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.
Lecture 15 – Tuesday 3/12/2013
Enzymatic Reactions
 Michealis-Menten Kinetics
 Lineweaver-Burk Plot
 Enzyme Inhibition
 Competitive
 Uncompetitive
 Non-Competitive
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Review Last Lecture
Active Intermediates and PSSH
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Review Last Lecture
Active Intermediates and PSSH
1.In the PSSH, we set the rate of formation of the active
intermediates equal to zero. If the active intermediate A* is
involved in m different reactions, we set it to:
m
rA*.net   rA*i  0
i 1
2. The azomethane (AZO) decomposition mechanism is
k ( AZO) 2
 rN 2 
1  k ' ( AZO)
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By applying the PSSH to AZO*, we show the rate law, which
exhibits first-order dependence with respect to AZO at high
AZO concentrations and second-order dependence with
respect to AZO at low AZO concentrations.
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
Enzymes provide 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
 can only catalyze only one reaction.
A given enzyme
Example, Urea is decomposed by the enzyme urease.
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Enzymes - Urease
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
The corresponding mechanism is:
E  S  E  S
k1
E  S  E  S
k2
E  S  W  P  E
k3
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Enzymes - Michaelis-Menten Kinetics
rP  k3 E  S W 
rES  0  k1 E S   k2 E  S   k3W E  S 
k1 E S 
E  S  
k2  k3W
Et  E   E  S 
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Et
E  
 k1S 

1  
 k2  k3W 
Enzymes - Michaelis-Menten Kinetics
Vmax



k3W Et S
kcat Et S
rP  k3 E  S W  

k2  k3W
K

S
M
S
k1


kcat
KM
VmaxS
rP  k3 E  S W  
Km  S
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Enzymes - Michaelis-Menten Kinetics
Vmax=kcatEt
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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Enzymes - Michaelis-Menten Kinetics
Michaelis-Menten Equation
VmaxS
rP  rS 
KM  S
(Michaelis-Menten plot)
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Vmax
Solving:
-rs
KM=S1/2
S1/2
CS
Vmax
VmaxS1/ 2

2
K M  S1/ 2
therefore KM is the
concentration at which the rate
is half the maximum rate.
Enzymes - Michaelis-Menten Kinetics
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) Rate Laws:
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
C I E
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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  K M 1
 rS Vmax Vmax CS
Increasing C
I
Competitive
No Inhibition
1
rS
slope 
Intercept 
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1
Vmax
KM
Vmax
Competitive
1
1
K M  CI
1 


 rS Vmax Vmax  K I
1
CS
Intercept does not change, slope increases as
inhibitor concentration increases
 1

 CS
Uncompetitive Inhibition
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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  kcat E  S 
rES  0  k1 E S   k2 E  S   kcat E  S   k4 I E  S   k5 I  E  S 
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rIES  0  k4 I E  S   k5 I  E  S 
(1)
(2)
Uncompetitive Inhibition
Adding (1) and (2)
k1 E S   k2 E  S   kcat E  S   0
k1 E S  E S 
E  S  

k2  kcat
KM
From (2)
I  E  S   k4 I E  S   I E  S   I E S 
k5
KI
k5
KI 
k4
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kcat E S 
rp  kcat E  S  
KM
KI KM
Uncompetitive Inhibition
Total enzyme
Et  E   E  S   I  E  S 


S  I S  

 E 1 

 KM KI KM 
kcat Et S 
rp 


S  I S  

K M 1 

 KM KI KM 
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Vmax S 
 rS  rP 
 I  

K M  S 1 
 KI 
Uncompetitive Inhibition
 I   
1
1 
 

K M  S 1 


 rS Vmax S  
 KI 
1
K  1 
1  I  
1 

 
 M 
 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
Non-competitive Inhibition
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Non-competitive Inhibition
E+S
+I
Increasing I
1

rS
-I
(inactive)I.E + S
Both slope and intercept
changes
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-I
P+E
+I
I.E.S (inactive)
 rS 
No Inhibition
1
CS
E·S
VmaxCS

k M  CS 1  CI
 kI
1
1  CI
1 

 rS Vmax  k I
 kM  1

 
 Vmax  CS



 C I
1 
 k I



Summary: Types of Enzyme Inhibition
Lineweaver–Burk plots for three types of enzyme inhibition.
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End of Lecture 15
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