Question

The K_M for the reaction chymotrypsin with N-acetylvaline ethyl ester is $\mathbf{8}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{‐}\mathbf{2}}\mathbf{M}$, and the ${\mathbf{K}}_{\mathbf{M}}$ for the reaction of chymotrypsin with N-acetyltyrosine ethyl ester is $\mathbf{6}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{‐}\mathbf{4}}\mathbf{M}$. (a) Which substrate has the higher apparent affinity for the enzyme? (b) Which substrate is likely to give a higher value for ${\mathbf{V}}_{\mathbf{max}}$?

Short answer

1. The substrate N-acetyltyrosine ethyl ester has a higher apparent affinity for the enzyme chymotrypsin.
2. ${\mathrm{K}}_{\mathrm{M}}$ and ${\mathrm{V}}_{\max }$ are not related, so the substrate likely to give a higher V_maxvalue cannot be determined.

Step-by-step solution

Introduction

Enzymes are biological protein catalysts that speed up biological processes. The study of how enzymes catalyze chemical processes is known as enzyme kinetics. The reaction rate is determined by the rate at which the enzyme substrate interacts with the enzyme and produces the products.

${\mathrm{K}}_{\mathrm{M}}$ stands for Michaelis-Menten constant. The ${\mathrm{K}}_{\mathrm{M}}$value is the concentration of S at which the maximal velocity is half. ${\mathrm{V}}_{\max }$is the greatest rate at which an enzyme catalyzes a reaction.

Explanation for (a)

The "affinity"of an enzyme for its substrate may be calculated using ${\mathrm{K}}_{\mathrm{M}}$. A high ${\mathrm{K}}_{\mathrm{M}}$ enzyme has a low affinity for its substrate, whereas a low ${\mathrm{K}}_{\mathrm{M}}$ enzyme has a high affinity. Thus, the ethyl ester of N-acetyltyrosinehas a higher apparent affinity for chymotrypsin because its${\mathrm{K}}_{\mathrm{M}}$ value is lower.

Explanation for (b)

The values of ${\mathrm{K}}_{\mathrm{M}}$ and${\mathrm{V}}_{\max }$ are independent of one another as ${\mathrm{K}}_{\mathrm{M}}$ has nothing to do with the enzyme maximal catalytic rate. Thus, it is not possible to determine which substrate will give a higher V_max.