# 12. enzyme kinetics

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Slides for BiochemistryTRANSCRIPT

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

Atorvastatin (Lipitor)

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

An enzymes overall catalytic efficiency is expressed as kcat/KM.

A LineweaverBurk 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 enzymes 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

enzymes 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 reactionthe # 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

decomposeits half-lifeis 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 --- ES

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

Michaelis-Menten Kinetics

Enzyme Kinetic Parameters

19

7. Catalytic constant: An enzymes 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

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