Question

Write the Lineweaver–Burk (double reciprocal) equation and describe the features of a Lineweaver–Burk plot.

Short answer

The double reciprocal equation of the Lineweaver Burk plot is:

$\frac{1}{\mathrm{V}}=\frac{{\mathrm{K}}_{\mathrm{M}}}{{\mathrm{V}}_{\max }}\frac{1}{\left[\mathrm{S}\right]}+\frac{1}{{\mathrm{V}}_{\max }}$

The main feature is that it provides a more precise estimation of ${\mathrm{V}}_{\max }$ on inhibition.

Step-by-step solution

Introduction

A Lineweaver Burk plot, also known as a double-reciprocal plot, is a graphical depiction of the Lineweaver Burk equation of enzyme kinetics.

Lineweaver-Burk plot

The Michaelis-Menten equation is:

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

On taking the reciprocal of both sides of the Michaelis-Menten equation, the Lineweaver-Burk plot (double reciprocal equation) is obtained.

$\frac{1}{\mathrm{V}}=\frac{{\mathrm{K}}_{\mathrm{M}}}{{\mathrm{V}}_{\max }}\frac{1}{\left[\mathrm{S}\right]}+\frac{1}{{\mathrm{V}}_{\max }}$

Where

$\mathrm{V}=$Reaction velocity

${\mathrm{K}}_{\mathrm{M}}=$Michaelis-Menten constant

${\mathrm{V}}_{\max }=$Maximum reaction velocity

$\left[\mathrm{S}\right]=$Substrate concentration

Lineweaver-Burk plot graphical diagram

Thus, it provides a more precise estimate of ${\mathbf{V}}_{\mathbf{max}}$and information on inhibition. By linearizing the data, it improvesaccuracy.