Reactions


Competitive Inhibition


Uncompetitive Inhibition


Noncompetitive Inhibition


Michaelis-Menten Enzyme-Substrate-Inhibitor Interaction

Competitive Inhibition
Ki= IC50/(S/Km+1)

Uncompetitive Inhibition
Ki= IC50/(Km/S+1)

Noncompetitive Inhibition
Ki= IC50

Michaelis-Menten Enzyme-Substrate-Inhibitor Interaction for Tigthly Bound Inhibitors

Competitive Inhibition
Ki= (IC50- E/2)/(S/Km+1)

Uncompetitive Inhibition
Ki= (IC50- E/2)/(Km/S+1)

Noncompetitive Inhibition
Ki= IC50- E/2

Protein-Ligand-Inhibitor Interaction

Competitive Species

Ki = I50/[(L50/Kd) + (P0/Kd)+1]

[P0], free protein at 0% inhibition (positive control)
P0 = [-(Kd+L-P)+((Kd+L-P)2+4PKd)0.5]/2

[L0], free ligand at 0% inhibition (positive control)
L0 = L - PL0

[PL0], protein-ligand complex at 0% inhibition (positive control)
PL0 = P-P0

[P50], free protein at 50% inhibition
P50 = Kd * PL50/L50

[L50], free ligand at 50% inhibition
L50 = L-PL50

[PL50]. protein-ligand complex at 50% inhibition
PL50 = PL0/2

[I50], free inhibitor at 50% inhibition
I50 = IC50 - P +PL50[1+(Kd/L50)]

[PLI50], protein-inhibitor complex at 50% inhibition
PLI50 = IC50 - I50

Noncompetitive Species

Ki = I50/[(2P0/(P-P0))-(Kd/L50)+1]

[P0], free protein at 0% inhibition (positive control)
P0 = [-(Kd+L-P)+((Kd+L-P)2+4PKd)0.5]/2

[L0], free ligand at 0% inhibition (positive control)
L0 = L - PL0

[PL0], protein-ligand complex at 0% inhibition (positive control)
PL0 = P-P0

[P50], free protein at 50% inhibition
P50 = Kd * PL50/L50

[L50], free ligand at 50% inhibition
L50 = [-(P-L)+((P-L)2-4(-PL0Kd/2))0.5]/2

[PL50]. protein-ligand complex at 50% inhibition
PL50 = PL0/2

[I50], free inhibitor at 50% inhibition
I50 = IC50 - P+(PL0/2)(1+(Kd/L50))

[PLI50], protein-ligand-inhibitor complex at 50% inhibition
PLI50 = P - PL50 - P50