Question

At what concentration of $\mathbf{S}$ (expressed as a multiple of ${\mathbf{K}}_{\mathbf{M}}$ ) will ${\mathbf{v}}_{\mathbf{0}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{95}{\mathbf{V}}_{\mathbf{max}}$?

Short answer

The concentration of $\mathrm{S}$at which ${\mathrm{v}}_0=0.95{\mathrm{V}}_{\max }$is$19{\mathrm{K}}_{\mathrm{M}}$.

Step-by-step solution

Introduction

The substrate or reactant is the molecule that binds to the enzyme, and the enzyme converts it into the product. ${\mathrm{v}}_0$ is the enzyme initial velocity. It stimulates the formation of the product from the reactant. ${\mathrm{V}}_{\max }$is the maximum rate of the reaction.

Michaelis-Menten equation

According to Michaelis-Menten equation,

${\mathrm{v}}_0=\frac{{\mathrm{V}}_{\max }\left[\mathrm{S}\right]}{{\mathrm{K}}_{\mathrm{M}}+\left[\mathrm{S}\right]}$

where

${\mathrm{v}}_0$is the initial velocity.

${\mathrm{V}}_{\max }$is the maximum velocity.

$\left[\mathrm{S}\right]$is the concentration of the substrate

${\mathrm{K}}_{\mathrm{M}}$is the Michaelis-Menten constant.

Calculation of substrate concentration

On substituting the values in the equation,

$$\begin{gathered} 0.95{\mathrm{V}}_{\max }=\frac{{\mathrm{V}}_{\max }\left[\mathrm{S}\right]}{{\mathrm{K}}_{\mathrm{M}}+\left[\mathrm{S}\right]} \\ 0.95\left[\mathrm{S}\right]+0.95{\mathrm{K}}_{\mathrm{M}}=\left[\mathrm{S}\right] \\ 0.05\left[\mathrm{S}\right]=0.95{\mathrm{K}}_{\mathrm{M}} \\ \left[\mathrm{S}\right]=\frac{0.95{\mathrm{K}}_{\mathrm{M}}}{0.05} \\ \left[\mathrm{S}\right]=19{\mathrm{K}}_{\mathrm{M}} \end{gathered}$$

Thus, the concentration of the substrate is 19K_M.