Enzyme Inhibition

Michaelis-Menton (MM) Kinetics

Competitive 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]
[E_total] = [E] + [ES]
V_max = k₃ [E_total]
K_M = (k₂+ k₃)/k₁= [S]_1/2
where V = (1/2) V_max

V / V_max = [S] / ([S] + K_M ) -- MM equation


	[E] + [S]
	+
	[I]
k_I	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 [ES_n]
[E_total] = [E] + [ES] + [EI]
V_max = k₃ [E_total]
K_M = (k₂+ k₃)/k₁
K_M^app = K_M ( 1 + [I] / K_I ) = ([S]_1/2) where V = (1/2) V_max

V / V_max = [S] / ([S] + K_M^app )

Noncompetitive Inhition

Uncompetitive Inhibiton


	[E] + [S]
	+
	[I]
k_I	k_-I
	[EI]

k₁

k₂


	[ES]
	+
	[I]
k_I	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 [ES_n]
[E_total] = [E] + [ES] + [EI] + [ESI]
V_max = k₃ [E_total]
V_max^app = V_max / ( 1 + [I] / K_I )
K_M = (k₂+ k₃)/k₁= ([S]_1/2)
where V = (1/2) V_max^app

V / V_max^app = [S] / ([S] + K_M )


	[E] + [S]

k₁

k₂


	[ES]
	+
	[I]
k_I	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 [ES_n]
[E_total] = [E] + [ES] + [ESI]
V_max = k₃ [E_total]
V_max^app = V_max / ( 1 + [I] / K_I )
K_M = (k₂+ k₃)/k₁
K_M^app = K_M / ( 1 + [I] / K_I ) = ([S]_1/2) where V = (1/2) V_max^app

V / V_max^app = [S] / ([S] + K_M^app )

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