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Tables of Contents for Enzyme Kinetics
Chapter/Section Title
Page #
Page Count
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