Lecture on Enzyme Kinetics
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Kinetics of Enzymes
Enzymes follow zero order kinetics when substrate
concentrations are high. Zero order means there is no increase
in the rate of the reaction when more substrate is added.
Given the following breakdown of sucrose to glucose and
fructose
Sucrose + H20
Glucose + Fructose
H
H
H
H OH
O
HO
H
H
H
O
HO
OH
H
HO
H
H
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OH
OH
OH
OH
H
HO
H
k1
E  S  ES  E  P
k2
k -1
E = Enzyme S = Substrate P = Product
ES = Enzyme-Substrate complex
k1 rate constant for the forward reaction
k-1 = rate constant for the breakdown of the ES to
substrate
k2 = rate constant for the formation of the
products
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When the substrate concentration becomes large
enough to force the equilibrium to form completely
all ES the second step in the reaction becomes rate
limiting because no more ES can be made and the
enzyme-substrate complex is at its maximum value.
d P 
v
 k 2 ES 
dt
[ES] is the difference between the
rates of ES formation minus the
rates of its disappearance. 1
d ES 
 k1 E S  k 1 ES   k 2 ES 
dt
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Assumption of equilibrium
k-1>>k2 the formation of product is so
much slower than the formation of the ES
complex. That we can assume:
k 1 E S
Ks 

ES
k1
Ks is the dissociation constant for the ES complex.
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Assumption of steady state
Transient phase where in the course of a reaction the
concentration of ES does not change
2
d ES 
0
dt
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ET  E  ES
3
Combining 1 + 2 + 3
k1 ET - ESS  k -1  k 2 ES
rearranging
ESk-1  k 2  k1S  k1ET S
Divide by k1 and solve for [ES]

E T S
ES 
K M  S
Where
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k -1  k 2
KM 
k1
k2 ET S
 d P 
vo  
  k2 ES 
K M  S
 dt t 0
vo is the initial velocity when the reaction is just starting out.
And
Vmax  k 2 ET
Vmax S
vo 
K M  S
is the maximum velocity
The Michaelis - Menten
equation
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The Km is the substrate concentration where vo equals
one-half Vmax
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The KM widely varies among different enzymes
The KM
can be expressed as:
KM
k 1 k 2
k2

  Ks 
k1 k1
k1
As Ks decreases, the affinity for the substrate
increases. The KM can be a measure for substrate
affinity if k2<k-1
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There are a wide range of KM, Vmax , and efficiency
seen in enzymes
But how do we analyze kinetic data?
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The double reciprocal plot
1  KM
 
vo  Vmax
 1
1
 
 S Vmax
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Lineweaver-Burk plot: slope = KM/Vmax,
1/vo intercept is equal to 1/Vmax
the extrapolated x intercept is equal to -1/KM
For small errors in at low [S] leads to large errors in 1/vo
kcat
Vmax

ET
kcat is how many reactions an
enzyme can catalyze per second
The turnover number
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For Michaelis -Menton kinetics k2= kcat
When [S] << KM very little ES is formed and [E] = [E]T
and
k cat
k2
ET S  ES
vo 
KM
KM
Kcat/KM is a measure of catalytic efficiency
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What is catalytic perfection?
When k2>>k-1 or the ratio
Then
kcat
 k1
KM
k1k 2
k 1  k 2
is maximum
Or when every substrate that hits
the enzyme causes a reaction to
take place. This is catalytic
perfection.
Diffusion-controlled limit- diffusion rate of a substrate
is in the range of 108 to 109 M-1s-1. An enzyme lowers
the transition state so there is no activation energy
and the catalyzed rate is as fast as molecules collide.
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Reaction Mechanisms
A: Sequential Reactions
• All substrates must combine with enzyme
before reaction can occur
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Bisubstrate reactions
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Random Bisubstrate Reactions
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Ping-Pong Reactions
• Group transfer reactions
• One or more products released before all
substrates added
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Kinetic data cannot unambiguously
establish a reaction mechanism.
Although a phenomenological description can be
obtained the nature of the reaction intermediates
remain indeterminate and other independent
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measurements are needed
.
Inhibition kinetics
There are three types of inhibition kinetics competitive,
mixed and uncompetitive.
•Competitive- Where the inhibitor competes with the
substrate.
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Competitive Inhibition
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
EI
KI 
EI 
Vmax S
vo 
K M  S


I 
  1  
 KI 
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HIV protease inhibitors
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Competitive Inhibition: Lineweaver-Burke Plot
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Uncompetitive Inhibition
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Uncompetitive Inhibition: Lineweaver-Burke Plot
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Mixed inhibition
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Mixed inhibition is when the inhibitor binds to the
enzyme at a location distinct from the substrate
binding site. The binding of the inhibitor will either
alter the KM or Vmax or both.

EI
KI 
EI 

ESI
KI 
ESI 
 I 
Vmax S
   1  
vo 

K

K M   S
I 

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The effect of pH on kinetic parameters
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