INHIBITION 158 Leslie J.1 Alternate Substrate Inhibition / 159 13.1 Alternative Substrate Inhibition / 169 13.2 Suicide Inhibition / 170 14 PUTTING KINETIC PRINCIPLES INTO PRACTICE 174 Kirk L.1 Were Initial Velocities Measured? / 175 14.2 Does the Michaelis–Menten Model Fit? / 177 14.3 What Does the Original [S] versus Velocity Plot Look Like? / 179 14.4 Was the Appropriate [S] Range Used? / 181 14.5 Is There Consistency Working Within the Context of a Kinetic Model? / 184 14.6 Conclusions / 191 xii CONTENTS 15 USE OF ENZYME KINETIC DATA IN THE STUDY OF STRUCTURE–FUNCTION RELATIONSHIPS OF PROTEINS 193 Takuji Tanaka and Rickey Y.1 Are Proteins Expressed Using Various Microbial Systems Similar to the Native Proteins? / 193 15.2 What Is the Mechanism of Conversion of a Zymogen to an Active Enzyme? / 195 15.3 What Role Does the Prosegment Play in the Activation and Structure–Function of the Active Enzyme? / 198 15.4 What Role Do Specific Structures and/or Residues Play in the Structure–Function of Enzymes? / 202 15.5 Can Mutations be Made to Stabilize the Structure of an Enzyme to Environmental Conditions? / 205 15.3 Disulfide Linkages / 210 15.7 Abbreviations Used for the Mutation Research / 213 BIBLIOGRAPHY 217 Books / 217 Selection of Classic Papers / 218 INDEX 221 PREFACE We live in the age of biology—the human and many other organisms’ genomes have been sequenced and we are starting to understand the function of the metabolic machinery responsible for life on our planet.
Thousands of new genes have been discovered, many of these coding for enzymes of yet unknown function. Understanding the kinetic behavior of an enzyme provides clues to its possible physiological role. From a biotechnological point of view, knowledge of the catalytic properties of an enzyme is required for the design of immobilized enzyme-based industrial processes. Biotransformations are of key importance to the pharmaceutical and food industries, and knowledge of the catalytic properties of enzymes, essential.
This book is about understanding the principles of enzyme kinetics and knowing how to use mathematical models to describe the catalytic function of an enzyme. Coverage of the material is by no means exhaustive. There exist many books on enzyme kinetics that offer thorough, in-depth treatises of the subject. This book stresses understanding and practicality, and is not meant to replace, but rather to complement, authoritative treatises on the subject such as Segel’s Enzyme Kinetics.
This book starts with a review of the tools and techniques used in kinetic analysis, followed by a short chapter entitled “How Do Enzymes Work?”, embodying the philosophy of the book. Characterization of enzyme activity; reversible and irreversible inhibition; pH effects on enzyme activity; multisubstrate, immobilized, interfacial, and allosteric enzyme kinetics; transient phases of enzymatic reactions; and enzyme xiii xiv PREFACE stability are covered in turn. In each chapter, models are developed from first principles, assumptions stated and discussed clearly, and applications shown. The treatment of enzyme kinetics in this book is radically different from the traditional way in which this topic is usually covered.
In this book, I have tried to stress the understanding of how models are arrived at, what their limitations are, and how they can be used in a practical fashion to analyze enzyme kinetic data. With the advent of computers, linear transformations of models have become unnecessary—this book does away with linear transformations of enzyme kinetic models, stressing the use of nonlinear regression techniques. Linear transformations are not required to carry out analysis of enzyme kinetic data. In this book, I develop new ways of analyzing kinetic data, particularly in the study of pH effects on catalytic activity and multisubstrate enzymes.
Since a large proportion of traditional enzyme kinetics used to deal with linearization of data, removing these has both decreased the amount of information that must be acquired and allowed for the development of a deeper understanding of the models used. This, in turn, will increase the efficacy of their use. The book is relatively short and concise, yet complete. Time is today’s most precious commodity.
This book was written with this fact in mind; thus, the coverage strives to be both complete and thorough, yet concise and to the point. ALEJANDRO MARANGONI Guelph, September, 2001 ENZYME KINETICS CHAPTER 1 TOOLS AND TECHNIQUES OF KINETIC ANALYSIS 1.1 GENERALITIES Chemists are concerned with the laws of chemical interactions. The the- ories that have been expounded to explain such interactions are based largely on experimental results. Two main approaches have been used to explain chemical reactivity: thermodynamic and kinetic.
In thermodynam- ics, conclusions are reached on the basis of changes in energy and entropy that accompany a particular chemical change in a system. From the mag- nitude and sign of the free-energy change of a reaction, it is possible to predict the direction in which a chemical change will take place. Thermo- dynamic quantities do not, however, provide any information on the rate or mechanism of a chemical reaction. Theoretical analysis of the kinetics, or time course, of processes can provide valuable information concerning the underlying mechanisms responsible for these processes.
For this pur- pose it is necessary to construct a mathematical model that embodies the hypothesized mechanisms. Whether or not the solutions of the resulting equations are consistent with the experimental data will either prove or disprove the hypothesis. Consider the simple reaction A + B C. The law of mass action states that the rate at which the reactant A is converted to product C is pro- portional to the number of molecules of A available to participate in the chemical reaction.
Doubling the concentration of either A or B will double the number of collisions between molecules that lead to product formation. 1 2 TOOLS AND TECHNIQUES OF KINETIC ANALYSIS The stoichiometry of a reaction is the simplest ratio of the number of reactant molecules to the number of product molecules. It should not be mistaken for the mechanism of the reaction. For example, three molecules of hydrogen react with one molecule of nitrogen to form ammonia: N2 + 3H2 2NH3.
The molecularity of a reaction is the number of reactant molecules par- ticipating in a simple reaction consisting of a single elementary step. Reac- tions can be unimolecular, bimolecular, and trimolecular. Unimolecular reactions can include isomerizations (A → B) and decompositions (A → B + C). Bimolecular reactions include association (A + B → AB; 2A → A2 ) and exchange reactions (A + B → C + D or 2A → C + D).