Purich Contemporary Enzyme Kinetics and Mechanism

Selected Methods in Enzymology
1. Auflage 1983
ISBN: 978-1-4832-1422-1
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 566 Seiten

Selected Methods in Enzymology: Contemporary Enzyme Kinetics and Mechanism provides an introduction to enzyme kinetics and mechanism at an intermediate level. This book covers a variety of topics, including temperature effects in enzyme kinetics, cryoenzymology, substrate inhibition, enol intermediates enzymology, and heavy-atom isotope effects. Organized into 19 chapters, this book begins with an overview of derivation of rate equations as an integral part of the effective usage of kinetics as a tool. This text then examines the practical aspects of initial rate enzyme assay. Other chapters consider the basic procedures used in making decisions concerning kinetic mechanisms from initial-rate data. This book discusses as well the various aspects of both the theoretical background and the applications. The final chapter deals with the importance of achieving proficiency in formulating quantitative relationships describing enzyme behavior. This book is a valuable resource for students and research workers. Enzymologists and chemists will also find this book useful.

Autoren/Hrsg.

Purich, Daniel L.

Inhaltsverzeichnis

1;Front
Cover;1
2;Contemporary Enzyme Kinetics and Mechanism;4
3;Copyright Page;5
4;Table of Contents;6
5;List of Contributors;8
6;Foreword;10
7;Preface;12
8;Contents of Methods in Enzymology Volumes 63, 64, and 87;14
9;Chapter 1. Derivation of Initial Velocity and Isotope Exchange Rate Equations;20
9.1;Derivation of Initial Velocity Equations;20
9.2;THE DETERMINANT METHOD;22
9.3;THE KING AND ALTMAN METHOD;24
9.4;THE METHOD OF VOLKENSTEIN AND GOLDSTEIN;28
9.5;THE SYSTEMATIC APPROACH;31
9.6;COMPARISON OF DIFFERENT STEADY-STATE METHODS;35
10;Chapter Chapter 2. Practical Considerations in the Design of Initial Velocity Enzyme Rate Assays;52
10.1;General Experimental Design;52
11;Chapter 3. Plotting Methods for Analyzing Enzyme Rate Data;72
11.1;Definition of Initial-Rate Studies;73
11.2;Treatment of Initial Rate Data;74
11.3;Evaluation of . and Haldane Relationships;88
11.4;Examples of Initial-Rate Studies;89
11.5;Concluding Remarks;92
11.6;Acknowledgments;92
12;Chapter 4. Regression Analysis, Experimental Error, and Statistical Criteria in the Design and Analysis of Experiments for Discrimination Between Rival Kinetic Models;94
12.1;Basic Concepts;94
12.2;Discrimination
between Rival Mathematical Models (Rate Equations);95
12.3;Design of Experiments;104
12.4;Experimental Error;109
12.5;Guidelines for Design and Analysis of Kinetic Experiments;112
12.6;Acknowledgments;114
13;Chapter 5 . Effects of pH on Enzymes ;116
13.1;Theory;116
13.2;A Simplified System;122
13.3;Methods of Obtaining Ionization Constants;124
13.4;Complications;131
13.5;Interpretation of the Results of pH Experiments;140
13.6;pH-Independence of Km;140
13.7;Limitations of the Methods;152
13.8;Practical Aspects;153
13.9;Examples of pH Studies;160
14;Chapter 6. Temperature Effects in Enzyme Kinetics;168
14.1;Separation of Rate Constants;169
14.2;Reactions Involving More Than One Substrate;179
14.3;Diffusional Effects in Enzyme Systems;185
14.4;Enzyme Inactivation;188
15;Chapter 7. Cryoenzymology: The Study of Enzyme Catalysis at Subzero Temperatures1;192
15.1;Theory;195
15.2;Cryosolvents;208
15.3;Preparation of Cryosolvent Solutions;213
15.4;Mixing Techniques;216
15.5;Low-Temperature Production and Control;218
15.6;Rapid-Reaction Techniques at Subzero Temperatures;222
15.7;Conclusions;225
16;Chapter 8. Product Inhibition and Abortive Complex Formation;226
16.1;Theory;229
16.2;Abortive Complexes;234
16.3;Saturation Techniques;239
16.4;Iso Mechanisms;240
16.5;Prediction of Inhibition Patterns;244
16.6;Practical Aspects;245
16.7;Examples and Limitations of Product Inhibition Studies;246
16.8;Alternative Product Inhibition;250
16.9;Concluding Remarks;250
16.10;Acknowledgment;251
17;Chapter 9. Use of Competitive Inhibitors to Study Substrate Binding Order;252
17.1;Theory;252
17.2;Practical Aspects;262
17.3;Examples;264
17.4;Limitations;269
17.5;Concluding Remarks;270
17.6;Acknowledgments;270
18;Chapter 10.
Substrate Inhibition;272
18.1;Theory;273
18.2;Methods of Data Analysis;282
19;Chapter 11. Cooperativity in Enzyme Function: Equilibrium and Kinetic Aspects;286
19.1;Measures of Cooperativity;288
19.2;Evaluation of Constants of Saturation Functions;300
19.3;Kinetic and Equilibrium Aspects of Cooperativity;306
19.4;Equilibrium Models for Cooperativity;311
19.5;Consideration of Induced Fit vs. Preexisting Equilibrium Mechanisms of Ligand Binding and the Utilization of Rapid Relaxation Techniques;332
19.6;Status and Prospects;337
20;Chapter 12. Application of Affinity Labeling for Studying Structure and Function of Enzymes;340
20.1;Uses of Affinity Labeling;340
20.2;Considerations in the Design of Active-Site-Directed Reagents;352
20.3;Evaluation of Active-Site-Directed Reagents;357
20.4;Facilitation of Reaction Achieved with Active-Site-Directed Reagents;366
20.5;Concluding Remarks;370
20.6;Acknowledgments;370
21;Chapter 13. Criteria for Evaluating the Catalytic Competence of Enzyme-Substrate Covalent Compounds;372
21.1;Experimental Methods with Covalent Intermediates;372
21.2;Concluding Remarks;389
22;Chapter 14 .Enzymology of Enol Intermediates;390
22.1;Importance of Enolization in Reaction Mechanisms;390
22.2;Displacement of Keto-Enol Equilibria;397
22.3;Structure Homology;391
22.4;Proton Isotope Exchange;392
22.5;Oxidation;393
22.6;Coupled Elimination;393
22.7;Spectroscopic Methods;394
22.8;Reaction-Based Inactivators;395
22.9;Enols as Normal Products;395
22.10;Destruction Analysis;396
22.11;Direct Testing of Enols as Substrates;397
22.12;Generation of Enols from Ketones or Aldehydes in Solution;402
22.13;Acknowledgments;402
23;Chapter 15. Stereochemistry of Enzymic Phosphoryl and Nucleotidyl Transfer;404
23.1;The Phosphorothioates;405
23.2;Stereochemical Data Obtained with Phosphorothioates Is Valid;414
23.3;Participation of Covalent Intermediates in Enzymic Reactions;417
23.4;Conclusion;419
24;Chapter 16. Isotope Exchange Methods for Elucidating Enzymic Catalysis;422
24.1;Systems at Equilibrium;423
24.2;Enzyme Systems Away from Equilibrium;455
24.3;Enzyme Interactions Affecting Exchange Behavior;457
24.4;Concluding Remarks;465
25;Chapter 17. The Use of Isotope Effects to Determine Transition-State Structure for Enzymic Reactions;466
25.1;Primary and Secondary Isotope Effects;466
25.2;The Number of Isotope-Sensitive Steps;467
25.3;Determining the Intrinsic Deuterium Isotope Effect by Northrop's
Method;474
25.4;Determining Commitments;475
25.5;Conclusions;482
26;Chapter 18. Determination of
Heavy-Atom Isotope Effects On Enzyme-Catalyzed Reactions;484
26.1;Methods;485
26.2;Interpretation of Heavy-Atom Isotope Effects;499
26.3;Examples and Applications;501
26.4;Conclusion;504
27;Chapter 19. Selected Exercises and Problems;506
27.1;Exercises and Problems;506
27.2;Answers and/or Comments;525
28;Index;540

Leseproben

1

Derivation of Initial Velocity and Isotope Exchange Rate Equations

CHARLES Y. HUANG

A rate equation for an enzymic reaction is a mathematical expression that depicts the process in terms of rate constants and reactant concentrations. It serves as a link between the experimentally observed kinetic behavior and a plausible model or mechanism. The characteristics of the rate equation permit tests to be designed to verify the mechanism. Conversely, the experimental observations provide clues to what the mechanism may be, hence, what form the rate expression shall take.Derivation of rate equations is an integral part of the effective usage of kinetics as a tool. Novel mechanisms must be described by new equations, and familiar ones often need to be modified to account for minor deviations from the expected pattern. The mathematical manipulations involved in deriving initial velocity or isotope exchange-rate laws are in general quite straightforward, but can be tedious. It is the purpose of this chapter, therefore, to present the currently available methods with emphasis on the more convenient ones.

Derivation of Initial Velocity Equations

The derivation of initial velocity equations invariably entails certain assumptions. In fact, these assumptions are often conditions that must be fulfilled for the equations to be valid. Initial velocity is defined as the reaction rate at the early phase of enzymic catalysis during which the formation of product is linear with respect to time. This linear phase is achieved when the enzyme and substrate intermediates reach a steady state or quasi-equilibrium. Other assumptions basic to the derivation of initial rate equations are as follows:

1. The enzyme and the substrate form a complex.

2. The substrate concentration is much greater than the enzyme concentration, so that the free substrate concentration is equivalent to the total concentration. This condition further requires that the amount of product formed is small, such that the reverse reaction or product inhibition is negligible.

3. During the reaction, constant pH, temperature, and ionic strength are maintained.

Steady-State Treatment

During the steady state, the concentrations of various enzyme intermediates are essentially unchanged; that is, the rate of formation of a given intermediate is equal to its rate of disappearance. This assumption was first introduced to the derivation of enzyme kinetic equation by Briggs and Haldane.1

To derive a rate equation, the first step is to write a reaction mechanism. The nomenclature used by Fromm in Volume 63 [3] will be adopted here with the exception that rate constants in the forward and reverse directions will be denoted by positive and negative subscripts. For example, the simplest one substrate-one product reaction can be written as:

(1)

Since both the –1 and 2 steps (or branches) lead from EA to E, the two branches, as has been shown by Volkenstein and Goldstein,2 can be combined into a single branch. This simplification procedure will be used whenever feasib

?k-1+K2k1AEA

The intial rate is given by

= dP/dt = k2 (EA)

Applying the steady-state assumption, we have

(EA)/dt = k1A(E) - (k-1+k2)(EA)=0 (2)

(2)

To obtain an expression for (EA), the enzyme conservation equation

  enzyme=E0=E+EA (3)

(3)

is required. Substitution of (E) = (E0 – EA) into Eq. (2) yields

EA)=E0A[(k-1+k2)/k1]+A

and

=k2(EA)=k2E0A[(k-1+k2)/k1]+A                         =V1Akm+A (4)

(4)

where 1 is the maximum velocity in the forward direction and m is the Michaelis constant.

It should be noted that the validity of the steady-state method does not depend on the assumption Without setting Eq. (2) equal to zero, one can obtain the following expression from Eqs. (2) and (3):

EA)=k1AE0-d(EA)/dtk1A+k-1+k2

Wong3 has pointed out that the steady-state approximation only requires that be small compared with 1AE0. In the early phase of the reaction, if A E0, the rate of change of EA due to diminishing A will be relatively slow. It is clear that the validity of steady state is intimately tied to the condition of high substrate to enzyme ratio.

THE DETERMINANT METHOD

For a mechanism involving several enzyme-containing species, derivation of the rate equation can be done by solving the simultaneous algebraic equations by the determinant method. Consider the mechanism described by Eq. (1) with the addition of an EP intermediate.

?k-1k1AEA?k-2k2EP?k3E+P (5)

(5)

The three simultaneous equations are given in the following form:

E/dt=dEA/dt=dEP/dt=|EEAEP-k1Ak-1k3k1A-(k-1+k2)k-20k2-(k-2+k3)|=0=0=0

The determinant, or distribution term, for E, for example, can be calculated from the coefficients listed above, after deleting the E column. For a mechanism of intermediates, only 1 equations are needed. Thus, by leaving out the EP row, we can write

E)=|k-1k3-(k-1+k2)k-2|=k-1k-2+k3(k-1+k2)

If the E/ row is omitted instead, we have

E)=|-(k-1+k2)k-2k3-(k-2+k3)|          =k-1(k-2+k3)+k2(k-2+k3)-k2k-2          =k-1k-2+k3(k-1+k2)

Note that deletion of different equations often leads to different amounts of algebraic manipulations. Application of the same operations to EA and EP yields

EA)=k1(k-2+k3)A(EP)=k1k2A

The rate equation is readily obtained as

E0=k3(EP)(E)+(EA)+(EP)        =k1k2k3Ak-1k-2+k3(k-1+k2)+k1(k-2+k3)A+k1k2A

or

=k2k3E0A/(k2+k-2+k3){[k-1k-2+k3(k-1+k2)]/[k1(k2+k-2+k3)]}+A=V1AKm+A (6)

(6)

Equation (6) is identical in form with Eq. (4). In fact, if 3 2, –2, Eq. (6) reduces to Eq. (4). Although Eq. (5) is a more realistic mechanism compared with Eq. (1), especially when the rapid-equilibrium treatment is applied to the reversible reaction, the information obtainable from initial-rate studies of such unireactant system remains nevertheless the same: 1 and m This serves to justify the simplification used by the kineticist; that is, the elimination of certain intermediates to maintain brevity of the rate equation (provided the mathematical form is unaltered). Thus, the reaction of an ordered Bi Bi mechanism is generally written as diagrammed below.

=k2k3E0A/(k2+k-2+k3){[k-1k-2+k3(k-1+k2)]/[k1(k2+k-2+k3)]}+A=V1AKm+A

The use of the determinant method for complex enzyme mechanisms is time-consuming because of the stepwise expansion and the large number of positive and negative terms that must be canceled. It is quite useful, however, in computer-assisted derivation of rate equations (cf. Chapter [5] by From, in Volume 63).

THE KING AND ALTMAN METHOD

King and Altman4 developed a schematic approach for deriving steady-state rate equations, which has contributed to the advance of enzyme kinetics. The first step of this method is to draw an geometric figure with each enzyme form as one of the corners. Equation (5), for instance, can be rewritten as:

=k2k3E0A/(k2+k-2+k3){[k-1k-2+k3(k-1+k2)]/[k1(k2+k-2+k3)]}+A=V1AKm+A

The second step is to draw all the possible patterns that connect all the enzyme species without forming a loop. For a mechanism with enzyme species, or a figure with corners, each pattern should contain 1 lines. The number of valid patterns for any single-loop mechanism is equal to the number of enzyme forms. Thus, there are three patterns for the triangle shown above:

The determinant for a given enzyme species is obtained as the summation of the product of the rate constants and concentration factors associated with all the branches...