Biocatalysts

1. Enzyme Kinetics and Catalysis II

2. Kinetics of Enzymes
Enzymes follow zero order kinetics when substrate concentrati
ons 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 fruc
tose
Sucrose + H20 Glucose + Fructose
O
H
HO
H
HO
H
OH
OH
H
H
OH
OH
HO
H
H OH
O
H
H
HO
H
H
H
OH

3. P
E
ES
S
E 2
1
1
-
k
k
k



 
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 produc
ts

4. When the substrate concentration becomes large enough to fo
rce 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 maximu
m value.
   
ES
P
2
k
dt
d
v 

[ES] is the difference between the
rates of ES formation minus the r
ates of its disappearance.
        
ES
ES
S
E
ES
2
1
1 k
k
k
dt
d


 
1

5. Assumption of equilibrium
k-1>>k2 the formation of product is so muc
h slower than the formation of the ES complex. T
hat we can assume:
  
 
ES
S
E
1
1

 
k
k
Ks
Ks is the dissociation constant for the ES complex.

6. Assumption of steady state
Transient phase where in the course of a reaction the co
ncentration of ES does not change
  0
ES

dt
d
2

7.      
ES
E
E T 
 3
Combining 1 + 2 + 3
   
     
ES
k
k
S
ES
-
E
k 2
1
-
T
1 

   
     
S
E
k
S
k
k
k
ES T
1
1
2
1
- 


     
 
S
K
S
E
ES T


M
1
2
1
-
k
k
k
K


M
rearranging
Divide by k1 and solve for [ES] Where

8.        
 
S
K
S
E
ES
P T
2
2
0 









 M
t
o
k
k
dt
d
v
vo is the initial velocity when the reaction is just starting out.
And is the maximum velocity
 T
2
max E
k
V 
 
 
S
K
S
Vmax


M
o
v
The Michaelis –Menten
equation

9. The Km is the substrate concentration where vo equals one
-half Vmax

10. The KM widely varies among different enzymes
The KM
can be expressed as:
1
2
1
2
1
1
K
K
k
k
k
k
k
k
s
M 


 
As Ks decreases, the affinity for the substrate increase
s. The KM can be a measure for substrate affinity if k2
<k-1

12. Inhibition kinetics
There are three types of inhibition kinetics competitive,
mixed and uncompetitive.
•Competitive- Where the inhibitor competes with the substrat
e.

13. Competitive Inhibition

14.  
 
S
K
S
V
M
max



o
v
 










I
K
I
1

  
 
EI
I
E
KI 

16. HIV protease inhibitors

17. Uncompetitive Inhibition

18. Mixed or Non competitive inhibition