Lecture 13: Kinetics IIMichaelis-Menten KineticsMargaret A. DaughertyFall 2003Enzyme 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 = productBIOC 205Return to a simple case: single-order kineticsrate of disappearance of A: v = -d[A]/dt = k[A]A Bk1k-1BIOC 205A Bk1k-1v = k1[A]BIOC 205Enzyme kinetics: substrate saturation!(substrate saturation curves)BIOC 205Enzyme kinetics: what do we want to know?How well does an enzyme bind a substrate?Km How fast does an enzyme do its chemistry?Vmax What is it’s maximal catalytic activity?kcat How efficient is the enzyme?kcat/KmBIOC 205k1E + S ES E + Pk-1kcatMichaelis-Menton Kinetics: IONE SUBSTRATE ---------> ONE PRODUCTREVERSIBLEIRREVERSIBLE(minimally reversible)BIOC 205ES E + PkcatMichaelis-Menton Kinetics: IInclusive in the kcat step:ES --> ES‡Enzyme creates strain on substrate so that chemistry can occurES‡ --> EPEnzyme performs chemistry on substrateEP --> E + PProduct dissociates from enzyme; enzyme free to go another roundBIOC 205Michaelis-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. time vo = rate of product formation = d[P]/dtk1E + S ES E + Pk-1kcatRATE OF FORMATION OF “P”V = kcat[ES]Need to measure both kcat and [ES]*BIOC 205Michaelis-Menton Kinetics: IIIMichaelis-Menton Kinetics: IVk1E + S ES E + Pk-1kcatTOTAL CONCENTRATION OF ENZYME[E]t = [E] + [ES]Express the rate in terms of [S] and [E]tBIOC 205Progress Curves for anEnzyme Catalyzed ReactionE + S ES E + P• [E]f as [ES] ;• [S] as [P] ;Pre-steady state: ES formingSteady state:[ES] almost constantBIOC 205Michaelis-Menton Kinetics: Vk1E + S ES E + Pk-1kcatSTEADY STATE ASSUMPTIONFormation ES = Breakdown ESk1[E][S] = k-1[ES] + kcat[ES]Formation fromE + SBreakdown intoE + SBreakdown intoE + PBIOC 205Michaelis-Menton Kinetics: VIk1E + S ES E + Pk-1kcatFormation ES = Breakdown ESrearrange equation:[ES] = [E][S]k1k-1 + kcatk1k-1 + kcatBIOC 205Michaelis-Menton Kinetics: VIIk1E + S ES E + Pk-1kcatk1k-1 + kcatKM = Michaelis constantBIOC 205Michaelis-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]Solve for [ES][ES] = [E]t[S]KM + [S]BIOC 205Returning to:Michaelis-Menton Kinetics: IIIk1E + S ES E + Pk-1kcatRATE OF FORMATION OF “P”V = kcat[ES]Replaced the need to measure both kcat and [ES]V = kcat[E]t[S]KM + [S]BIOC 205Michaelis-Menton Kinetics: IXk1E + S ES E + Pk-1kcatV = Vmax [S]KM + [S]BIOC 205MICHAELIS-MENTON PLOTVmax=kcat[E]t;Vmax α [E]tKM: Substrateconcentration whenV = Vmax/2BIOC 205Vmax, KM and kcatVmax: reached when enzymemolecules are saturated; everyenzyme carrying out a catalyticreactionKM:Substrate concentrationwhen V = Vmax/2; the higher theKM, the higher the concentrationof S to reach a given velocity.kcat: direct measure of thecatalytic ability of an enzymeBIOC 205Significance of KMThus, KM is the substrate concentration at which thereaction velocity is half-maximal.Note: KM is unique for EACH enzyme-substrate pair! KM range: 10-1 to 10-8 MWhere [S] = KM, v = Vmax2BIOC 205Area in pinkhighlights atheoreticalconcentrationrange of anenzyme;Typical Km valuesusually just abovethis concentrationrange.How does Km relate to physiological concentrations ofsubstrate?Glucose metabolism and you; small changes in bloodglucose activate different metabolic pathways.fedfastingstarvedless**Turnover NumberKcat = turnover number of the enzyme : number of reactionprocesses (turnovers) that each active site catalyses perunit time.kcat varies for each substrate with an enzyme! BIOC 205Catalytic EfficiencyCatalytic efficiency = kcat/KMBIOC 205Vmax, KM and kcatkcat/KM: ratio measures“enzyme efficiency” “catalytic perfection”109 M-1sec-1kcat/KM = largeArises from large kcat or a small KMBIOC 205Experimental DesignI want to measure the reactivity of my enzyme… how?• Measure production of [P]• Measure the decrease of [S]• const [E]• const T• const pHk1E + S ES E + Pk-1kcatExpt must have...Note: The velocity ofan enzyme-catalyzedreaction is dependentupon the substrateconcentration [S]Lineweaver-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 + bExtrapolateBIOC 205REVIEWFree 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