Lecture 15
Chemical Reaction Engineering (CRE) is the
field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in
which they take place.
Today’s lecture
 Enzymes
 Michealis-Menten Kinetics
 Lineweaver-Burk Plot
 Enzyme Inhibition
 Competitive
 Uncompetitive
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Last lecture
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Last lecture
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Enzymes
Michaelis-Menten Kinetics.
Enzymes are protein like substances with catalytic properties.
Enzyme unease. [From Biochemistry, 3/E by Stryer, copywrited 1988 by Lubert
Stryer. Used with permission of W.H. Freeman and Company.]
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Enzymes
It provides a pathway for the substrate to proceed at a faster
rate.The substrate, S, reacts to form a product P.
S
Slow
P
ES
Fast
A given enzyme can only catalyze only one reaction.

Example, Urea is decomposed by the enzyme urease.
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A given enzyme can only catalyze only one reaction. Urea is
decomposed by the enzyme urease, as shown below.
2O
NH2CONH2  UREASE H

2NH3  CO2  UREASE
2O
S  E H

PE
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The corresponding mechanism is:
E  S  E  S
k1
E  S  E  S
k2
E  S  W  P  E
k3
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Michaelis-Menten Kinetics
rP  k 3 E  SW
rES  0  k1 ES  k 2 E  S  k 3WE  S
k1 E S
E  S 
k 2  k 3W
E t  E  E  S
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Et
E  
 k1S 

1  
 k 2  k 3W 
Michaelis-Menten Kinetics
Vmax


k 3 W E tS
k catE t S
rP  k 3 E  SW  

k 2  k 3W
K

S
m
S
k1


k cat
Km
VmaxS
rP  k 3 E  SW  
Km  S
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Vmax=kcat* Et
Turnover Number: kcat
Number of substrate molecules (moles) converted to product
in a given time (s) on a single enzyme molecule
(molecules/molecule/time)
For the reaction
kcat
H2O2 + E →H2O + O + E
40,000,000 molecules of H2O2 converted to product per second
on a single enzyme molecule.
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Summary
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Michaelis-Menten Equation
VmaxS
rP  rS 
KM  S
(Michaelis-Menten plot)
Vmax
Vmax
VmaxS1/ 2

2
K M  S1/ 2
Solving:
-rs
KM=S1/2
S1/2
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CS
therefore KM is the
concentration at which the
rate is half the maximum rate
Inverting yields
1
1
KM  1 


 
 rS Vmax Vmax  S 
Lineweaver-Burk Plot
1/-rS
slope = KM/Vmax
1/Vmax
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1/S
Types of Enzyme Inhibition
Competitive
E  I  I  E (inactive)
Uncompetitive
E  S  I  I  E  S (inactive)
Non-competitive
E  S  I  I  E  S (inactive)
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I  E  S  I  E  S (inactive)
Competitive Inhibition
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Competitive Inhibition
k3
k1
E  S 
E  S 
EP


k2
k4
E  I


E

I
(
inactive
)

k5
1) Mechanisms:
E  S  E S
E S  P  E
EI  E  I
rP  k 3C ES
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E S  E  S
E  I  EI
Competitive Inhibition
2) Rates:
rES  0  k1CSCE  k 2CES  k 3CES
k1CSC E CSC E
C ES 

k 2  k3
Km
k 3CSCE
rP 
Km
rIE  0  k 4CICE  k 5CIE
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C I E
CICE

KI
k5
KI 
k4
Competitive Inhibition
C Etot  C E  C ES  C IE
k 3C EtotCS
rP 
CI K m
K m  CS 
KI
VmaxCS
 rS 
 CI 

CS  K m 1 
 KI 
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1
1
k m  CI  1
1 



 rS Vmax Vmax  K I  CS
C Etot
CE 
CS C I
1

Km KI
Competitive Inhibition
From before (no competition):
1
1
Km 1


 rS Vmax Vmax CS
Increasing CI
Competitive
No Inhibition Competitive
1
rS
slope
Intercept
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1
Vmax
Km
Vmax
1
1
K m  CI  1
1  


 rS Vmax Vmax  K I  CS
1
CS
Intercept does not change, slope increases
as inhibitor concentration increases
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Uncompetitive Inhibition
Inhibition only has affinity for enzyme-substrate complex
E S
k1


k2
k3
E  S 
P
k4

I  E S
I  E  S (inactive)

k5
Developing the rate law
rP  rS  k cat E  S
rES  0  k1 ES  k 2 E  S  k cat E  S  k 4 IE  S  k 5 I  E  S (1)
rIES  0  k 4 IE  S  k 5 I  E  S
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(2)
Adding (1) and (2)
k1 E S  k 2 E  S  k cat E  S  0
k1 E S E S
E  S 

k 2  k cat
KM
From (2)

k4
I E  S I E S
I  E  S  IE  S 

k5
KI
K IK M
k5
KI 
k4
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k cat E S
rp  k cat E  S 
KM
Total enzyme
E t  E  E S I E S
 S IS 
 E 1


 K M K I K M 
rp 

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k cat E t S
 S IS 
K M 1


K
K
K

M
I M 
Vmax S
 rS  rP 
 I  

K M  S1 
 KI 
 I 
1
1 

K M  S1 
rS Vmax S  
 K I 
1
K M  1  1  I 

 
1 
rS Vmax S  Vmax  K I 
Slope remains the same but intercept changes as inhibitor
concentration
is increased

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Lineweaver-Burk Plot for uncompetitive inhibition
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Noncompetitive Inhibition (Mixed)
E+S
+I
E·S
-I
-I
(inactive)I.E + S
P+E
+I
I.E.S (inactive)
Increasing I
1

rS
No Inhibition
Both slope and
intercept changes
1
CS
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 rS 
VmaxCS
 CI 
k m  CS 1  
 kI 
1
1  C I  k m  1  C I 
 1  
1   

 rS Vmax  k I  Vmax  CS  k I 
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End of Lecture 15
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