南京大学-杨荣武生物化学-英文版-第二篇-EnzymeII

EnzymesII-Michaelis-MentenKineticsLeonorMichaelis(1875-1949)MaudMenten(1879-1960)IntroductiontoEnzymeKineticsKineticsconcernswiththeratesofchemicalreaction.Enzymekineticsaddressesthebiologicalrolesofenzymaticcatalystsandquantifytheremarkablefunctionofbiologicalenzymes;Enzymekineticsinformationcanbeexploitedtocontrolandmanipulatethecourseofmetabolicevents.Pharmaceuticalsordrugsareoftenspecialinhibitorstargetedataparticularenzyme.ThusthescienceofpharmacologyreliesonsuchinformationEnzymeKinetics•Therateofunimolecularreactionisproportionaltotheconcentrationofthereactant.Thusrateislinearilydependenton[A].•Butifthisreactioniscatalyzedbyanenzyme,therateshowssaturationbehavior.Why?PA][][AkdtAdvv[A]PAEnzymev[A]TheMechaelis-MentenEquationYouneedtoknowhowthisisderived•Thisisthecompletechemicalformulaforanenzyme-catalyzed(E)reactionofsubstrate,Sandproduct,P;•Mechaelis-Mentenequationdescribestherelationshipbetweenreactionrateandsubstrateconcentration.Itcanexplainthesaturationbehaviorincatalyzedreactionsasshowninthepreviousslide.•Mechaelis-Mentenequationisderivedbasedonthefollowingthreeconditions:1)Statesteadyassumption;2)Initialvelocityassumption;3)Ratelaw.PEESSEk1K-1k2K-2InitialVelocityAssumption•Inthebeginningofthereaction,thereisverylittleproduct,or[P]issmall.Sotheamountof[ES]contributedbyE+Pisnegligible.•Thus,theMMequationconcernsthereactionratethatismeasuredduringearlyreactionperiod.•Inwhichcase,theenzymecatalyzedreactioncanbemodifiedto:•K-1PEESSEk1K-1k2PEESSEk1k2K-2RateLawinEnzymeCatalyzedReactions•Ratelawstillappliesinenzymecatalyzedreactions.•Theforwardvelocity,orrate,vfis,•Thereversevelocityorrate,ortherateofdisappearancevdis,•Atsteadystate,thereisnoaccumulationof[ES],thus:PEESSEk1K-1k2SEkvf1ESkkESkESkvd)(2121dfvvDerivationofMichaelis-MentenEquation•Weneedonemorecondition,thatis,thetotalenzymeconcentration,[Et]isthesumofthatofenzyme-substratecomplex,[ES],andthatoffreeenzyme,[E]:•Atsteadystate,theforwardrateshouldequaltothereverserate:•Rateofproductionformation(ratelaw),v=k2[ES].So:mtkkkKttttttKSSEESkkkSSEkkSkSEkESkkSkESSEkESkkSESkEkESkkSESkSEkESkkSESEkm121)(1212111211121112111211)())(())(()()()()(EESEtSESEkSEkvtf)(11mtKSSEkv2NotesontheMMEquations•Therateofproductionformationcanusuallybemeasuredexperimentallybymonitoringtheprogresscurveofproductionformation.•Themaximumratecanbereachedatsaturatingsubstrateconcentration,orwhen[S]SoMMequationcanbere-writtenas:mKSSvvmaxmax2][2][1vEkEkvtSKtSmEnzyme-catalyzedrateissaturatedUnderstandingKm•Kmisaconstantderivedfromrateconstants•Kmis,undertrueMichaelis-Mentenconditions,anestimateofthedissociationconstantofEfromS,becauseatequilibrium,Reversiblereaction,dissociationconstantisSosmallKmmeanstightsubstratebinding;highKmmeansweaksubstratebinding.•Kmequalstothesubstrateconcentrationatwhichv=1/2vmax121kkkKmESSEk1k-111][][kkESSEKd][][11ESkSEkUnderstandingVmaxThetheoreticalmaximalvelocityVmaxisaconstantVmaxisthetheoreticalmaximalrateofthereaction-butitisNEVERachievedinrealityToreachVmaxwouldrequirethatALLenzymemoleculesaretightlyboundwithsubstrateVmaxisasymptoticallyapproachedassubstrateisincreasedThedualnatureoftheMichaelis-MentenequationCombinationof0-orderand1st-orderkineticsWhenSislow,theequationforrateis1storderinSWhenSishigh,theequationforrateis0-orderinSTheMichaelis-MentenequationdescribesarectangularhyperbolicdependenceofvonS!TheturnovernumberAmeasureofcatalyticactivitykcat,theturnovernumber,isthenumberofsubstratemoleculesconvertedtoproductperenzymemoleculeperunitoftime,whenEissaturatedwithsubstrate.IftheM-Mmodelfits,k2=kcat=Vmax/EtValuesofkcatrangefromlessthan1/sectomanymillionspersecThecatalyticefficiencyNameforkcat/KmAnestimateofhowperfecttheenzymeiskcat/Kmisanapparentsecond-orderrateconstantItmeasureshowtheenzymeperformswhenSislowTheupperlimitforkcat/Kmisthediffusionlimit-therateatwhichEandSdiffusetogetherDeterminingtheVMAXandKM:Lineweaver-Burkplot1V=1VMAX+KMVMAX•1[S]y=mx+bxintercept=-1/KM01/[S]1/Vyintercept=1/VMAX