PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Steady-State Enzyme Kinetics Scott Morrical [email protected] Given Bldg.General References:Textbook: Frey & Hegeman, Chapter 2, pp. 69-128Reserve: Cornish-Bowden (1979) Enzyme Kinetics, Butterworth & Co., LondonWebsites:Dr. Peter Birch, University of Paisleyhttp://www-biol.paisley.ac.uk/kinetics/contents.htmlTerre Haute Medical Collegehttp://web.indstate.edu:80/thcme/mwking/enzyme-kinetics.htmlSteady-State Derivation of Michaelis-Menton Equation (Briggs & Haldane)timeE + S ES E + Pk1k-1k2Upon mixing of enzyme and substrate [ES] rises rapidly and reaches a steady state, where the rate of formation and breakdown of [ES] are equal, i.e. v1= k1 [E][S] and v2= k-1 [ES] + k2[ES] so that at steady state v1 = v2Free enzyme conc. [E]= [Et] -[ES]; note that [E] cannot be measured, but [Et] is known, as is [S] since initial velocities, and [P] can be measured. Now solve for the unknown [ES].v1= k1 ([Et] -[ ES])[S] = v2 = k-1[ES] + k2[ES] rearrange ([Et] -[ES])[S]/[ES] = (k-1+ k2) /k1 = Km Solving for [ES] gives [ES] = [Et][S]/ (Km + [S]) the velocity (v) of the reaction will be proportional to the formation of [ES], so v= k2 [ES] (substitute in the value for ES in red above) to get: v=k2 [Et][S]/ (Km + [S]) and at saturating [S], Vmax = k2[Et] (substitute Vmax for the k2 [Et] in the above equation), then v= Vmax [S]/ (Km + [S]) which is the same as the Michaelis-Menton equationNote importance ofinitial velocities (vo)The Meaning of Km & VRecall from the Briggs & Haldane derivation (Lecture 1) that for the 2-step reactionthe velocity at steady-state is given by the equationv = k2[Et][S] / ((k-1 + k2)/k1 + [S]) = V[S] / (Km + [S])where V = k2[Et] and is thus a function of total enzyme concentration,and Km = (k-1 + k2)/k1 is derived from multiple rate constants. The complexity of this term increases for more complicated kinetic mechanisms.The value of Km is taken as an indicator of an enzyme’s affinity for substrate, but it is not a true dissociation constant. For step one of the two-step mechanism above, Kd = k-1/k1 and Km only closelyapproximates this value when k-1 >> k2, i.e. when substrate binding is in rapidequilibrium w.r.t. the slow step of catalysis and product release.THIS IS NOT ALWAYS THE CASEE + S ES E + Pk1k-1k2Steady-State Enzyme KineticsLecture 2:InhibitionEnzyme Inhibitors in Steady-State Kinetics-- Drugs, poisons, mechanistic probes-- Reversible, irreversible, suicide-- Competitive, noncompetitive, mixed, uncompetitive-- Product inhibition-- Substrate inhibition-- Transition state analogsReversible Inhibitors:E + I EIFast acting.Generally non-covalent EI complex.Removal restores enzyme activity.Irreversible Inhibitors:E + I EIOften slow, time-dependent inactivation.Often covalent EI complex.Enzyme permanently disabled.Suicide Inhibitors:E + I* EI* EIEnzyme converts precursor into irreversible inhibitor.Competitive Inhibitors1. Competitive Inhibition by Active Site Binding-- reversible-- inhibitor (usually) structurally similar to substrate-- inhibitor competes directly for substrate binding to active site(mutually exclusive binding)-- effects can be overcome by increasing substrate concentrationQuickTime™ and aGIF decompressorare needed to see this picture.Competitive Inhibitors2. Competitive Inhibition by Conformational Change-- reversible-- substrate and inhibitor may be dissimilar -- inhibitor binds to remote site on enzyme, but causes a conformationalchange that precludes substrate binding to the active site-- likewise, substrate binding to active site causes a conformational changethat precludes inhibitor binding to its site-- binding is still mutually exclusive-- effects of inhibitor can still be overcome by increasing substrate concentrationKinetics of Competitive InhibitorsRemember: Inhibitor & substrate binding are mutually exclusive, also rapid & reversible.High [I] competes out substrate, so enzyme isalmost completely inhibited.High [S] competes out inhibitor, so enzyme is almost fully active.Effect on Km. -- Km is an indicator of enzyme-substrate affinity (like a dissociation constant).-- With inhibitor present, both free enzyme (E) and EI complex exist.-- E has normal affinity for S; EI has no affinity for S.-- Solution average affinity decreases, therefore Km increases.Effect on V.-- V is the velocity at very high [S]; i.e., conditions that compete out inhibitor.-- Thus V is unchanged.E + S ESE + I EIEI + S EISES + I EISKinetics of Competitive InhibitorsEffect on V/Km. --V/Km is the rate constant at low [S]. Why?At [S] << Km, the Michaelis-Menten equationsimplifies from v = V[S] / (Km + [S]) to:v = (V/Km)[S] = k[S]E + S ESE + I EIEI + S EISES + I EISv[S]Slope = V/KmAnything that affectsV or Km affects V/Km.-- Km increases, V unchanged.-- Therefore V/Km decreases.+ inhibitorEffects of Competitive Inhibitor on Lineweaver-Burk Plot= Km/V, i.e. reciprocal of rate constant V/Km1/v = (Km/V)(1/[S]) + 1/VNon-Competitive / Mixed Inhibitors-- Binds to site on enzyme remote from active site.-- Causes conformational change in enzyme that prevents conversion of substrate to product, but does not prevent substrate binding to enzyme.-- I, S binding is not mutually exclusive.-- Comes in 2 varieties: Classic & Mixed1. Classic Non-Competitive Inhibitors (Rare).-- do not alter affinity of substrate binding.2. Mixed Inhibitors (Common).-- typically lower the affinity of substrate binding.Kinetics of Non-Competitive / Mixed InhibitorsRemember: Inhibitor & substrate binding are NOT mutually exclusive.EIS complex forms by either of two routes, but cannot convert substrate to product.Substrate cannot compete out the inhibitor, so inhibitor works well at low and high [S].Effect on Km. -- CLASSIC Non-Competitive Inhibitor: no effect on substrate affinity; Km unchanged.-- MIXED Inhibitor: allows substrate binding but lowers affinity; Km increases.Effect on V.-- Both CLASSIC & MIXED inhibitors work at high [S], so V decreases.Effect on V/Km.-- Both CLASSIC & MIXED inhibitors also work at low [S], so V/Km decreases.E + S ESE + I EIES + I EISEI + S