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lecture13.pdflecture13.pdflecture13c.pdfEnzyme Kinetics• Kinetics of Enzyme-Catalyzed Reactions: Michaelis-Menten Kinetics• Enzyme Inhibition• Kinetics of Two-Substrate Reactions• Ribozymes and AbzymesHow Enzymes Work• Enzyme-catalyzed reactions are characterized by the formation of a complexbetween the enzyme and its substrate (the ES complex)• Substrate binding occurs in a pocket on the enzyme called the active site• Enzymes accelerate reactions by lowering the free energy of activation DG‡.The equilibrium of the reaction remains unaffected by the enzyme• Enzymes do this by binding the transition state of the reaction better than thesubstrateWhere Does the Energy Come From?• Enzyme-substrate interactions are predominantly non-covalent–ionic–H-bonds–hydrophobic• The active site is structured so that more of these interactions occur in thetransition state• These bonds account for a significant part of the energy required to reduce DG‡• The rest comes from the folding free energy of the enzyme in its ESconformationThe Michaelis-Menten Equationcan we find the relationship between rate and [S]?Step 1. Formation of the ES complex:forward rate v1 = k1[S][E]backward rate v-1 = k-1[ES]S + E ESThis is an equilibrium where the equilibrium constant K = k1/k-1k1k-1Step 2. Formation of products:forward rate v2 = k2[ES]backward rate v-2 = k-2[E][P]ES E + PBreakdown of ES to form products is assumed to be slower than formation ofES (v1) or breakdown of ES to re-form E and S (v-1)k2k-2Assumption 1• Only consider early times in the reaction– [P] is very small– v-2 is negligible– step 2 is essentially irreversibleE + S ES E + P• So the initial rate v0 = k2[ES]• We can easily measure initial rates, but [ES] is very difficult to measurek1k-1k2An Expression for [ES]• Recall that [E]total = [E] + [ES]• How fast is the enzyme-substrate complex formed and broken down?E + S ES E + PStep 1: rate of formation of ES = k1[S]([E]total - [ES])Steps 1 and 2: rate of breakdown of ES = k-1[ES] + k2[ES]k1k-1k2Assumption 2Briggs-Haldane Steady State Assumptionrate of ES formation = rate of ES breakdownk1[S]([E]total - [ES]) = k-1[ES] + k2[ES][ES] = k1[S][E]total k-1 + k2 + k1[S][ES] = [S][E]total [S] + k-1 + k2 k1Substitute for [ES] in the initial rate equationv0 = k2[ES][ES] = [S][E]total [S] + k-1 + k2 k1v0 = k2[S][E]total [S] + k-1 + k2 k1Assumption 3• [S] >> [E]total• The enzyme is saturated with substrate• [ES] = [E]total• So we can define a maximum rate Vmax whereVmax = k2[E]totalv0 = Vmax[S] [S] + k-1 + k2 k1Now group the constants: Km = (k-1 + k2)/k1v0 = Vmax[S] Km + [S]• The Michaelis-Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction• It quantitatively relates the initial rate, the maximum rate, and the initial substrateconcentration to the Michaelis constant KmUnderstanding KmThe "kinetic activator constant"• Km is a constant with units M• Km is a constant derived from rate constants• Km is, under true Michaelis-Menten conditions, an estimate of the dissociationconstant of E from S• Small Km means tight binding; high Km means weak bindingUnderstanding Vmaxtheoretical maximal velocity• Vmax is a constant with units s-1• Vmax is the theoretical maximal rate of the reaction - but it is NEVER achievedin reality• To reach Vmax would require that ALL enzyme molecules are tightly bound withsubstrate• Vmax is asymptotically approached as [S] is increasedThe Dual Nature of the Michaelis-Menten Equationcombination of zero and 1st-order kinetics• When [S] is low, the equation for rate is 1st order in [S]• When [S] is high, the equation for rate is zero-order in S• The Michaelis-Menten equation describes a rectangular hyperbolicdependence of v0 on [S]The Turnover Numbera measure of catalytic activity• kcat, the turnover number, is the number of substrate molecules converted toproduct per enzyme molecule per unit of time, when E is saturated with substrate• If the M-M model fits, k2 = kcat = Vmax/Etotal• Values of kcat range from less than 1/sec to many millions per secCatalytic Efficiencykcat/Km• An estimate of "how perfect" the enzyme is• kcat/Km is an apparent second-order rate constant• It measures how the enzyme performs when [S] is low• The upper limit for kcat/Km is the diffusion limit - the rateat which E and S diffuse together (108 to 109 s-1)Linear Plots of the Michaelis-Menten Equationbe able to derive these relationships• Lineweaver-Burk (double reciprocal)• Hanes-Woolf• Hanes-Woolf is best• Smaller and more consistent errors across the plotLineweaver-Burk PlotHanes-Woolf PlotLineweaver-Burk Plots• Note how the straight line fit can be weighted by unreliable values atsmall [S] and v0• The Lineweaver-Burk plot is useful for comparing inhibition mechanismsEnzyme Inhibitorsreversible versus irreversible• Irreversible inhibitors interact with an enzyme via covalent associations• Nerve agents like sarin are irreversible inhibitors of acetylcholine esterase• Reversible inhibitors interact with an enzyme via noncovalent associations• For therapeutic drug design we’re almost always interested in reversibleinhibitors2x10-44x10-46x10-48x10-410-3200400600800Vmax[S] (M)v0 (s-1)1x10-35x10-41.5x10-32x10-31/Vmax-1/KmVmax= 1000 s-1Km= 1x10-4 M0-5000 5000 100001/[S] (M-1)1/v0 (M-1s)slope = Km/VmaxReversible Inhibition• Competitive inhibition - I binds to E, not to ES• Substrate and inhibitor compete for the active site• Vmax unchanged• In principle we can always add enough substrate to produce saturated ES(though not in practice)• Km becomes Km + Km[I]/KI where KI is the equilibrium constant for E + I = EI• The apparent ES association gets weaker (Km gets larger)Reversible Inhibition• Noncompetitive inhibition - I binds either to ES or to E and ES• Pure noncompetetive inhibition (uncommon)–The binding of I to E has no effect on the binding of S–E + I = EI and ES + I = ESI have the same KI–S and I bind at different sites and the active site is unaffected by I–Km is unchanged–The inhibitor is not binding at the active site, so Vmax cannot berecovered by raising [S]–Vmax becomes Vmax/(1 + [I]/KI)–I only


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UVM CHEM 205 - Enzyme Kinetics

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