Enzyme Kinetics Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems

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ISBN: 9780471303091 | 0471303097
Cover: Paperback
Copyright: 5/17/1993

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Covers enzyme kinetics from its most elementary aspects to such modern subjects as steady-state, multi-reactant kinetics and isotope exchange. Offers an understanding of the behavior of enzyme systems and the diagnostic tools used to characterize them and determine kinetic mechanisms. Illustrates and explains current subjects such as cumulative, concerted and cooperative feedback inhibition and metal ion activation.

Introduction---Enzymes As Biological Catalysts

The Discovery of Enzymes and the Development of Enzymology

(3)

Life, Energy, and Coupled Reactions

(1)

Enzymes as Catalysts

(2)

The Active Site

(2)

Three-Point Attachment

(1)

The Flexible Enzyme-Induced Fit Hypothesis

(2)

Factors Responsible for the Catalytic Efficiency of Enzymes

(2)

Enzyme Kinetics

(4)

References

(3)

Kinetics of Unireactant Enzymes

The Henry Equation and the Michaelis-Menten Equation

(4)

General Rules for Writing Velocity Equations for Rapid Equilibrium Systems

(3)

The Van Slyke Equation

(1)

The Briggs-Haldane Steady-State Approach

(4)

Reversible Reactions---Effect of Product on Forward Velocity

(5)

Haldane Relatioship Between Kinetic Constants and the Equilibrium Constant

(3)

Specific (or Relative or Reduced) Substrate Concentration and Velocity

(1)

Velocity Versus Substrate Concentration Curve

(1)

Reaction Order

(5)

Graphical Determination of Km and Vmax

(10)

Lineweaver-Burk Reciprocal Plot: 1/v versus 1/[S]

(1)

Substrate Concentration Range

(1)

Labeling the Axes of Reciprocal Plots

(4)

Graphical Analysis as a Method of Solving Simultaneuous Equations

(1)

Effect of Impure Substrate on Km and Vmax

(1)

Eisenthal, Cornish-Bowden Plot and New Dixon Plot

(2)

Log v Versus Log [S] Plot

(1)

Integrated Form of the Henri-Michaelis-Menten Equation

(10)

Integrated Rate Equation Assuming No Product Inhibition (Kms ≪ Kmp) and that Keq Is Very Large

(3)

Determination of Km and Vmax from [S] and v

(2)

Integrated Rate Equation Where Kmp ≌ Kms and Keq Is Very Large

(2)

Integrated Rate Equation Where Kmp ≌ Kms and Keq Is Not Very Large

(3)

Multiple Enzymes Catalyzing the Same Reaction

(8)

Kinetic Behavior at High Enzyme Concentrations

(5)

Enzyme Assays

(12)

Initial Velocity as a Function of [E]t

(1)

Enzyme Units and Specific Activities---Quantitating [E]t

(1)

Turnover Number

(1)

Quantitation of [E]t Using the Integrated Velocity Equation

(1)

Reporting Data

(1)

Enzyme Purification

(2)

Determination of v

(1)

Assays with Auxillary Enzymes

(2)

Kinetics of Coupled Assays

(4)

Effects of Endogenous Substrates

(11)

References

(3)

Simple Inhibition Systems

Competitive Inhibition (Simple Intersecting Linear Competitive Inhibition)

100

(25)

Effect of Concentration Range on Degree of Inhibition

106

(1)

Reciprocal Plot for Competitive Inhibition Systems

107

(1)

Replots of Slope and Kmapp Versus [I]

108

(1)

Dixon Plot for Competitive Inhibition: 1/v versus [I]

109

(2)

General Principles

111

(1)

Integrated Rate Equation in the Presence of a Competitive Inhibitor

112

(1)

Competitive Inhibition and Total Velocity with Mixed Alternative Substrates

113

(5)

Apparent Competitive Inhibition by Carrier Dilution (Isotope Competition)

118

(2)

Competitive Product Inhibition Where [S] + [P] is Constant (Regulation Via ``Energy Charge'')

120

(5)

Noncompetitive Inhibition (Simple Intersecting Linear Noncompetitive Inhibition)

125

(11)

General Principles

132

(1)

Reciprocal Plot for Noncompetitive Inhibition Systems

132

(1)

Replots of Slope 1/s and 1/Vmax, Versus [I]

133

(1)

Dixon Plot for Noncompetitive Inhibition: 1/v Versus [I]

134

(1)

Integrated Rate Equation in the Presence of a Noncompetitive Inhibitor

135

(1)

Uncompetitive Inhibition (Simple Linear Uncompetitive Inhibition)

136

(7)

Reciprocal Plot for Uncompetitive Inhibition

141

(1)

Replots of 1/Vmax, and 1/Kmapp Versus [I]

141

(2)

Dixon Plot for Uncompetitive Inhibition: 1/v Versus [I]

143

(1)

Integrated Rate Equation in the Presence of an Uncompetitive Inhibitor

143

(1)

Effects of Contaminating Inhibitors on the Initial Velocity Versus Enzyme Concentration Plot

143

(7)

Other Factors Producing Nonlinear v Versus [E]t Plots

147

(1)

Contaminating Inhibitors in the Substrate

147

(3)

Tightly Bound Inhibitors

150

(11)

References

159

(2)

Rapid Equilibrium Partial and Mixed-Type Inhibition

Partial Competitive Inhibition (Simple Intersecting Hyperbolic Competitive Inhibition)

161

(5)

Partial Noncompetitive Inhibition (Simple Intersecting Hyperbolic Noncompetitive Inhibition)

166

(4)

Mixed-Type Inhibition

170

(32)

Linear Mixed-Type Inhibition

170

(8)

Hyperbolic Mixed-Type Inhibition

178

(4)

Intersection Points in Mixed Inhibition Systems

182

(10)

Two-Site Model for Partial Inhibition

192

(4)

Apparent Partial or Mixed-Type Inhibition Resulting from Multiple Enzymes

196

(2)

Reduction of Steady-State Velocity Equation to Rapid Equilibrium Form

198

(4)

Reciprocal Plot Nomenclature

202

(1)

Interaction Between Inhibitor and Substrate

203

(5)

Other Methods of Plotting Enzyme Kinetics Data

208

(19)

The Hanes-Woolf Plot: [S]/v Versus [S]

210

(1)

The Woolf-Augustinsson-Hofstee Plot: v Versus v/[S]

210

(4)

The Eadie-Scatchard Plot: v/[S] Versus v

214

(1)

The Eadie-Scatchard Plot: v/[S] Versus v

214

(4)

The Scatchard Plot for Equilibrium Binding Data: [S]b/[S]f Versus [S]b or [S]b/[S]f[E]t Versus [S]b/[E]t

218

(2)

Isotope Competition in Equilibrium Ligand Binding

220

(4)

References

224

(3)

Enzyme Activation

Nonessential Activation

227

(15)

General Scheme for Nonessential Activation

227

(4)

Inhibitor Competitive with Nonessential Activator

231

(1)

Nonessential Activation By Two Competing Activators that Alter Only Ks

232

(2)

Nonessential Activator Acts as Deinhibitor (Anti-inhibitor)

234

(6)

``Energy Charge'' Regulation: [I] + [A] Pool Is Constant

240

(2)

Substrate-Activator Complex Is the True Substrate

242

(32)

Only SA Binds to the Enzyme

245

(5)

SA and S Bind to the Enzyme

250

(5)

SA and A Bind to the Enzyme

255

(3)

SA, S, and A Bind to the Enzyme

258

(5)

A Is an Essential Activator

263

(4)

A Is a Nonessential Activator; Only SA Binds to the Catalytic Site

267

(3)

Both S and SA Are Substrates (ES and ESA Are Catalytically Active)

270

(2)

References

272

(2)

Rapid Equilibrium Bireactant and Terreactant Systems

Random Bireactant Systems

274

(46)

Initial Velocity Studies

274

(9)

Inhibitor Competes With One Substrate

283

(10)

I Is a Nonexclusive Inhibitor

293

(6)

Product Inhibition in Rapid Equilibrium Random Bireactant Systems

299

(10)

Substrate Inhibition in Rapid Equilibrium Random Systems

309

(11)

Ordered Bireactant Systems

320

(10)

Random Terreactant Systems

330

(7)

Ordered and Hybrid Random-Ordered Terreactant Systems

337

(5)

Rules for Predicting Inhibition Patterns in Rapid Equilibrium Systems

342

(4)

References

344

(2)

Multisite and Allosteric Enzymes

Enzymes With Multiple Catalytic Sites

346

(39)

Noncooperative Sites

346

(7)

Allosteric Enzymes---Cooperative Binding

353

(2)

Adair-Pauling Simple Sequential Interaction Model

355

(1)

Interaction Factors

355

(3)

A Note on Terminology Regarding ``Interaction Factors''

358

(2)

A Simplified Velocity Equation for Allosteric Enzymes---The Hill Equation

360

(2)

Sigmoidicity of the Velocity Curve

362

(1)

Inflection Point of the Velocity Curve

362

(3)

Lineweaver-Burk Plot for Allosteric Enzymes

365

(2)

Eadie-Scatchard Plot for Allosteric Enzymes

367

(4)

The Hill Plot---Logarithmic Form of the Hill Equation

371

(3)

Summary of Differen Uses of the Symbol n

374

(1)

Effect of Interaction Strengths on the Velocity Curve

375

(2)

Negative Cooperativity

377

(5)

Interaction that Affects Vmax

382

(3)

Inhibition and Activation in Multisite Systems

385

(19)

Pure Competitive Inhibition, Exclusive at Both Substrate Sites (``Ligand Exclusion'')

385

(2)

Inhibition Competitive at Two Sites

387

(2)

General Equation for the Two-Site Pure Competitive System

389

(1)

Partial Competitive Inhibition

390

(8)

Substrate Activation

398

(3)

Multiple Essential Activator Sites

401

(2)

Cooperative Essential Activation

403

(1)

The General Sequential Interaction Model of Koshland, Nemethy, and Filmer (Restricted Interactions Between Sites)

404

(17)

Dimer Model

407

(4)

Tetramer Models

411

(4)

Nonidentical Subunits

415

(1)

Inhibition and Activation---A Dimer Model

416

(3)

Independent Binding Model

419

(2)

Summary

421

(1)

The Symmetry Model of Allosteric Enzymes (The Concerted Transition Model of Monod, Wyman, and Changeux)

421

(39)

Derivation of the General Velocity Equation

422

(5)

Exclusive Ligand Binding

427

(1)

Effect of L and c on Cooperativity

428

(3)

V Systems

431

(1)

Mixed K and V Systems

432

(1)

Comparison and Formal Equivalence of the Sequential and Concerted Models

432

(2)

Inhibition in Exclusive Binding K Systems

434

(6)

Activation in Exclusive Binding K Systems

440

(5)

Horn-Bornig Plot to Determine n and L (When c = 0)

445

(4)

Combinations of Alternative Effectors

449

(1)

Competitive Inhibition

450

(1)

Nonexclusive Substrate and Effector Binding

451

(1)

Determination of KST, KSR, and c in Nonexclusive K Systems

452

(2)

Determination of n

454

(1)

Determination of L' and L

455

(1)

Consequences of Nonexclusive Ligand Binding

455

(2)

General and Hybrid Models

457

(3)

Alternative Kinetic Explanations for Sigmoidal Responses

460

(5)

References

462

(3)

Multiple Inhibition Analysis

Multiple Sites for a Given Inhibitor

465

(9)

Hill Equation and Hill Plots for Multisite Inhibition

470

(4)

Inhibition by Mixtures of Different Inhibitors

474

(32)

Pure Competitive Inhibition by Two Different Exclusive Inhibitors

474

(5)

Noncompetitive and Mixed-Type Inhibition by Two Different Mutually Exclusive Inhibitors

479

(2)

Cooperative (Synergistic) Pure Competitive Inhibition by Two Different Nonexclusive Inhibitors

481

(7)

Cooperative (Synergistic) Noncompetitive Inhibition by Two Different Nonexclusive Inhibitors

488

(4)

Cooperative (Synergistic) Uncompetitive Inhibitors

492

(1)

I Is Competitive and X Is Noncompetitive With Respect to S

493

(2)

Two Partial Inhibitors

495

(3)

Concerted (Multivalent) Inhibition by Two Different Inhibitors

498

(6)

References

504

(2)

Steady-State Kinetics of Multireactant Enzymes

The King-Altman Method of Deriving Steady-State Velocity Equations

506

(9)

Uni Uni Reactions

506

(9)

Isomerization of Central Complexes

515

(1)

Simplification of Complex King-Altman Patterns

515

(8)

General Rules for Defining Kinetic Constants and Deriving Velocity Equations

523

(11)

Cleland Nomenclature

523

(1)

Maximal Velocities and Keq

523

(1)

Michaelis Constants

523

(1)

Inhibition Constants

524

(1)

Isoinhibition Constants

525

(1)

Velocity Equation for the Forward Direction

525

(1)

Velocity Equation for the Reverse Direction

526

(1)

Haldane Equations

527

(1)

A Shortcut for Obtaining Velocity Equations

528

(1)

Rate Constants

528

(1)

Distribution Equations

528

(2)

Alternative Nomenclature

530

(3)

Kslope and Kint Nomenclature

533

(1)

Iso Uni Uni System (Mobile Carrier Model of Membrane Transport)

534

(10)

Ordered Uni Bi and Ordered Bi Uni Systems

544

(16)

Complete Velocity Equation---Product Inhibition

551

(6)

Calculation of Rate Constants

557

(3)

Distribution Equations

560

(1)

Effect of Isomerizations

560

(1)

Ordered Bi Bi System

560

(31)

Initial Forward Velocity in the Absence of Products

564

(1)

Other Methods of Plotting Data

565

(9)

Complete Velocity Equation---Product Inhibition

574

(12)

Kislope and Kiint

586

(2)

Calculation of Rate Constants

588

(1)

Distribution Equations

589

(1)

Effect of Isomerizations

589

(1)

Agreement of Kinetic Data With the Haldane Equations

589

(2)

Partial Rapid Equilibrium Ordered Bi Bi System

591

(2)

Theorell-Chance Bi Bi System

593

(13)

Product Inhibition

595

(2)

Rate Constants

597

(7)

Distribution Equations

604

(1)

Effect of Isomerizations

604

(1)

Reduction of Ordered Bi Bi to Theorell-Chance

605

(1)

Evaluating the Kinetic Significance of the Central Complexes

605

(1)

Ping Pong Bi Bi System

606

(19)

Initial Forward Velocity in the Absence of Products

608

(4)

Haldane Equations

612

(4)

Product Inhibition

616

(5)

Distribution Equations

621

(1)

Effect of Isomerizations

621

(1)

Effect of Impure Substrates

621

(1)

Prestedy-State ``Burst'' Phenomenon With Ping Pong Enzymes

621

(2)

Ordered Bi Bi Systems That Appear to be Ping Pong

623

(2)

Partial Rapid Equilibrium Ping Pong Bi Bi Systems

625

(1)

Hybrid Ping Pong---Rapid Equilibrium Random (Two-Site) Bi Bi Systems

626

(8)

Iso Bi Bi Systems

634

(5)

Hybrid Theorell-Chance Ping Pong (and Iso Ping Pong) Systems

639

(4)

Rapid Equilibrium Random Bi Bi Systems

643

(3)

Steady-State Random Mechanisms

646

(3)

Partial Rapid Equilibrium Random Bi Bi System

649

(8)

Varieties of Nonhyperbolic Velocity Curves

657

(8)

Random Bi Bi Systems

657

(1)

Unireactant Systems

658

(2)

Hybrid Ping Pong-Ordered and Ping Pong-Random Bi Bi Systems

660

(5)

Ordered Ter Bi System

665

(19)

Velocity Equation, Kinetic Constants, and Haldane Equations

665

(2)

Rate Constants

667

(1)

Distribution Equations

667

(1)

Effect of Isomerizations

668

(1)

Initial Velocity Studies in the Forward Direction

669

(3)

Plots With Two Changing Fixed Substrates

672

(2)

Varying Two Substrates Together

674

(1)

Product Inhibition

675

(5)

Reverse Direction---Ordered Bi Ter

680

(3)

Reduction to Rapid Equilibrium Ordered Ter Bi

683

(1)

Bi Uni Uni Uni Ping Pong Ter Bi System

684

(15)

Reaction Sequence

684

(1)

Velocity Equation, Kinetic Constants, and Haldane Equations

684

(2)

Rate Constants

686

(1)

Distribution Equations

686

(1)

Effect of Isomerizations

687

(1)

Initial Velocity Studies in the Forward Direction

687

(3)

Plots With Two Changing Fixed Substrates

690

(1)

Varying Two Substrates Together

691

(1)

Product Inhibition Studies

692

(4)

Reverse Direction---Uni Uni Uni Bi Ping Pong Bi Ter

696

(2)

Multiple Inhibition Studies

698

(1)

Alternate Designation---Uni Bi Uni Uni Ping Pong Bi Ter

699

(1)

Ordered Ter Ter System

699

(5)

Velocity Equation, Kinetic Constants, and Haldane Equations

699

(3)

Rate Constants

702

(1)

Distribution Equations

702

(1)

Effect of Isomerizations

703

(1)

Initial Velocity in the Forward and Reverse Directions

704

(1)

Product Inhibition Studies

704

(1)

Partial Rapid Equilibrium Ordered Terreactant Systems

704

(2)

Ordered Terreactant Systems With Rapid Equilibrium Random Sequences

706

(5)

Random A--B, Ordered C

706

(4)

Ordered A, Random B-C

710

(1)

Bi Uni Uni Bi Ping Pong Ter Ter System

711

(8)

Reaction Sequence

711

(3)

Velocity Equation, Kinetic Constants, and Haldane Equations

714

(2)

Rate Constants

716

(1)

Distribution Equations

716

(1)

Effect of Isomerizations

716

(1)

Initial Velocity Studies in the Forward Direction

717

(1)

Product Inhibition Studies

717

(2)

Bi Bi Uni Uni Ping Pong Ter Ter System

719

(8)

Reaction Sequence

719

(1)

Velocity Equation, Kinetic Constants, and Haldane Equations

720

(2)

Rate Constants

722

(1)

Distribution Equations

722

(1)

Effect of Isomerizations

723

(1)

Initial Velocity Studies in the Forward Direction

723

(1)

Product Inhibition Studies

723

(3)

Reverse Direction---Uni Uni Bi Bi Ping Pong Ter Ter

726

(1)

Hexa Uni Ping Pong System

727

(9)

Velocity Equation, Kinetic Constants, and Haldane Equations

727

(2)

Rate Constants

729

(1)

Distribution Equations

729

(1)

Effect of Isomerizations

730

(1)

Initial Velocity Studies in the Forward Direction

730

(1)

Product Inhibition Studies

731

(5)

Summary of Nonrandom Terreactant Systems

736

(4)

Other Possible Terreactant Systems

740

(9)

Theorell-Chance Systems

740

(1)

Terreactant Ping Pong Systems With Rapid Equilibrium Segments

741

(1)

Terreactant Ping Pong Systems With Rapid Equilibrium Random Segments

742

(2)

Hybrid (Two-Site) Rapid Equilibrium Random-Ping Pong Bi Bi Uni Uni System

744

(5)

Quadreactant Systems

749

(1)

General Rules for Predicting Initial Velocity Patterns

749

(18)

Intercept Effects

750

(1)

Exceptions to the Intercept Rule

750

(1)

Slope Effects

751

(1)

Effect of Irreversible Sequences

752

(5)

Substrates That Add Twice

757

(1)

Product Inhibition

757

(1)

Establishing a Reversible Connection by Adding Another Product

758

(1)

Modification of Slope and Intercept Rules for Steady-State Systems With Rapid Equilibrium Segments

759

(8)

Dead-End Inhibition

767

(16)

General Rules

779

(1)

Multiple Inhibition Analysis

780

(3)

Dead-End Inhibitors Versus Alternative Substrates

783

(1)

Mixed Dead-End and Product Inhibition

783

(10)

Velocity Equations

788

(3)

Dead-End Complexes With the Normal Enzyme Form

791

(2)

Inhibition by Alternative Substrates

793

(20)

Ordered Bi Bi With Alternative A

793

(5)

Ordered Bi Bi With Alternative B

798

(4)

Alternative Substrates That Promote a Partial Reaction in an Ordered Sequence

802

(1)

Ping Pong Bi Bi With Alternative Substrates

803

(7)

Alternative Substrates That Promote a Partial Ping Pong Reaction Sequence

810

(1)

Measurement of Common Product

811

(2)

Inhibition by Alternative Products

813

(5)

Substrate Inhibition

818

(12)

Substrate Inhibition in an Ordered Bireactant System

819

(7)

Substrate Inhibition in Ping Pong Systems

826

(4)

A Review of Inhibition Systems

830

(17)

Linear Inhibition

831

(2)

Parabolic Inhibition

833

(1)

Hyperbolic Inhibition

833

(3)

More Complex Types of Nonlinear Inhibition Systems

836

(5)

References

841

(6)

Isotope Exchange

Ordered Bi Bi

847

(6)

Random Bi Bi System

853

(1)

Isotope Exchange During A Net Reaction

854

(1)

Ping Pong Systems

855

(5)

Determining Exchange Velocities

860

(4)

Determining Keq

864

(1)

Derivation of Isotope Exchange Velocity Equations

864

(20)

References

882

(2)

Effects of pH and Temperature

Effect of pH

884

(42)

Effect of pH on Enzyme Stability

884

(4)

System A1. All Forms of ``E'' Bind S; Only E``S Yields Product

888

(5)

Plots of Vmaxapp Versus pH and 1/slope Versus pH

893

(3)

Dixon-Webb Log Plots

896

(2)

Correction for Ionization of the Substrate

898

(4)

Varieties of pH Responses

902

(1)

System A2. Only E'' Binds S; Only E``S Yields Product

902

(2)

Treating H+ as a Substrate

904

(3)

System A3. En and En+1 Bind S; Only EnS and En-1S Yield Product

907

(6)

System A5. General System: All Forms of ``E'' Bind S; All Forms of ``E''S Yield Product

913

(1)

A Diprotic System Where Successive pK Values of the Enzyme are Closer Than 3.5 pH Units

914

(3)

Displacement of pK Values Under Nonrapid Equilibrium Conditions

917

(3)

Effect of the Ionization of EP

920

(3)

Limitations of pH Studies

923

(1)

Choice of Buffers

924

(1)

Ionic Strength Effects

924

(2)

Effect of Temperature

926

(17)

Temperature Effects on Enzyme Stability

926

(3)

Identifying Prototropic Groups From ΔHion

929

(1)

Effect of Temperature on Km and Ki

930

(1)

The Collision Theory and the Arrhenius Equation---Energy of Activation

931

(3)

Eyring Transition State Theory---Absolute Reaction Rates

934

(7)

Thermodynamics of Enzyme Inactivation

941

(1)

References

941

(2)

Appendix Least Squares Method

943

(2)

Index

945

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Enzyme Kinetics Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems

Summary

Author Biography

Table of Contents

Supplemental Materials