[Substrate] affects rate and it changes during reaction Can measure just initial rate, V o , when [S]>>[E] E +

1. Enzyme Kinetics [Substrate] affects rate and it changes during reaction Can measure just initial rate, Vo, when [S]>>[E] E + S ES E + P k2 k1 k-2 k-1 Slow step Rate-limiting maximum velocity Velocity (V) = k [S]

2. Enzyme Kinetics Michaelis-Menten Michaelis-Menten equation k2 k1 E + S ES E + P k-2 k-1 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, so k1([Et] - [ES])[S] = k-1[ES] + k2[ES] Rearrange: k1[Et][S] = (k1[S] + k-1 +k2) [ES] k1[Et][S] [ES] = (k1[S] + k-1 +k2)

3. Enzyme Kinetics Michaelis-Menten k1[Et][S] [ES] = (k1[S] + k-1 +k2) [Et][S] Km = (k-1 +k2) / k1 [ES] = [S] + (k-1 +k2) / k1 Km = Michaelis constant [Et][S] Remember V0 = k2[ES] [ES] = [S] + Km k2 [Et][S] Vmax occurs when [ES] = [Et] Vmax = k2[Et] V0 = [S] + Km Vmax[S] Michaelis-Menten equation!! Rate equation for 1 substrate, enzyme-catalyzed reaction Km has units of concentration V0 = [S] + Km

4. Enzyme Kinetics Michaelis-Menten Vmax[S] V0 = Km V0 = Vmax Michaelis-Menten Vmax[S] V0 = [S] + Km When V0 = 1/2 Vmax Vmax[S] [S] 1 / 2 = Vmax / 2 = [S] + Km [S] + Km Km = [S] Low [S], Km >> [S] High [S], [S] >> Km

5. Enzyme Kinetics Transform Michaelis-Menten Equation Vmax[S] Km 1 1 + V0 = Vmax[S] V0 = Vmax [S] + Km Double reciprocal or Lineweaver-Burk plot plot 1/V vs. 1/[S] Straight line --> slope, y-intercept, x-intercept More accurate determination of Vmax

6. Enzyme Kinetics Km and kcat k2 + k-1 Km = k1 Km measurement --> affinity of enzyme for its substrate kcat = Vmax/[E]T kcat is catalytic constant or turnover number (first order rate constant, s-1) CATALYTIC EFFICIENCY

7. Enzymes can be Inhibited Competitive inhibitor competes with substrate for active site Noncompetitive inhibitor binds elsewhere, influencing binding at active site

8. Enzymes can be Inhibited Competitive Inhibition Substrate Active site of enzyme Inhibitor Substrate and Inhibitor can bind to active site Inhibitor prevents binding of substrate

9. Enzymes can be Inhibited Noncompetitive Inhibition Substrate Active site of enzyme Inhibitor Inhibitor site Inhibitor and substrate can bind simultaneously, rate slowed Substrate can bind to active site product forms Inhibitor binding distorts active site

10. Enzymes can be Inhibited Competitive Inhibition Competitive inhibitor Apparent Km will increase No effect on Vmax Increasing concentration of inhibitor -1/aKm

11. 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 dehydrogenase Therapy for methanol poisoning is IV with ethanol, formaldehyde not formed as readily, little tissue damage, kidneys excrete methanol

12. Enzymes can be Inhibited Noncompetitive Inhibition +Noncompetitive inhibitor 1/V No inhibitor -1/Km 0 1/[S] Noncompetitive inhibitor Apparent Km not affected Lowering of Vmax

13. Enzymes can be Inhibited Noncompetitive Inhibition Also called allosteric inhibition Example of noncompetitive inhibitor = aspirin Aspirin 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

14. 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)