MM Equation is V= VmaxS/(KM+S) VmaxS = V*(KM+S) S/V= (KM+S)/Vmax S/V = (KM/Vmax)

Question

MM Equation is V= VmaxS/(KM+S)

VmaxS = V*(KM+S)

S/V= (KM+S)/Vmax

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

so a plot of S/V vs S gives slope of 1/Vmax and intercept is Km/Vmax ,this plot is known ad Hanes plot

lineweaver-burk plot is 1/V= (KM/Vmax)*1/S + 1/Vmax

so a plot of 1/V vs 1/S gives straight linr whose slope is KM/Vmax and intercept is 1/Vmax. This plot is constructed 1st and the data points along with the plot is shown below.

from the plot, 1/vmax= intercept = 0.0656 min , Vmax= 1/0.0656=15.2439 mM/min and slope is KM/Vmax= 6.9289

Km= 6.9289*15.2439=105.6235 mM

2. since V= Vmax*S/ (KM+S)

V*(KM+S)= Vmax*S

V*KM+V*S= Vmax*S

VKM/S+V= Vmax

V= -VKM/S+Vmax

so a plot of V V/S gives gives an intercept of Vmax and slope of -KM.

This is also drawn and shown below.

from the plot, slope -KM=-105.25, Km= 105.24 mM and intecept is Vmax= 15.215 mM/min

3. Hanes plot is a plot of S/V vs S gives slope of 1/Vmax and intercept is Km/Vmax

so a plot of S/V vs S is created and shown below

intercept is KM/Vmax= 6.9121 and slope is 1/Vmax= 0.0658, Vmax= 1/0.0658=15.19 mM/min and Km=6.9121*15.19 =105.05 mM/min

Explanation / Answer

3. (40 pts) In class we derived two linearized versions of the Michaelis-Menten (MM) kinetics equation, namely the Lineweaver-Burke and the Eadie-Hofstee plots. There is another one called the Hanes plot, which is a plot of [S]/v vs. [S]. Starting with the MM equation, derive the Hanes plot equation. What are the slope and y-intercept for the Hanes plot in terms of the parameters Vma and Km? Use the following data to make a Lineweaver-Burke, Eadie-Hofstee. and Hanes plots and compare the value of max and Km for all three plots 250 10.70 400 [S] (mM v (mM/min) 30 60 100 150 3.37 5.53 7.42 8.94 12.04

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