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Enzyme Kinetics Velocity (V) = k [S]
[Substrate] affects rate and it changes during reaction Can measure just initial rate, Vo, when [S]>>[E] E + S ES E + P k1 k2 k-1 k-2 Slow step Rate-limiting maximum velocity Velocity (V) = k [S]
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Enzyme Kinetics Michaelis-Menten Michaelis-Menten equation Derive:
E + S ES E + P k-1 k-2 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)
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Enzyme Kinetics Michaelis-Menten [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] V0 = Michaelis-Menten equation!! Rate equation for 1 substrate, enzyme-catalyzed reaction Km has units of concentration [S] + Km
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Enzyme Kinetics Michaelis-Menten Km = [S] Vmax[S] V0 = [S] + Km
When V0 = 1/2 Vmax Vmax[S] [S] Vmax / 2 = 1 / 2 = [S] + Km [S] + Km Km = [S] Vmax[S] Km V0 = Low [S], Km >> [S] High [S], [S] >> Km Vmax V0 =
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Transform Michaelis-Menten Equation
Enzyme Kinetics Transform Michaelis-Menten Equation Vmax[S] Km 1 1 V0 = + V0 = Vmax[S] [S] + Km Vmax Double reciprocal or Lineweaver-Burk plot plot 1/V vs. 1/[S] Straight line --> slope, y-intercept, x-intercept More accurate determination of Vmax
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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
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Enzymes can be Inhibited
Competitive inhibitor competes with substrate for active site Noncompetitive inhibitor binds elsewhere, influencing binding at active site
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Enzymes can be Inhibited
Competitive Inhibition Active site of enzyme Substrate Inhibitor Substrate and Inhibitor can bind to active site Inhibitor prevents binding of substrate
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Enzymes can be Inhibited
Noncompetitive Inhibition Active site of enzyme Substrate Inhibitor Inhibitor site Substrate can bind to active site product forms Inhibitor binding distorts active site Inhibitor and substrate can bind simultaneously, rate slowed
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Enzymes can be Inhibited
Competitive Inhibition Competitive inhibitor Apparent Km will increase No effect on Vmax Increasing concentration of inhibitor -1/aKm
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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
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Enzymes can be Inhibited
Noncompetitive Inhibition +Noncompetitive inhibitor 1/V No inhibitor -1/Km 1/[S] Noncompetitive inhibitor Apparent Km not affected Lowering of Vmax
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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
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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)
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