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