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  • 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