Competition between substrates for the same enzyme (or, why do we care about

enzyme kinetics?):

A. For an enzyme that follows Michaelis-Menten kinetics, under what specific condition can

the Michaelis constant, Km, be approximately equal to the dissociation constant of the

enzyme-substrate complex (Kd = [S][E]/[ES])? Use the mathematical definition of Km

(expressed in terms of the relevant reaction rate constants) for your explanation.

B. For this same enzyme, suppose that two similar substrates inside a cell, X and Y, compete

for binding to it’s active site. In such a physiologically relevant scenario, the way an

enzyme chooses to utilize one substrate over the other (i.e., kinetically discriminates

between the two substrates) is predominantly based on which substrate has a higher

reaction rate (V0) compared to the other. Assuming that the specific condition that you have

explained above is valid in case of both the substrates, show that the relative rates of

utilizations of these substrates (i.e., the ratio, V0X/V0Y) can be expressed in terms of their

catalytic efficiencies (kcatX/KmX and kcatY/KmY) and their respective concentrations in

solution ([X] and [Y]).