enzyme kinetics
DESCRIPTION
enzyme kinetics course notesTRANSCRIPT
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IBSB – Industrial Biotechnology and Systems Biology Research Group
Marmara University, Department of Bioengineering, Istanbul, Turkey
Ebru Toksoy Öner
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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]
Dt1
a= -
D[B]
Dt1
b=
D[C]
Dt1
c=
D[D]
Dt1
d
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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
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A product
rate = -
D[A]
Dt
rate = k [A]0
k = rate M/s= [A] is the concentration of A @ any t
D[A]
Dt= k-
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D[A]
Dt= k-
[A] is the concentration of A @ any t
[A]0 is the concentration of A @t=0
t½ = t when [A] = [A]0/2
t½ =[A]0
2k
The half-life, t½, is the time required for
the concentration of a reactant to
decrease to half of its initial
concentration.
[A] = [A]0 - kt
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A product
rate = -
D[A]
Dt
rate = k [A]
k = rate
[A]= 1/s or s-1
M/s
M= [A] is the concentration of A @ any t
D[A]
Dt= k [A]-
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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
ln[A]0
[A]0/2
k=t½
ln2
k=
0.693
k=
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A product
rate = -
D[A]
Dt
rate = k [A]2
k = rate
[A]2= 1/M s or M-1s-1
M/s
M2= [A] is the concentration of A @ any t
D[A]
Dt= k [A]2-
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D[A]
Dt= k [A]2-
[A] is the concentration of A @ any t
[A]0 is the concentration of A @t=0
1
[A]=
1
[A]0
+ kt
t½ =1
k[A]0
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Order Rate Law
Concentration-Time
Equation Half-Life
0
1
2
rate = k
rate = k [A]
rate = k [A]2
ln[A] = ln[A]0 - kt
1
[A]=
1
[A]0
+ kt
[A] = [A]0 - kt
t½ln2
k=
t½ =[A]0
2k
t½ =1
k[A]0
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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.
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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]
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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])
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[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
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Michaelis-Menten Equation
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Michaelis-Menten Equation
First order Zero order
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A. Low [S] B. 50% [S] or Km C. High, saturating [S]
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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.
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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.
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The catalytic constant of an enzyme is defined as: kcat = Vmax/[ET]
kcat = k2
kcat = 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
enzyme.
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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.
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Determination of KM and vmax by Lab experiments
Graphical Approach
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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
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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
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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.
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Increase [S] to overcome inhibition
Ki = dissociation constant
for inhibitor
Vmax unaltered, Km increased
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Km unaltered, Vmax decreased
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Km and Vmax both change
Uncompetitive Inhibition
Inhibitor binds ES complex.
Works best when S is high.
Rare.
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= noncovalent interaction away from the active site.
Protein-protein interactions.
Small molecules.
Common in multi-subunit protein complexes.
Feedback inhibition
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Feedback inhibition
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Feedback inhibition
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Allosteric enzymes often show sigmoid
kinetics (i.e., non-Michaelis-
Menten)
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.
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Thank you for your listening !
http://ibsb. marmara.edu.tr