Enzyme Inhibition

Michaelis-Menton (MM) KineticsCompetitive Inhibiton
[E] + [S]
k1

k2
[ES]
k3
 
[E] + [P]
Assumptions and givens:
  • d[ES]/dt = 0 -- steady-state approximation
  • [P] = 0 -- at time zero
  • V = d[P]/dt = k3 [ES]
  • [Etotal] = [E] + [ES]
  • Vmax = k3 [Etotal]
  • KM = (k2+ k3)/k1= [S]1/2
    where V = (1/2) Vmax
V / Vmax = [S] / ([S] + KM ) -- MM equation
  
 [E] + [S]
 +
 [I]
kI k-I
 [EI]
k1

k2
 
[ES]
k3
 
 
[E] + [P]
Assumptions and givens:
  • d[ES]/dt = 0 -- steady-state approximation
  • [P] = 0 -- at time zero
  • V = d[P]/dt = k3 [ESn]
  • [Etotal] = [E] + [ES] + [EI]
  • Vmax = k3 [Etotal]
  • KM = (k2+ k3)/k1
  • KMapp = KM ( 1 + [I] / KI ) = ([S]1/2) where V = (1/2) Vmax
V / Vmax = [S] / ([S] + KMapp )

 

Noncompetitive InhitionUncompetitive Inhibiton
  
 [E] + [S]
 +
 [I]
kI k-I
 [EI]
k1

k2
  
 [ES]
 +
 [I]
kI k-I
 [ESI]
k3
 
 
[E] + [P]
Assumptions and givens:
  • d[ES]/dt = 0 -- steady-state approximation
  • [P] = 0 -- at time zero
  • V = d[P]/dt = k3 [ESn]
  • [Etotal] = [E] + [ES] + [EI] + [ESI]
  • Vmax = k3 [Etotal]
  • Vmaxapp = Vmax / ( 1 + [I] / KI )
  • KM = (k2+ k3)/k1= ([S]1/2)
    where V = (1/2) Vmaxapp
V / Vmaxapp = [S] / ([S] + KM )
  
 [E] + [S]
  
  
  
  
k1

k2
  
 [ES]
 +
 [I]
kI k-I
 [ESI]
k3
 
 
[E] + [P]
Assumptions and givens:
  • d[ES]/dt = 0 -- steady-state approximation
  • [P] = 0 -- at time zero
  • V = d[P]/dt = k3 [ESn]
  • [Etotal] = [E] + [ES] + [ESI]
  • Vmax = k3 [Etotal]
  • Vmaxapp = Vmax / ( 1 + [I] / KI )
  • KM = (k2+ k3)/k1
  • KMapp = KM / ( 1 + [I] / KI ) = ([S]1/2) where V = (1/2) Vmaxapp
V / Vmaxapp = [S] / ([S] + KMapp )

Continue the kinetic analysis of enzymes by opening the following Excel spreadsheet

Graphical Analysis of Enzyme Inhibition


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Duane W. Sears
Revised: July 27, 1998