You are analyzing a membrane transporter of substrate X that is known to have ty

Question

You are analyzing a membrane transporter of substrate X that is known to have typical Michaelis-Menten kinetics with a turnover nuber of 200 sec-1. Upon reconstitution of this transporter into proteoliposomes and performing kinetic analysis, you note that the concentration of X required to reach half-maximal transport velocity is 25uM.

A) When Vo=1.6 uMsec-1 and concentration of X is 100uM. Calculate the total concentration of active transporers in your sample.

B) What is maximal initial transport velocity that could be achieved by this preparation of transporter?

C) Assuming the system is saturated with substrate X, how long would it take a given transporter to undergo 100 transport cycles?

There isn't any more given information. My first approach for A was to use v=Vmax[S]/(Km+S) to calculate Vmax. Doesn't the last line in the question mean Km=25uM?

My professor didn't give us either of those values. Couldn't you calculate Vmax from MM equation and then use that to calc the Enzyme concentration?

Explanation / Answer

Answer:

A. Vmax = Kcat x Et -------------------------------(1)

Given, Vo = 1.6 uMsec-1, [S] = 100uM, Km = 25uM, Kcat = 200 sec-1

Vo = Vmax x [S] / Km + [S]

1.6 = (Vmax x 100) / (25 x 100)

Vmax x 100 = 1.6 x 2500 = 4000

Vmax = 40 uMsec-1

Putting this value in equation 1, we get,

Et = Vmax/ Kcat = 40/200 = 0.2 uM (Et is the total active transporters)

B. Vmax = 40 uMsec-1 (Calculated in A)

C. Kcat = 200 sec-1

So, 200 transport cycles takes 1 second.

Therefore, 100 transport cycles takes 1/200 x 100 = 1/2 seconds = 0.5 seconds.

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