Chapter 14 Rates of Enzymatic ReactionsEnzyme KineticsThe Michaelis-Menten EquationThe dual nature of the Michaelis-Menten equationPowerPoint PresentationSlide 6Slide 7Slide 8Slide 9Slide 10Understanding KmUnderstanding VmaxThe turnover number (also known as the molecular activity of the enzyme)Catalytic efficiency of an enzymeSlide 15Slide 16Slide 17Enzyme InhibitorsClasses of InhibitionSlide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Chapter 14Rates of Enzymatic ReactionsReading:V&V pp. 472-487Chymotrypsin with bound substrateEnzyme KineticsSeveral terms to know: •rate or velocity •rate constant •rate law •order of a reaction •molecularity of a reaction •Enzymes accelerate reactions by lowering the free energy of activation •Enzymes do this by binding the transition state of the reaction better than the substrateThe Michaelis-Menten Equation•Louis Michaelis and Maude Menten's theory •It assumes the formation of an enzyme-substrate complex •It assumes that the ES complex is in rapid equilibrium with free enzyme •Breakdown of ES to form products is assumed to be slower than (1) formation of ES and(2) breakdown of ES to re-form E and SThe dual nature of the Michaelis-Menten equationCombination of zero-order and 1st-order kineticsE + S ES E + P k1k-1k2Vo = k2 [ES]Rate of ES formation = k1 [E][S] = k1 ([Etotal] - [ES]) [S]Rate of ES breakdown = k-1 [ES] + k2 [ES]k1 ([Etotal] - [ES]) [S] = k-1 [ES] + k2 [ES](steady state assumption)(k-2 is insignificant early in rxn)k1 [Etotal][S] - k1[ES][S] = ( k-1 + k2 )[ES]k1 [Etotal][S] = (k1[S] + k-1 + k2 )[ES][ES] = [Etotal][S]________________________ [S] + (k2 + k-1 ) ___________ k1= [Etotal][S] ____________ KM + [S]Vo = k2 [ES]Vo = k2 [Etotal][S] ____________ KM + [S]Vo = Vmax when [Etotal] = [ES] (at saturation) Therefore Vmax = k2 [Etotal]Vo = Vmax[S] ____________ KM + [S]The dual nature of the Michaelis-Menten equationCombination of zero-order and first-order kinetics •When [S] is low, the equation for rate is first order in [S] •When [S] is high, the equation for rate is zero-order in [S] •The Michaelis-Menten equation describes a rectangular hyperbolic dependence of Vo on [S]Vo =Vmax[S]_________Km + [S]Vmax[S]Vo = ____________ KM + [S] KM = [S] when Vo = Vmax _____ 2Enzyme Kinetics: Michaelis-Menton EquationFrom LehningerPrinciples of BiochemistryThe following data were obtained in a study of an enzyme known to follow Michaelis Menten kinetics:V0 Substrate added(mmol/min) (mmol/L)————————————— 216 0.9 323 2 435 4 489 6 647 2,000—————————————Calculate the Km for this enzyme.Without graphingVmax = 647Vmax /2 = 647 / 2 = 323.5Km = 2 mmol/LKm is the substrate concentration that corresponds to Vmax 2Understanding Km•Km is a constant •Km is a constant derived from rate constants •Km is, under true Michaelis-Menten conditions, an estimate of the dissociation constant of E from S •Small Km means tight binding; high Km means weak bindingEnzyme Substrate Km (mM)Glutamate dehydrogenase NH4+57Glutamate 0.12Carbonic anhydrase CO212Understanding VmaxThe theoretical maximal velocity •Vmax is a constant •Vmax is the theoretical maximal rate of the reaction - but it is NEVER achieved in reality •To reach Vmax would require that ALL enzyme molecules are tightly bound with substrate •Vmax is asymptotically approached as substrate is increasedThe turnover number (also known as the molecular activity of the enzyme)A measure of its maximal catalytic activity •kcat, the turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate. •If the M-M model fits, k2 = kcat kcat = Vmax/Et •Values of kcat range from less than 1/sec to many millions per secTurnover number comparisonCatalase 40,000,000 sec-1Lysozyme 0.5 sec-1Catalytic efficiency of an enzymeName for kcat/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 •Catalytic efficiency cannot exceed the diffusion limit - the rate at which E and S diffuse together •WT and a mutant protein kcat/Km comparisionWT sulfite oxidase 1.1 Mutant R160K 0.015Double-Reciprocal or Lineweaver-Burk Plot 1 KM 1 ______ = _______ + ______ Vo Vmax[S] Vmax From LehningerPrinciples of BiochemistryUse linear plot and intercepts to determine Km and VmaxpH must be specified!Enzyme InhibitorsReversible versus Irreversible •Reversible inhibitors interact with an enzyme via noncovalent associations •Irreversible inhibitors interact with an enzyme via covalent associationsClasses of InhibitionTwo real, one hypothetical •Competitive inhibition - inhibitor (I) binds only to E, not to ES •Uncompetitive inhibition - inhibitor (I) binds only to ES, not to E. This is a hypothetical case that has never been documented for a real enzyme, but which makes a useful contrast to competitive inhibition•Noncompetitive (mixed) inhibition - inhibitor (I) binds to E and to ESInhibitor (I) binds only to E, not to ES Inhibitor (I) binds only to ES, not to E. This is a hypothetical case that has never been documented for a real enzyme, but which makes a useful contrast to competitive inhibitionInhibitor (I) binds to E and to ES.Enzyme InhibitionFrom LehningerPrinciples of BiochemistryCompetitive Uncompetitive Noncompetitive Inhibition Inhibition (Mixed) InhibitionKmchanges while Vmax does not Km and Vmax both changeKm and Vmax both changeFrom LehningerPrinciples of BiochemistrySuccinate dehydrogenase is a classic example of competitive inhibitionFrom LehningerPrinciples of BiochemistryMalonate is a strong competitive inhibitor of succinate dehydrogenase1/[S]1/V+ INo I-1 / Km-1 / KmappCompetitive InhibitionKmchanges while Vmax does not Where Kmapp = Km = 1 + [I] KI1/[S]1/V+ INo I-’ / Km-1 / Km‘ = 1 + [I] KIUncompetitive inhibition’/Vmax/VmaxType of inhibition VmaxappKMappNo inhibitor VmaxKMCompetitive VmaxKMUncompetitive Vmax/’ KM/’Noncompetitive (Mixed) Vmax/’ KM/’ = 1 + [I] ’ = 1 + [I] KI KI’Effects of Inhibitors on the parameters of Michaelis-Menten
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