BIOSC 1000 Lecture 9: Lecture 9

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12 Apr 2019
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Lecture9(2/7)
Thursday,February7,2019 10:56AM
EnzymeKinetics&Regulation
Forfirstorderreactions,reactionvelocity(v)asafunctionofsubstrateconcentrationishyperbolic.
Atlowlevels,itisessentiallylinear.
Itmaxesoutandisalmostvelocity
vmax
Thereisalimittohowfasttheenzymecanbind&converttoproduct.
Michaelis‑MentenKinetics(1913)
Generaltheoryofenzymeactionbasedontheassumptionthatanenzymeandsubstrateassociate
reversiblytomakeanenzyme‑substratecomplex(ES)
Thesaturationeffectonvvs.[S]curvessuggestedthatanESexists.
k1
[ES][E][S]
k‑1
Wherek1istherateconstantforassociationandk−1istherateconstantfordissociationoftheES
complex
Assumingarapidequilibrium,therateofdissociationequalstherateofassociation.
k−1[ES]=k1[E][S]
Productisformedinasecondstep.
Michaelis&Mentenprovidedamodeltoexplainobservedreactionbehavior.
Briggs&Haldane(1925)refinedMichaelis&Menten’smodeltodescribethesystemmathematically.
Twoassumptions:
SteadyStateassumption
InitialVelocityAssumption
Steady‑StateAssumption
Assumesthat[ES]reachesasteady‑statevaluequickly
ESformedfromE+SasquicklyasitisbrokendowntoP
d[ES]/dt=0
Lecture 9
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InitialVelocityAssumption
[P]isnegligibleearlyinthereaction
ExperimentallycanmeasurevelocitybeforePaccumulatesandbackreaction(E+P‑‑>ES)becomes
significant
[S]consideredconstant
Mathematically:
v=v0=k2[ES]
TheMichaelisMentenEquationistherateequationforaone‑substrateenzymecatalyzedreaction.
Vmaxisthevelocityofthereactionwhentheenzymeisfullysaturated.
Theoreticalmaximum,notmeasurable
UnitsofConcentration/time(M/sec)
KMistheMichaelisConstant
Concentrationofsubstrateathalfmaximalreactionvelocity(1/2Vmax)
Unitsofconcentration(M,etc)
Ratioofratesofdissociation(ESbreakingdown)torateofassociation(ESformation)
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KMisconstantforagivenenzymeandsubstrate.
Hexokinasephosphorylatesglucose&fructose
LowerKMmeansbetteraffinity
Vmax&KMcanbedeterminedexperimentallyfromahyperbolicplot.
ALineweaver‑Burkplotisadoublereciprocalplotof1/v0asafunctionof1/[S].
Fromhyperbolatoline
InverseoftheMichaelis‑Mentenequation
TurnoverNumber(kcat)istherateofsubstrateconvertedtoproductwhentheenxymeisfullysaturated
withsubstrate.
kcat=vmax/[ET]
Unitsofkcat:sec‑1
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