Lecture 13:Michaelis-Menten KineticsMargaret A. DaughertyFall 2004Increasing [A] increases velocityA Bk1v = k1[A]Enzyme Reactions• Physically interact with their substrates toeffect catalysis;• Substrates bind to the enzyme’s activesiteE + S ES ES* EP E + PE = enzymeES = enzyme-substrate complexES* = enzyme/transition state complexEP = enzyme product complexP = productEnzyme kinetics: substrate saturation!k1E + S ES E + Pk-1kcatMichaelis-Menton Kinetics: IONE SUBSTRATE ---------> ONE PRODUCTREVERSIBLEIRREVERSIBLE(minimally reversible)Michaelis-Menton Kinetics: IIk1E + S ES E + Pk-1kcat1) Equilibrium is fast. k1E + S ESk-1KS = k-1/k1 = [E][S][ES]2). Steady-state: When [S] >>> [E]d[ES]dt= 0BIOC 2053). Initial velocity measurements:No E + P --> EPInitial velocity (vo) measurementsDetermine vo by analyzing early time pointsMeasure absorbance fluorescencevs. timeDetermine initial velocity for aMichaelis-Menton plot. Measureamount of product formed atincreasing concentration of substrates(increasing substrate means increasingproduct). The slope of the curve atthe beginning time points will give youvo at each substrate concentration. vo=rate of product formation = d[P]/dtMichaelis-Menton Kinetics: IIIk1E + S ES E + Pk-1kcatRATE OF FORMATION OF “P”V = kcat[ES]Need to measure both kcat and [ES]Michaelis-Menton Kinetics: IVk1E + S ES E + Pk-1kcatTOTAL CONCENTRATION OF ENZYME[E]t = [E] + [ES]Express the rate in terms of [S] and [E]tProgress Curves for anEnzyme Catalyzed ReactionE + S ES E + PPre-steady state: ES formingSteady state:[ES] almost constantMichaelis-Menton Kinetics: Vk1E + S ES E + Pk-1kcatSTEADY STATE ASSUMPTIONFormation ES = Breakdown ESk1[E][S] = k-1[ES] + kcat[ES]Michaelis-Menton Kinetics: VIk1E + S ES E + Pk-1kcatFormation ES = Breakdown ESrearrange equation:[ES] = [E][S]k1k-1 + kcatk1k-1 + kcatMichaelis-Menton Kinetics: VIIk1E + S ES E + Pk-1kcatk1k-1 + kcatKM = Michaelis constantMichaelis-Menton Kinetics: VIIIk1E + S ES E + Pk-1kcatNow, we have a definition for KM & [E]tRewriting the previous equation:KM[ES] = [E]t[S] - [ES][S][ES] = [E]t[S]KM + [S]Returning to:Michaelis-Menton Kinetics: IIIk1E + S ES E + Pk-1kcatRATE OF FORMATION OF “P”V = kcat[ES]Need to measure both kcat and [ES]V = Kcat[E]t[S]KM + [S]Michaelis-Menton Kinetics: IXk1E + S ES E + Pk-1kcatV = Vmax [S]KM + [S]Vmax, KM and kcatVmax: reached whenenzyme molecules aresaturatedKM:Substrate concentrationwhen V = Vmax/2kcat: direct measure of thecatalytic ability of an enzymeThus, KM is the substrate concentration atwhich the reaction velocity is half-maximal.Note: KM is unique for EACH enzyme-substrate pair! KM range: 10-1 to 10-8 MWhere [S] = KM, v = Vmax2Significance of KMTurnover NumberKcat = turnover number of the enzyme : number ofreaction processes (turnovers) that each activesite catalyses per unit time.Catalytic EfficiencyCatalytic efficiency = kcat/KMExperimental DesignI want to measure the reactivity of my enzyme… how?• Measureproduction of [P]• Measure thedecrease of [S]k1E + S ES E + Pk-1kcatLineweaver-Burke Plot• Also called the double reciprocal plot;• Actual values for KM and Vmax can bedetermined. V = Vmax[S] KM + [S] = . + Vmax KM1V 11[S]Vmaxy = mx + bExtrapolatepH and Temperature Affect Influence Enzyme ActivityTemperaturepHREVIEWFree energy provides information on whether a reaction isfavorable, not its rate.Enzymes are biological catalysts (usually proteins) that resultin higher reaction rates; they do not affect thethermodynamics of a reaction.Enzymes lower the activation energy of the transition statefor a reaction.Michaelis-Menten kinetics describe the simple catalyzedreaction of one substrate - one product.The Lineweaver-Burke plot (double-reciprocal plot) permitsVmax and Km to be accurately determined.What is the significance of Vmax, KM, kcat and catalyticefficiency
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