Fundamentals of

Biochemistry Fourth Edition

Chapter 12 Enzyme Kinetics, Inhibition, and Control

Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved.

Donald Voet • Judith G. Voet •

Charlotte W. Pratt

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Atorvastatin PDBid 1HWK

Chapter 12 Reaction Kinetics

Key Concepts 12.1

Simple rate equations describe the progress of first-order and second-order reactions.

The Michaelis–Menten equation relates the initial velocity of a reaction to the maximal reaction velocity and the Michaelis constant for a particular enzyme and substrate.

An enzyme’s overall catalytic efficiency is expressed as kcat/KM.

A Lineweaver–Burk plot can be used to present kinetic data and to calculate values for KM and Vmax.

Bisubstrate reactions can occur by an Ordered or Random sequential mechanism or by a Ping Pong mechanism.

Kinetics 1. Kinetics: the study of the rates at which chemical reactions occur; the rate of

a reaction and how this rate changes in response to different conditions is

intimately related to the path followed by the reaction and is therefore indicative

of its reaction mechanism

2. Enzyme Kinetics

a. Through kinetic studies the binding affinities of substrates and inhibitors to

an enzyme can be determined and the maximum catalytic rate of an

enzyme can be established.

b. By observing how the rate of an enzymatic reaction varies with the

reactions conditions and combining this information with that obtained from

chemical and structural studies of the enzyme, the enzyme’s catalytic

mechanism may be elucidated.

c. Most enzymes function as members of metabolic pathways; the study of

the kinetics of an enzymatic reaction leads to an understanding of that

enzyme’s role in an overall metabolic process.

d. Under proper conditions, the rate of an enzymatically catalyzed reaction is

proportional to the amount of the enzyme present and therefore most

enzyme assays are based on kinetic studies of the enzyme; Measurements

of enzymatically catalyzed reaction rates are therefore among the most

commonly employed procedures in biochemical and clinical analyses 4

Rates of Reaction

1. Simpler molecular processes by which a reaction may occur

A I1 I2 P

where I1 and I2 symbolize intermediates and thus its mechanistic description

2. Rates of Reactions

a. The order of a reaction can be experimentally determined by

measuring [A] or [P] as a function of time:

b. v = - d[A] = d[P]

dt dt

where v is the instantaneous rate (velocity) of the reaction

c. The order of a specific reaction can be determined by

measuring the reactant or product concentrations as a function

of time and comparing the fit of these data to equations

describing this behavior for reactions of various orders. 5

Rate Equation

6

1. Rate of a process is proportional to the frequency with which the

reacting molecules simultaneously come together to the products of

the concentrations of the reactants

2. Rate = k [A]a [B]b . . . [Z]z

where k is a proportionality constant—

rate constant order of a reaction is defined as (a + b + … + z)

3. Rate order corresponds to the molecularity of the reaction—the # of

molecules that must simultaneously collide in the elementary reaction

First Order Reaction

1. A plot of ln [A] versus t will

yield a straight line whose

slope is -k and whose intercept

on the ln [A] axis is ln [A]0

2. The time for half of the reactant

initially present to

decompose—its half-life—is a

constant and hence

independent of the initial

concentration of the reactant

3. Unstable substances such as

radioactive nuclei decompose

through first-order reactions.

7

8

Box 12-1a

Second Order Reaction

1. Second-order progress curve descends more steeply than the first-

order curve before the first half-time, after which the first-order curve

is the more rapidly decreasing of the two

2. The half-time for a second-order reaction is expressed t1/2 = 1/k [A]0;

therefore it is dependent on the initial reactant concentration

9

Enzyme Kinetics

Nomenclature

• Kinetic Mechanism --- A detailed

description of a series of elementary

reactions that describe an enzyme-catalyzed

reaction.

• Chemical Mechanism --- A detailed

description of the chemistry of each step

including structures of transition states,

resonance etc.

11

Nomenclature

• Enzyme --- E

• Reactants --- A, B, C…..

• Products --- P, Q, R…..

• Inhibitors --- I, J, K….

• Non-covalent complex --- E·S

• Commonly abbreviate [E] by omitting the brackets (eg.

E assumes molar concentration)

• Rate constants --- k1, k-1, k2, etc.

12

Rate Equation for an Enzyme-Catalyzed

Unimolecular reaction (The Michaelis-

Menten Model)

13

Michaelis-

Menten Model

1. Enzyme-substrate complex: when the substrate concentration

becomes high enough to entirely convert the enzyme to the ES

form (Michaelis complex), the second step of the reaction

becomes rate limiting and the overall reaction rate becomes

insensitive to further increases in substrate concentration

2. Assumption of equilibrium: k-1 >> k2 so that the first step of the

reaction achieves equilibrium

3. Assumption of Steady State: [ES] remains approximately

constant until the substrate is nearly exhausted

14

Progress Curve: Simple Enzyme-

Catalyzed Reaction

16

4. The Michaelis-Menten Equation for enzyme kinetics

v0 = Vmax [S]/(Km + [S])

5. KM is the substrate concentration at which the reaction velocity is

half-maximal; KM is also a measure of the affinity of the enzyme for

its substrate providing k2/k1 is small compared with Ks, that is, k2 <<

k-1

6. Ks is the dissociation constant; as Ks decreases, the enzyme’s affinity

for substrate increases

Michaelis-Menten Equation

Michaelis-Menten Kinetics

Enzyme Kinetic Parameters

19

7. Catalytic constant: An enzyme’s kinetic parameter that describes its

catalytic efficiency

kcat = (Vmax/[E]T)

Quantity is also known as turnover number because it is the number of reaction processes

that each active site catalyzes per unit time

8. Diffusion-controlled limit is in the range of 108 to 109M-1s-1 where k1 can be

no greater than the frequency with which enzyme and substrate molecules

collide with each other in solution; enzymes within this range must catalyze a

reaction almost every time they encounter a substrate molecule

9. At very high values of [S], v0 asymptotically approaches Vmax

Page 373

Lineweaver-Burke Equation

10. Lineweaver-Burk equation for determining the values of Vmax

1/v0 = (Km/Vmax) x (1/[S]) + (1/Vmax)

20

Double-Reciprocal

(Lineweaver-Burk) Plot

Enzyme Reactions May Pass Through a

Variety of Intermediates

Steady State Kinetics Incapable of

Revealing Enzyme Intermediates

Figure 12-5

24

Bisubstrate Reactions

1. Enzymatic reactions involving two substrates and yielding two

products account for ~60% of known biochemical reactions.

2. Two types:

a. Transferase reactions in which enzyme catalyzes the transfer

of a specific functional group from one of the substrates to the

other

b. Oxidation-reduction reactions in which reducing equivalents

are transferred between the two substrates

Page 375

Bisubstrate Reactions

25

Terminology by W. W. Cleland for representing enzymatic

reactions:

1.Substrates are designated by letters A, B, C, and D in the order

that they add to the enzyme

2.Stable enzyme forms are designated E, F, and G with E being the

free enzyme. A stable enzyme form is defined as one that by itself is

incapable of converting to another stable enzyme form

26

3. Products are designated P, Q, R, and S in the order that

they leave the enzyme

4. The number of reactants and products in a given reaction

are specified, in order, by the terms Uni (one), Bi (two), Ter

(three), and Quad (four)

Bisubstrate Reactions

Bisubstrate Reaction: Group Transfer

Bisubstrate Reactions

Page 376

Sequential reactions

1. Reactions in which all substrates must combine with the

enzyme before a reaction can occur and products be released

2. Ordered mechanism: a compulsory order of substrate

addition to the enzyme

3. Random mechanism: no preference for the order of substrate

addition

4. Characteristic feature of sequential Bi Bi reactions is that the

lines intersect to the left of the 1/v0 axis 29

Bisubstrate Reactions

Ordered Bisubstrate Reaction

Random Bisubstrate Reaction

Page 376

32

Rate Equations

1.Steady state kinetic measurements can be used to distinguish

among the foregoing bisubstrate mechanisms

2.Vmax is the maximal velocity of the enzyme obtained when both

A and B are present at saturating concentrations; KAM and KBM

are the respective concentrations of A and B necessary to

achieve ½ Vmax in the presence of a saturating concentration of

the other; KAS and KBS are the respective dissociation constants

of A and B from the enzyme E

Bisubstrate Reactions

33

Ping Pong Reactions

1.Mechanisms in which one or more products are released before all

substrates have been added

2.Also known as double-displacement reactions where substrates A and B

do not encounter one another on the surface of the enzyme

3.Parallel lines are diagnostic for Ping Pong mechanisms

Isotope Exchange

1.Sequential and Ping Pong bisubstrate mechanisms may be

differentiated using isotope exchange studies

2.Enzymes sucrose phosphorylase and maltose phosphorylase provide

two clearcut examples of enzymatically catalyzed isotopic reactions

Bisubstrate Reactions

Double-Displacement (Ping Pong)

Bisubstrate Reaction

Chapter 12 Reaction Kinetics

Checkpoint 12.1

• Write the rate equations for a first-order and a second-order reaction. • If you know a reaction’s half-life, can you determine its rate constant? What other information do you need? • What are the differences between instantaneous velocity, initial velocity, and maximal velocity for an enzymatic reaction? • Derive the Michaelis–Menten equation.

Chapter 12 Reaction Kinetics

Checkpoint 12.1 • What do the values of KM and kcat/KM reveal about an enzyme? • Why can’t an enzyme have a kcat/KM

value greater than 109 M–1 · s–1? • Write the Lineweaver–Burk (double reciprocal) equation and describe the features of a Lineweaver–Burk plot. • Why can’t enzyme kinetics prove that a particular enzyme mechanism is correct? • Use Cleland notation to describe Ordered and Random sequential reactions and a Ping Pong reaction.

Chapter 12 Enzyme Inhibition

Key Concepts 12.2

•Enzyme inhibitors interact reversibly or irreversibly with an enzyme to alter its KM and/or Vmax values. •A competitive inhibitor binds to the enzyme’s active site and increases the apparent KM for the reaction. •An uncompetitive enzyme inhibitor affects catalytic activity such that both the apparent KM and the apparent Vmax decrease. •A mixed enzyme inhibitor alters both catalytic activity and substrate binding such that the apparent Vmax decreases and the apparent KM may increase or decrease.

Page 378

Inhibitors

1. Inhibitors: Substances that reduce an enzyme’s activity

2. Structurally resemble their enzyme’s substrate but either

do not react or react very slowly compared to substrate

3. Used to probe the chemical and conformational nature of

a substrate-binding site as part of an effort to elucidate the

enzyme’s catalytic mechanism

38

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Transition State Analog Inhibitor

1. Competitive inhibitor: A

substance that

competes directly with a

normal substrate for an

enzyme-binding site

2. Inhibitor resembles the

substrate to the extent

that it specifically binds

to the active site but

differs from it so as to

be unreactive

42

Competitive Inhibitors

Page 377

43

Competitive Inhibitors

Page 378

44

3. I, the inhibitor, binds reversibly to the enzyme and

is in rapid equilibrium with it so that KI+ and EI—

enzyme-inhibitor complex—is catalytically inactive.

4. Acts by reducing the concentration of free enzyme

available for substrate binding.

Competitive Inhibitors

Figure 12-6

45

Competitive Inhibitors

5. The inhibitor does not affect the turnover number of the enzyme

Page 380

46

6. Inactivator: if the inhibitor binds irreversibly to the enzyme and

somehow inactivates the enzyme

Competitive Enzyme Inhibition

Competitive Inhibition: Ethanol

Treatment of Methanol Poisoning

Competitive Enzyme Inhibition

Competitive Enzyme Inhibition

Page 381

Uncompetitive Inhibition

1. Inhibitor binds directly to the enzyme-substrate complex

but not to the free enzyme

2. UI need not resemble the substrate

3. At high values of [S], v0 asymptotically approaches Vmax/α’

so that the effects of uncompetitive inhibition on Vmax are

not reversed by increasing the substrate concentration

51

Uncompetitive Enzyme Inhibition

53

4. A series of Lineweaver-Burk plots at various uncompetitive

inhibitor concentrations consists of a family of parallel lines—

indicative of a uncompetitive inhibition

Uncompetitive Inhibition

Uncompetitive Enzyme Inhibition

Page 382

Mixed Inhibition (Non-competitive)

1. Both the enzyme and the enzyme-substrate complex bind

inhibitor where both of the inhibitor-binding steps are assumed

to be at equilibrium with different dissociation constants

2. A mixed inhibitor binds to enzyme sites that participate in both

substrate binding and catalysis

3. Michaelis-Menten equation for mixed inhibition

v0 = (Vmax [S]) / (Km + ’[S])

55

Mixed (Noncompetitive)

Enzyme Inhibition

Mixed (Noncompetitive)

Enzyme Inhibition

Mixed Inhibition

4. Mixed inhibitors are therefore effective at both high and low substrate

concentrations

Enzyme Inhibitor Effects

Applied Enzyme

Inhibition

60

1. Acquired immunodeficiency

syndrome (AIDS) is caused by

human immunodeficiency virus

type 1

2. HIV -1 is targeted to and

specifically replicates within

helper T cells, essential

components of the immune

system

3. Reverse transcriptase inhibitors

are only partially effective

a. 3’-azido-3’-deoxythymidine

(AZT) was the first drug to be

approved by the FDA to fight

AIDS, but only slowed the

progression of an HIV

infection

b. Under the selective pressure

of an anti-HIV drug such as

AZT, the drug’s target

receptor rapidly evolves to a

drug-resistant form

4. HIV-1 polyproteins are cleaved by HIV-1 protease

5. Aspartic proteases and their catalytic mechanism

a. Proteolytic enzymes have three essential

catalytic components

i. A nucleophile to attack the carbonyl C

atom of the scissile peptide to form a

tetrahedral intermediate

ii. An electrophile to stabilize the negative

charge that develops on the carbonyl O

atom of the tetrahedral intermediate

iii. A proton donor so as to make the amide N

atom of the scissile peptide a good leaving

group

61

Enzyme Inhibition

62

Enzyme

Inhibition

6. HIV-1 protease

inhibitors are effective

anti-AIDS agents

a. HIV-1 protease

differs from

eukaryotic aspartic

proteases in that it

is a homodimer of

99-residue

subunits, even

though its x-ray

structure

resembles those of

eukaryotic aspartic

proteases

Chapter 12 Enzyme Inhibition

Checkpoint 12.2 • What distinguishes an inhibitor from an inactivator? • Why might an enzyme’s substrate, transition state, and product all serve as starting points for the design of a competitive inhibitor? • Describe the effects of competitive, uncompetitive, and mixed inhibitors on KM and Vmax. • How can inhibitor binding to an enzyme be quantified? • How does pure noncompetitive inhibition differ from other forms of inhibition?

Chapter 12 Control of Enzyme Activity

Key Concepts 12.3

•Allosteric effectors bind to multisubunit enzymes such as aspartate transcarbamoylase, thereby inducing cooperative conformational changes that alter the enzyme’s catalytic activity. •Phosphorylation and dephosphorylation of an enzyme such as glycogen phosphorylase can control its activity by shifting the equilibrium between more active and less active conformations.

Page 386

Regulation of

Enzymatic

Activity

1. Control of enzyme availability: The

amount of a given enzyme in a cell

depends on both its rate of synthesis

and its rate of degradation

2. Control of enzyme activity: An

enzyme’s catalytic activity may be

directly regulated through

conformational or structural alterations

a. Rate of enzymatically catalyzed

reaction is directly proportional to the

concentration of its enzyme-

substrate complex

b. Catalytic activity of an enzyme can

be controlled through the variation of

its substrate-binding affinity

c. An enzyme’s substrate-binding

affinity may likewise vary with the

binding of small molecule effectors,

thereby changing the enzyme’s

catalytic activity 65

Aspartate Transcarbamoylase Reaction

67

The feedback inhibition of ATCase regulates Pyrimidine

Biosynthesis

1. Aspartate transcarbamoylase catalyzes the formation of N-

carbamoylaspartate from carbamoyl phosphate and aspartate

2. ATCase is heterotropically inhibited by cytidine triphosphate (CTP)

and is heterotropically activated by adenosine triphosphate (ATP);

CTP therefore decreases the enzyme’s catalytic rate, whereas

ATP increases it

Regulation of Enzymatic Activity

Allosteric Effectors: ATCase Reaction

69

3. Feedback inhibition: A

common mode of

metabolic regulation in

which the concentration

of a biosynthetic

pathway product

controls the activity of

an enzyme near the

beginning of that

pathway

Regulation of Enzymatic Activity

Figure 12-12 70

Structural Basis of Allosterism in

ATCase

1. Region of protein that

undergoes the most

profound conformational

rearrangement upon the

TR transition is a

flexible loop composed of

residues 230 to 250 in the

catalytic subunit

2. Both the inhibitor CTP and

activator ATP bind to the

same site on the outer

edge of the regulatory

subunit about 60 Å away

from the nearest catalytic

site

Regulation of

Enzymatic

Activity

Page 388

71

Allosteric changes alter ATCase’s substrate-binding sites

1. The regulatory subunits allosterically reduce the activity

of the catalytic subunits in the intact enzyme

2. ATP preferentially binds to ATCase’s R state whereas

CTP bind to the T state

3. TR transition maintains the protein’s D3 symmetry

4. ATCase’s substrates each bind to a separate domain of

the catalytic subunit

5. ATCase’s tertiary and quaternary shifts are so tightly

coupled through extensive intersubunit contacts that they

cannot occur independently

Regulation of

Enzymatic

Activity

ATCase: T-State vs. R-State

ATCase from E. coli PDBids 5AT1 and 8ATC

ATCase: Conformational Changes

Control by Covalent Modification:

Phosphorylation

Product of Glycogen Phosphorylase

Rabbit Muscle Glycogen Phosphorylase

Conformational Changes:

Glycogen Phosphorylase

Glycogen phosphorylase PDBids 8GPB and 7GPB

Glycogen Phosphorylase:

Control by Phosphorylation

Figure 12-14b

79

2. When there is high demand for ATP (low [ATP], low [G6P], and

high [AMP]), glycogen phosphorylase is stimulated and glycogen

synthase is inhibited, so flux favors glycogen breakdown

Protein Phosphorylation

Figure 12-15

80

3. When [ATP] and [G6P] are high, the reverse is true

and glycogen synthesis is favored

4. AMP promotes phosphorylase’s T(inactive)R(active)

conformational shift by binding to the R state of the

enzyme at its allosteric effector site

Protein Phosphorylation

Chapter 12 Control of Enzyme Activity

Checkpoint 12.3

• Compare and contrast the actions of an allosteric effector, a competitive enzyme inhibitor, and a noncompetitive inhibitor. • Explain the structural basis for cooperative substrate binding and allosteric control in ATCase. • Why are such allosteric enzymes composed of more than one catalytic subunit? • Describe how phosphorylation and dephosphorylation control the activity of glycogen phosphorylase. • List some advantages of phosphorylation/ dephosphorylation cascade systems over simple allosteric regulation.

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