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

by Segel, Irwin H.

• ISBN13: 9780471303091
• ISBN10: 0471303097
• Edition: 1st
• Format: Paperback
• Copyright: 1993-05-17
• Publisher: Wiley-Interscience

Summary

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.

Author Biography

Irwin H. Segel is the author of Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems, published by Wiley.

Table of Contents

Introduction---Enzymes As Biological Catalysts
The Discovery of Enzymes and the Development of Enzymology	1	(3)
Life, Energy, and Coupled Reactions	4	(1)
Enzymes as Catalysts	5	(2)
The Active Site	7	(2)
Three-Point Attachment	9	(1)
The Flexible Enzyme-Induced Fit Hypothesis	10	(2)
Factors Responsible for the Catalytic Efficiency of Enzymes	12	(2)
Enzyme Kinetics	14	(4)
References	15	(3)
Kinetics of Unireactant Enzymes
The Henry Equation and the Michaelis-Menten Equation	18	(4)
General Rules for Writing Velocity Equations for Rapid Equilibrium Systems	22	(3)
The Van Slyke Equation	25	(1)
The Briggs-Haldane Steady-State Approach	25	(4)
Reversible Reactions---Effect of Product on Forward Velocity	29	(5)
Haldane Relatioship Between Kinetic Constants and the Equilibrium Constant	34	(3)
Specific (or Relative or Reduced) Substrate Concentration and Velocity	37	(1)
Velocity Versus Substrate Concentration Curve	38	(1)
Reaction Order	39	(5)
Graphical Determination of Km and Vmax	44	(10)
Lineweaver-Burk Reciprocal Plot: 1/v versus 1/[S]	46	(1)
Substrate Concentration Range	46	(1)
Labeling the Axes of Reciprocal Plots	46	(4)
Graphical Analysis as a Method of Solving Simultaneuous Equations	50	(1)
Effect of Impure Substrate on Km and Vmax	50	(1)
Eisenthal, Cornish-Bowden Plot and New Dixon Plot	51	(2)
Log v Versus Log [S] Plot	53	(1)
Integrated Form of the Henri-Michaelis-Menten Equation	54	(10)
Integrated Rate Equation Assuming No Product Inhibition (Kms ≪ Kmp) and that Keq Is Very Large	54	(3)
Determination of Km and Vmax from [S] and v	57	(2)
Integrated Rate Equation Where Kmp ≌ Kms and Keq Is Very Large	59	(2)
Integrated Rate Equation Where Kmp ≌ Kms and Keq Is Not Very Large	61	(3)
Multiple Enzymes Catalyzing the Same Reaction	64	(8)
Kinetic Behavior at High Enzyme Concentrations	72	(5)
Enzyme Assays	77	(12)
Initial Velocity as a Function of [E]t	78	(1)
Enzyme Units and Specific Activities---Quantitating [E]t	78	(1)
Turnover Number	79	(1)
Quantitation of [E]t Using the Integrated Velocity Equation	80	(1)
Reporting Data	80	(1)
Enzyme Purification	81	(2)
Determination of v	83	(1)
Assays with Auxillary Enzymes	83	(2)
Kinetics of Coupled Assays	85	(4)
Effects of Endogenous Substrates	89	(11)
References	97	(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