[Substrate] affects rate and it changes during reactionCan measure just initial rate, Vo, when [S]>>[E]

E + S ES E + Pk1

k-1

k2

k-2

Slow stepRate-limiting

Enzyme Kinetics

maximum velocity

Velocity (V) = k [S]

E + S ES E + P

Enzyme KineticsMichaelis-Menten

k1

k-1

k2

k-2

Michaelis-Menten equation

Derive:Assume that [P] low at start and that k-2 is very small

V0 = k2[ES][ES] hard to measure, so [Et] used[Et] = [E] + [ES], [E] = [Et] - [ES]

[ES] small because [S] so large, [Et] = [E]

Formation of ES = k1([Et] - [ES])[S]Breakdown of ES = k-1[ES] + k2[ES]

Assume steady state [ES] ~ constant, sok1([Et] - [ES])[S] = k-1[ES] + k2[ES]

Rearrange:k1[Et][S] = (k1[S] + k-1 + k2) [ES]

k1[Et][S] (k1[S] + k-1 + k2)[ES] =

k1[Et][S]

Enzyme KineticsMichaelis-Menten

(k1[S] + k-1 + k2)[ES] =

[Et][S]

[S] + (k-1 + k2) / k1

[ES] = Km = (k-1 + k2) / k1

[Et][S]

[S] + Km [ES] =

RememberV0 = k2[ES]

k2 [Et][S]

[S] + Km V0 =

Vmax occurs when [ES] = [Et]Vmax = k2[Et]

Vmax[S]

[S] + Km V0 = Michaelis-Menten equation!!

Rate equation for 1 substrate, enzyme-catalyzed reactionKm has units of concentration

Km = Michaelis constant

Enzyme KineticsMichaelis-Menten

Low [S], Km >> [S]Vmax[S]

Km V0 =

High [S], [S] >> Km VmaxV0 =

Vmax[S]

[S] + Km Vmax / 2 =

When V0 = 1/2 Vmax

[S]

[S] + Km 1 / 2 =

Km = [S]

Vmax[S]

[S] + Km V0 =

Michaelis-Menten

Enzyme KineticsTransform Michaelis-Menten Equation

Double reciprocal or Lineweaver-Burk plotplot 1/V vs. 1/[S]

Straight line --> slope, y-intercept, x-interceptMore accurate determination of Vmax

Vmax[S]

[S] + Km V0 = V0 =

1 Km

Vmax[S] +

Vmax

1

Enzyme KineticsKm and kcat

kcat = Vmax/[E]T

kcat is catalytic constant or turnover number (first order rate constant, s-1)

Km =k2 + k-1

k1

Km measurement --> affinity of enzyme for its substrate

CATALYTIC EFFICIENCY

Enzymes can be Inhibited

Competitive inhibitor competes with substrate for active site

Noncompetitive inhibitor binds elsewhere, influencing binding at active site

Enzymes can be Inhibited

Competitive Inhibition

Substrate

Inhibitor

Active site of enzyme

Substrate and Inhibitor can bind to active siteInhibitor prevents binding of substrate

Enzymes can be Inhibited

Noncompetitive Inhibition

Substrate

Inhibitor

Active site of enzyme

Inhibitor binding distorts active site

Inhibitor site

Substrate can bind to active siteproduct forms

Inhibitor and substrate can bind simultaneously, rate slowed

Enzymes can be InhibitedCompetitive Inhibition

Competitive inhibitorApparent Km will increaseNo effect on Vmax

-1/Km

Increasing concentration of inhibitor

Enzymes can be Inhibited

Competitive Inhibition

Ingestion of methanol (gas-line antifreeze)In liver, alcohol dehydrogenase converts methanol to formaldehyde (BAD)

Ethanol competes effectively with methanol for binding to alcohol dehydrogenaseTherapy for methanol poisoning is IV with ethanol, formaldehyde not formed as readily, little tissue damage, kidneys excrete methanol

Enzymes can be Inhibited

Noncompetitive Inhibition

0

1/V

1/[S]-1/Km

No inhibitor

+Noncompetitive inhibitor

Noncompetitive inhibitorApparent Km not affectedLowering of Vmax

Enzymes can be Inhibited

Noncompetitive Inhibition

Also called allosteric inhibition

Example of noncompetitive inhibitor = aspirinAspirin inhibits a cyclo-oxygenase so that prostaglandins may not be synthesized, thereby reducing pain, fever, inflammation, blood clotting, etc.

Aspirin does not bind to the active site of cyclo-oxygenase but to a separate/allosteric site

Enzymes can be Inhibited

Irreversible Inhibition - Inhibitor binds covalently to or destroys essential functional group on enzyme

Suicide inactivators - undergoes first few steps of rxn and then converts to a reactive compound that combines irreversiby with enzyme (high specificity)

INHIBITS ornithine decarboxylase (cure for African sleeping sickness)