ENZYME INHIBITION

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V = Vmax [S]/([S]+Km)

Review: How do we characterize enzyme functions?

The rate of an enzymatic reaction depends on the concentration of substrate.

Product

Time

S4

S3

S2S1

Increasing substrateconcentration

The Michaelis-Menten equation relates the initial velocity of the reactionto the concentration of substrate.

V

[S]

Review: How do we characterize enzyme functions?

1/V = (Km/Vmax)(1/[S]) + 1/ Vmax

The Lineweaver-Burke and Eadie-Hofstee equations transform the Michaelis-Menten data to more accurately estimate Km and Vmax.

1/V

1/[S]

V

V/[S]

V = Vmax - Km(V/[S])

Inhibition of enzyme activity What changes the rate of enzyme activity in the cell? What is the mechanism of inhibition? How can we determine the mechanism of inhibition? Why do we care?

• Underst and norm al con trol of enzyme activity • Analogs for crystalography • Inhibitor y drugs

Focus on reversible inhibiti : on differ ent typ es ofmechanisms distinguishab le b y kinetics

• competitive • non-competitive • uncompetitive

Competitive inhibition Inhibitor binds to the active site, competing with substrate

S

I E

For a fixed concentration of inhibitor and increasing substrate, we expect Vmax to be the same and Km to increase.

Vo

[S]

-I +I

Equations: E + S ES E + P Km ~ [E][S]/[ES] E + I EI KI = [E][I]/[EI] ET = [E] + [ES] + [EI] See the textbook for derivation of a modified Michaelis-Menten equation: V = Vmax[S]/([S] + Km (1 + [I]/KI)) We can define Km, apparent = Km (1 + [I]/KI) Note the effect of 1+[I]/KI on Km: As [I] increases, Km, apparent = Km (1 + [I]/KI) increases. At [I] = KI , Km, apparent = 2Km (a reduced “affinity” for S). As [S] increases, [S] >> Km (1 + [I]/KI), and V -> Vmax.

How can we calculate KI? Since K m, apparent = Km (1 + [I]/KI), then KI = Km [I]/(Km,apparent – Km).

Lineweaver-Burke formulation: replace Km with Km (1 + [I]/KI) 1/V = {Km (1 + [I]/KI)/Vmax}(1/[S]) + 1/Vmax As [I] increases, the slope increases, the x intercept becomes smaller (less negative), and the y intercept is unchanged.

1/V

-1/Km - 1/Km, apparent1/[S]

Non-competitive inhibition Inhibitor and substrate bind to different sites For a fixed concentration of inhibitor and increasing substrate, we expect Km to be the same and Vmax to decrease.

S I

+I

-I

V

[S]

The governing equations: E + S ES E + P E + I EI EI + S EIS ES + I EIS Km ~ [E][S]/[ES]; K i = [E][I]/[EI] = [ES][I]/[ESI] V = (Vmax/(1 + [I]/Ki))[S] ([S] + Km) Define Vmax, apparent = Vmax/(1 + [I]/KI) As [I] increases, Vmax, apparent = Vmax/(1 + [I]/KI) decreases; At [I] = KI , Vmax, apparent = V max

Lineweaver-Burke formulation: replace Vmax with Vmax /(1 + [I]/KI) 1/V = {Km (1 + [I]/KI)/Vmax}(1/[S]) + (1 + [I]/KI)/Vmax As [I] increases, the slope increases, the y intercept becomes larger, and the x intercept is unchanged.

-I

+I

1/V

1/[S]

1/Vmax

1/Vmax,apparent

How can we calculate KI? Since V max, apparent = V max /(1 + [I]/KI), then KI = Vmax, apparent [I]/(V max – Vmax,apparent ).

Uncompetitive inhibition Inhibitor binds only to ES

S I

For a fixed concentration of inhibitor and increasing substrate, we expect both Km and Vmax to decrease.

-I

+IV

[S]

Governing equations: E + S ES E + P ES + I EIS V = (Vmax/(1 + [I]/Ki))[S] (Km/(1 + [I]/Ki)) + [S] Vmax, apparent = Vmax/(1 + [I]/Ki); Km, apparent = Km/(1 + [I]/Ki) 1/V = (Km/Vmax)(1/[S]) + (1 + [I]/Ki)/Vmax

+I

-I

1/Vmax

1/[S]

1/Vmax, apparent

-1/Km-1/Km,apparent

1/V

Expect a lower Vmax and a lower Km (Why? Because Vmax = k2[Etotal], Km = (k2 + k-1)/k1 and [I] lowers k2!)

Summary

•Enzyme activity can be inhibited by compounds that interactwith the enzyme’s active site (or with other sites that changethe enzyme’s structure).

•Competitive inhibitors bind to the active site and competewith substrate.

•Non-competitive inhibitors bind to a separate site and Inactivate the active site.

•Uncompetitive inhibitors bind to an enzyme-substrate complex.

•The type of competition and the enzyme-inhibitor binding affinity can be determined from Michaelis-Menten kinetic experiments.

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