(20 points) In class was derived the following form of the Michaels-Menten rate

Question

(20 points) In class was derived the following form of the Michaels-Menten rate law for a simple enzymatic reaction: Vmax [S]o " - where v is the initial rate of the reaction, [Slo is the initial substrate concentration, and Vmax and KM are constants. This equation may be rearranged to show that a plot of - vs. should give a line with intercept and slope a) State how the parameters Ky and Vmax are obtained from a plot of v vs. [S]o b) Demonstrate that a plot of v vs. Sshould give a line and indicate how Kwy and Vmax could 0 Vmax Vmax [S]o obtained from such a plot. SJo be c) Demonstrate that a plot of 0 vs. [S]o should give a line and indicate how KM and Vmax could be obtained from such a plot.

Explanation / Answer

the plot of V vs S is generated and shown above. The Vmax is point of Max rate and is drawn and shown above.

V= Vmax*So/(KM+SO)

when V= Vmax/2

SO= Km, So locate Vmax/2 and interesect the curve to obtain Km. This is also shown.

2. V= VmaxSo/(KM+SO)

V*(KM+SO)= VmaxSO

VKM +VSO = SO*Vmax

VKM= So*(Vmax-V)

Vmax-V = VKM/SO

V = Vmax- VKM/SO

So a plot of V vs V/SO gives straight line whose slope is -KM and intecept is Vmax

3. V= Vmax*SO/(KM+SO)

VKM+VSO= VmaxSO

dividing by V gives

KM + So = (Vmax/V)SO

SO/V = (KM/Vmax)+SO/Vmax

so a plot of SO/V vs SO gives a straight line whose slope is 1/Vmax and intercept of KM/Vmax

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