enzyme kinetics

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enzyme kinetics course notes


  • IBSB Industrial Biotechnology and Systems Biology Research Group

    Marmara University, Department of Bioengineering, Istanbul, Turkey

    Ebru Toksoy ner

  • Reaction rate is the change in the concentration of a reactant or a product with time (M/s).

    D[A, B, C, D] = change in concentration of A/B/C/D over time period Dt

    a A + b B c C + d D

    rate = -D[A]


    a= -










  • The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants.

    Rate = k [A]x [B] y

    rxn is xth order in A

    yth order in B

    (x +y)th order overall

    a A + b B c C + d D

  • A product

    rate = -



    rate = k [A]0

    k = rate M/s= [A] is the concentration of A @ any t


    Dt= k-

  • D[A]

    Dt= k-

    [A] is the concentration of A @ any t

    [A]0 is the concentration of A @t=0

    t = t when [A] = [A]0/2

    t =[A]0


    The half-life, t, is the time required for the concentration of a reactant to

    decrease to half of its initial


    [A] = [A]0 - kt

  • A product

    rate = -



    rate = k [A]

    k = rate

    [A]= 1/s or s-1


    M= [A] is the concentration of A @ any t


    Dt= k [A]-

  • D[A]

    Dt= k [A]-

    [A] is the concentration of A @ any t

    [A]0 is the concentration of A @t=0

    [A] = [A]0exp(-kt) ln[A] = ln[A]0 - kt








  • A product

    rate = -



    rate = k [A]2

    k = rate

    [A]2= 1/M s or M-1s-1


    M2= [A] is the concentration of A @ any t


    Dt= k [A]2-

  • D[A]

    Dt= k [A]2-

    [A] is the concentration of A @ any t

    [A]0 is the concentration of A @t=0




    [A]0+ kt

    t =1


  • Order Rate Law


    Equation Half-Life




    rate = k

    rate = k [A]

    rate = k [A]2

    ln[A] = ln[A]0 - kt




    [A]0+ kt

    [A] = [A]0 - kt



    t =[A]02k

    t =1


  • In the situation where [S] >> [E] and at initial velocity rates, it is assumed that the

    changes in the concentration of the intermediate ES complex are very small over time (vo).

    This condition is termed a steady-state rate, and is referred to as steady-state kinetics.

    Rate of ES formation will be equal to the rate ES breakdown.

  • k1 : forward rate constant for substrate binding

    k-1 : reverse rate constant for substrate binding

    k2 : catalytic rate constant

    The rate of the reaction is: v = d[P]/dt = k2[ES]

    The change in [ES] as a function of time:

    d[ES]/dt = k1[E][S] - k-1[ES] - k2[ES]

    During the steady state: d[ES]/dt = 0

    0 = k1[E][S] - k-1[ES] - k2[ES]

  • 0 = k1[E][S] - k-1[ES] - k2[ES]

    The goal is to relate this equation to readily measurable experimental parameters, such as:

    The total amount of enzyme: ET = [E] + [ES] The concentration of substrate: [S] The measured steady state velocity (v = k2 [ES])

    We do not have a suitable way to measure [E], so ET will be used in its place:

    [E] = ET - [ES]

    [ES](k-1 + k-2) = k1[S](ET -[ES])

    [ES](k-1 + k2) = k1 ET[ES] - k1[ES][S]

    [ES](k-1 + k2 + k[S]) = k1 ET[S]

    [ES] = k1ET[S]/(k-1 + k2 + k1 [S])

  • [ES] = k1ET[S]/(k-1 + k2 + k1 [S])

    The rate (velocity) of the reaction:

    v = k2[ES] = k1k2ET[S]/{k-1 + k2 + k1[S]}

    = k2ET[S]/{(k-1 + k2)/ k1+ [S]}

    Vmax = k2ET

    highest reaction rate that can be attained because all (i.e. ET) of the enzyme is saturated with substrate.

    The KM or Michaelis constant: KM = (k-1 + k2)/ k1

    Michaelis-Menten Equation

  • Michaelis-Menten Equation

  • Michaelis-Menten Equation

    First order Zero order

  • A. Low [S] B. 50% [S] or Km C. High, saturating [S]

  • The significance of Km change based on the different rate

    constants and which step is the slowest (also called the rate-

    limiting step).

    In the simplest assumption, the rate of ES breakdown to

    product (k2) is the rate-determining step of the reaction

    k -1 >> k2 and Km = k -1/k1.

    This relation is also called a dissociation constant for the ES

    complex and can be used as a relative measure of the affinity of

    a substrate for an enzyme.

    k2 >> k -1 or k2 and k-1 are similar, then Km remains more complex

    and cannot be used as a measure of substrate affinity.

  • Experimentally, Km is a useful parameter for

    characterizing the number and/or types of substrates that a particular

    enzyme will utilize

    comparing similar enzymes from different tissues or different organisms

    Km of the rate-limiting enzyme in many of the biochemical metabolic

    pathways that determines the amount of product and overall regulation

    of a given pathway.

    Clinically, Km comparisons are useful for evaluating the effects mutations

    have on protein function for some inherited genetic diseases.

  • The catalytic constant of an enzyme is defined as: kcat = Vmax/[ET]

    kcat = k2kcat = 1000 sec

    -1 : the enzyme can convert 1000 molecules of substrate into

    product each second at saturating [S].

    kcat (units of sec-1), is also called the turnover number because under

    saturating substrate conditions, it represents the number of substrate molecules

    converted to product in a given unit of time on a single enzyme molecule.

    In practice, kcat values (not Vmax) are most often used for comparing the catalytic

    efficiencies of related enzyme classes or among different mutant forms of an


  • Determination of KM and vmax by Lab experiments

    Nonlinear Approach : optimization technique, where the constants are

    adjusted so that the sum of square of the errors between the predicted

    rate and the observed rate is minimum.

    N is the number of data points collected during the experiments.

    Nonparametric Approach : find rate at different substrate concentrations

    and then solve the equations for the unknown parameters.

  • Determination of KM and vmax by Lab experiments

    Graphical Approach

  • At equilibrium,

    no net change of [S] & [P]

    or of [ES] & [E]

    At pre-steady-state,

    [P] is low (close to zero

    time), hence, V0 for

    initial reaction velocity

    At pre-steady state, we can ignore the back reactions

  • Too much substrate

    inhibitors bind to the enzyme substrate

    complex but not the enzyme itself

    inhibitor and substrate bind simultaneously

    to enzyme, binding of one does not

    influence the affinity of either species to

    complex with the enzyme.

    substrate and inhibitor

    compete for the enzyme

  • Increase [S] to overcome inhibition

    Ki = dissociation constant

    for inhibitor

    Ki values are used to characterize and compare the

    effectiveness of inhibitors.

    This parameter is especially useful and important

    in evaluating the potential therapeutic value of

    inhibitors (drugs) of a given enzyme reaction.

    For example, Ki values are used for

    comparison of the different types of HIV

    protease inhibitors.

    In general, the lower the Ki value, the tighter

    the binding, and hence the more effective

    an inhibitor is.

  • Increase [S] to overcome inhibition

    Ki = dissociation constant

    for inhibitor

    Vmax unaltered, Km increased

  • Km unaltered, Vmax decreased

  • Km and Vmax both change

    Uncompetitive Inhibition

    Inhibitor binds ES complex.

    Works best when S is high.


  • = noncovalent interaction away from the active site.

    Protein-protein interactions.

    Small molecules.

    Common in multi-subunit protein complexes.

    Feedback inhibition

  • Feedback inhibition

  • Feedback inhibition

  • Allosteric enzymes often show sigmoid

    kinetics (i.e., non-Michaelis-


    they are very sensitive to small

    changes in substrate concentration

    Sigmoid kinetics is a consequence of

    interaction between sites due to the presence of sites that bind substrate other than the

    active site.

  • Thank you for your listening !

    http://ibsb. marmara.edu.tr


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