CatalysisCatalysisCatalysis provides an additional mechanism by which reactantsCatalysis provides an additional mechanism by which reactantscan be converted to products. The can be converted to products. The alternative mechanism has a alternative mechanism has a lower activation energylower activation energy than the reaction in the absence of a than the reaction in the absence of acatalyst.catalyst.A Bvv00vvccvv00 no catalyst no catalystvvcc -- catalyst present(v(v00 = -d[A]/ = -d[A]/dt dt with no catalyst)with no catalyst)((vvcc = -d[A]/= -d[A]/dt dt with a catalyst)with a catalyst)Ea,fReaction coordinateReaction coordinatePotential EnergyEnergy barrier without catalystEnergy barrier without catalystEnergy barrierEnergy barrierwith catalystwith catalyst∆EEa,rEa,rProductsProductsEa,fEa,fReactantsReactantsDDE E NotNot affected affectedby catalystby catalystEEa,fa,f and E and Ea,ra,rare are loweredlowered bybycatalystcatalystGenerally a catalyst is defined as a substance which increases theGenerally a catalyst is defined as a substance which increases therate of a reaction without itself being changed at the end of therate of a reaction without itself being changed at the end of thereaction.reaction.This is strictly speaking not a good definition because some thingsThis is strictly speaking not a good definition because some thingscatalyze themselves, but we will use this definition for now.catalyze themselves, but we will use this definition for now.Catalyst supplies a reaction path which has a lower activationCatalyst supplies a reaction path which has a lower activationenergy than the reaction in the absence of a catalyst.energy than the reaction in the absence of a catalyst.Catalysis by EnzymesCatalysis by EnzymesEnzymes may be loosely defined as catalysts for biological systems.Enzymes may be loosely defined as catalysts for biological systems.They increase the rate of reactions involving biologically importantThey increase the rate of reactions involving biologically importantsystems.systems.Enzymes are remarkable as catalysts because they are usually Enzymes are remarkable as catalysts because they are usually amazingly specificamazingly specific (work only for a particular (work only for a particular kind of reaction.)kind of reaction.) They are also generally They are also generally very efficientvery efficient, achieving substantial, achieving substantialRate increases at concentrations as low as 10Rate increases at concentrations as low as 10-8-8 M! M!Typical enzyme molecular weights are 10Typical enzyme molecular weights are 1044-10-106 6 gm/mole gm/mole (protein molecules)(protein molecules)Summary of Enzyme CharacteristicsSummary of Enzyme Characteristics3) Very specific (work only on special types of reactions).3) Very specific (work only on special types of reactions). General Behavior of Enzyme Catalyzed ReactionsGeneral Behavior of Enzyme Catalyzed ReactionsIf the If the initial rateinitial rate of the reaction is plotted versus the of the reaction is plotted versus the initialinitialconcentrationconcentration of substrate S for a constant enzyme concentration, of substrate S for a constant enzyme concentration,the following behavior is found:the following behavior is found:1) Proteins of large to moderate weight 101) Proteins of large to moderate weight 1044 - 10 - 1066..2) Extremely efficient (work at 102) Extremely efficient (work at 10-8-8 M) M)S (substrate) ProductsS (substrate) ProductsEæ Æ æInitialInitialRateRateSubstrate ConcentrationSubstrate Concentration[S] concentration when V[S] concentration when Vii = V = VS S / 2/ 2VViiInitialInitialRateRateSubstrate ConcentrationSubstrate Concentration(Half maximum initial rate)(Half maximum initial rate)Maximum initial rateMaximum initial rate[S] concentration when V[S] concentration when Vii = V = VS S / 2/ 2VViiExplanation: Explanation: MichaelisMichaelis--MentenMenten Mechanism MechanismE is free enzyme and ES is an enzyme-substrate complexE is free enzyme and ES is an enzyme-substrate complexVVss is found to be directly proportional to the total enzyme is found to be directly proportional to the total enzyme concentration ( concentration (EEoo): V): Vss ~ ( ~ (EEoo) ) (S) concentration required to reach half maximum initial velocity(S) concentration required to reach half maximum initial velocity (V (Vi i = V= VSS/2) found to be independent of (/2) found to be independent of (EEoo). ). (S)(S)1/21/2 = K = KMMIt may generally be assumed that (S) >> (E) since E are so efficientIt may generally be assumed that (S) >> (E) since E are so efficient they catalyze reaction at very small concentration. they catalyze reaction at very small concentration.Steady State assumption:Steady State assumption:= kk11 (E) (S) - k (E) (S) - k-1-1 (ES) - k (ES) - k22 (ES) (ES)d(ES)dt0 =d(ES)dt(ES) =k1(E0)(S)k-1+ k2+ k1(S) MechanismMechanism kk11E + S E + S ÆÆ ES ES Step 1Step 1 kk-1-1ES ES ÆÆ E + S E + S Step 2Step 2 kk22ES ES ÆÆ P P ++ E E Step 3Step 3All are elementary kinetic steps.All are elementary kinetic steps.Step 1Step 1Step 2Step 2Step 3Step 3Divide top and bottom by kDivide top and bottom by k11 to get to get ÆÆ = k= k11EE00/[k/[k11+(k+(k-1-1+k+k22)/(S)])/(S)]Second Order ProcessSecond Order ProcessFirst Order ProcessFirst Order ProcessFirst Order ProcessFirst Order ProcessBonus * Bonus * Bonus * Bonus * Bonus * BonusBonus * Bonus * Bonus * Bonus * Bonus * BonusDepends linearly on [S] in region of low substrate concentration.Depends linearly on [S] in region of low substrate concentration. k22(E0) =k2(E0)1 +Km(S)12Case III : Case III : Km(S)>> 1dPdt=k2(E0)1 +Km(S)(S)(S)1/21/2 is the substrate concentration when the is the substrate concentration when the initial rate reaches half its maximum value.initial rate reaches half its maximum value.VVSS/2/2dPdt= V =Vmax1 +Km(S)KKmm is rate at which ES decomposes by two mechanisms (k is rate at which ES decomposes by two mechanisms (k-1-1 or k or k22))divided by rate constant for formation of ES.divided by rate constant for formation of ES.Large KLarge Kmm fifi weak binding of E to S weak binding of E to SSmall KSmall Kmm fifi strong binding of E to S strong binding of E to S{Lineweaver-Burke Plot} KKmm = = k-1+ k2k1 MechanismMechanism kk11E + S E + S ÆÆ ES ES Step 1Step 1 kk-1-1ES ES ÆÆ E + S E + S Step 2Step 2 kk22ES ES ÆÆ P P ++ EE Step 3Step