Initial Rate Enzyme Kinetics

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.

I Nomenclature, Definitions, and Evolution of the Kinetic Mechanism.- A. Nomenclature.- B. Evolution of Initial Rate Kinetics.- References.- II Derivation of Initial Velocity Rate Equations.- A. Definitions and Derivations.- 1. Steady-State.- 2. Initial Velocity.- 3. The Maximal Velocity and Michaelis Constant.- 4. Reverse Reaction Parameters and Rate Constants.- B. The Equilibrium Assumption.- C. Derivation of Complex Steady-State Rate Equations.- D. Derivation of the Rate Equation Using the Rapid Equilibrium Assumption.- 1. The Random Bi Bi Mechanism.- 2. The Ordered Bi Bi Mechanism.- E. Derivation of Initial Rate Equations Using a Combination of Equilibrium and Steady-State Assumptions.- F. Derivation of Steady-State Rate Equations by Using the Digital Computer.- References.- III Experimental Protocol and Plotting of Kinetic Data.- A. General Considerations.- B. Analysis of Radioactive Substrates and Determination of Radiopurity.- C. pH Effects.- D. Substrate Concentration.- E. Studies of Forward and Reverse Reactions.- F. Studies of Nucleotide Dependent Enzymic Reactions.- G. The Kinetic Assay.- 1. The Continuous Assay.- 2. The Stop-Time Assay.- H. Plotting Methods.- I. Graphical Procedures.- J. The Point of Convergence of Sequential Double Reciprocal Plots as a Criterion of Kinetic Mechanism.- K. Protocol and Data Plotting for Three Substrate Systems.- L. Graphical Methods for Differentiating between Steady-State and Equilibrium Ordered Bi Bi Mechanisms.- References.- IV Use of Competitive Substrate Analogs and Alternative Substrates for Studying Kinetic Mechanisms.- A. Competitive Inhibition.- B. Partial Competitive Inhibition.- C. Noncompetitive Inhibition.- D. Ucompetitive Inhibition.- E. Nonlinear Enzyme Inhibition.- F. The Use of Substrate Analogs for Studying Kinetic Mechanisms.- 1. Bireactant Enzymic Systems.- 2. Terreactant Systems.- 3. Kinetic Studies of Adenylosuccinate Synthetase Using Dead End Inhibitors.- G. Cleland’s Rules for Dead End Inhibition.- H. The Stereochemical Nature of Enzyme and Substrate Interaction.- I. Kinetics of Enzyme Specificity.- J. The Kinetics of Transition State Analogs.- References.- V Product, Substrate, and Alternative Substrate Inhibition.- A. Product Inhibition Experiments.- 1. Experimental Protocol.- 2. One Substrate Systems.- 3. Two Substrate Systems.- 4. Abortive Ternary Complex Formation.- 5. Calculation of Rate Constants from Product Inhibition Experiments.- 6. Noncompetitive Product Effects.- B. Substrate Inhibition.- 1. A Simple Model for Substrate Inhibition.- 2. Two Substrate Systems.- C. Alternative Substrate Inhibition.- 1. Alternative Substrates Acting as Inhibitors Only.- 2. Bireactant Systems.- 3. Terreactant Systems.- D. Alternative Product Inhibition.- E. Multisite Ping Pong Mechanisms.- F. Enzymes with Identical Substrate-Product Pairs.- References.- VI Isotope Exchange.- A. Abortive Complex Formation.- B. Derivation of Rate Equations.- 1. The Equilibrium Case: Ping Pong Bi Bi.- 2. The Steady-State Case: Ordered Bi Bi (Theorell-Chance).- 3. Random Bi Bi.- 4. Theorell-Chance Mechanism.- C. Substrate Synergism.- D. Calculation of Kinetic Parameters.- 1. The Ping Pong Bi Bi Mechanism.- 2. The Random Bi Bi Mechanism (Rapid Equilibrium).- E. Experimental Protocol.- F. Isotope-Trapping.- References.- VII Isomerization Mechanisms and the ? and Haldane Relationships.- A. The ? Relationships.- B. The Haldane Relationships.- 1. Ordered Bi Bi.- 2. Rapid Equilibrium Random Bi Bi.- 3. Steady-State Random Bi Bi.- C. Isomerization Mechanisms.- References.- VIII The Effect of Temperature and pH on Enzyme Activity.- A. Effect of pH on Enzyme Kinetics.- 1. pH Functions.- 2. The Effect of pH on Unireactant Models.- 3. Evaluation of Ionization Constants.- 4. Bisubstrate Systems.- 5. Cooperative Proton Binding.- 6. Identification of Amino Acid Residues from Studies of pH Kinetics.- 7. Some Limitations in the Study of pH Kinetics.- 8. Choosing a Buffer for Kinetic Experiments.- 9. The pH Kinetics of the Fumarase Reaction.- B. The Effect of Temperature on Enzyme Catalyzed Reactions.- 1. Collision Theory and the Arrhenius Equation.- 2. Transition-State Theory.- 3. Significance of Activation Enthalpy and Activation Entropy.- 4. Application of Transition-State Theory to the ?-Chymotrypsin Reaction.- References.- IX Cooperativity and Allostery.- A. Cooperativity.- 1. The Hill Equation.- 2. The Adair Equation.- 3. The Scatchard Plot.- B. Molecular Models.- 1. The Monod Model.- 2. The Adair-Koshland Model.- 3. Subunit-Subunit Polymerization.- 4. Protein Isomerization.- C. Kinetic Models.- 1. Kinetic Models Involving Subunit-Subunit Interaction.- 2. Kinetic Models Involving Alternative Pathways of Substrate Addition and Enzyme Isomerization.- D. Allostery.- 1. Nonsigmoidal Systems.- 2. The Monod Model.- 3. The Adair-Koshland Model.- 4. Enzyme Isomerization Mechanisms.- 5. Kinetic Models.- E. Product Effects.- References.- Appendix I Rate Equations, Determinants, and Haldane Expressions for Some Common Kinetic Mechanisms.- Appendix II A Computer Program for Deriving Enzyme Rate Equations.- Appendix III Plotting and Statistical Analysis of Kinetic Data Using the OMNITAB Program.