## Core Concepts

In this article, you will learn about the Lineweaver-Burk plot and its applications to biochemistry topics, specifically that of enzyme kinetics.

## Topics Covered in Other Articles

Enzymes – Function and Types | ChemTalk (chemistrytalk.org)

Michaelis-Menten Equation | ChemTalk (chemistrytalk.org)

Chemical Kinetics and Rate of Reaction | ChemTalk (chemistrytalk.org)

Reaction Rates & How to Determine Rate Law | ChemTalk (chemistrytalk.org)

## What Does a Lineweaver-Burk Plot Represent?

A Lineweaver-Burk plot, sometimes referred to as a double-reciprocal plot, can be made for enzymes obeying the Michaelis-Menten relationship. It relies on kinetics parameters such as [S], V_{o}, K_{m}, and the ratio between the two. [S] is the concentration of substrate while V_{o} is defined as relative activity, or initial rates of the reaction. K_{m} is is defined as the Michaelis constant which corresponds to the substrate concentration at which the rate of substrate capture and product release contribute equally to the overall rate. V_{max} is defined as the maximum rate observed at high substrate concentration.

A Lineweaver-Burk Plot is the most common linear transform used to illustrate enzyme kinetics trends. It is a plot of 1/V_{o} versus 1/[S], which form a linear relationship. The equation for this line and key values can be seen in the table below.

A typical Lineweaver-Burk plot is represented below, with special attention to the values of slope, intercepts, and units.

## How to Get the Necessary Data

In order to generate one of these plots, enzyme kinetics experiments must first be performed. Typical enzyme kinetics experiments involve collecting absorbances of the reaction over a certain period of time. Using this data, the rate of reaction can be calculated. Reaction rates can then be converted to activity, which when divided by the volume of enzyme added, leads to the determination of relative activity of the enzyme. Relative activity, represented by V_{o}, is then plotted in its inverse form on the y-axis.

## Applications of Lineweaver-Burk Plot Towards Inhibition

The presence of an inhibitor can affect the observed values in a reaction. These relationships of competitive, uncompetitive, and noncompetitive inhibition can be displayed using Lineweaver-Burk plots, as shown below in the following figures.

In instances of competitive inhibition, a competitive inhibitor binds to the free enzyme at the active site. This blocks catalysis, resulting in modification of the rate of substrate capture into the enzyme-substrate complex. This changes the value of the x-intercept and slope, while keeping the y-intercept, that represents the inverse rate of release from the enzyme-substate complex, the same.

In uncompetitive inhibition instances, although relatively rare, the inhibitor binds to the enzyme-substrate complex. This doesn’t change the rate of capture into the enzyme-substrate complex, so no change in slope is observed. It does however decrease the observed rate of release from the complex, lowering the Vmax value.

Mixed inhibition occurs when an inhibitor can bind to the free enzyme of the complex. This results in a large observed change to the Vmax value, while the Km value remains the same. The slope, which is a ratio of the two parameters, changes. Noncompetitive inhibition is a unique case of mixed inhibition where the inhibitor has the same affinity for the free enzyme and enzyme-substrate complex.

## Issues Associated with a Lineweaver-Burk Plot

Although considered to be one of the more traditional ways to display enzyme kinetic data by textbooks, a Lineweaver-Burk plot is not the most accurate. This is because the most accurate, or fastest, rates end up crowded around the y-axis. This leaves the slower rates, further away from the axis, to bias the results. If trying to determine kinetics parameters from experimental data, other linear transforms of the Michaelis-Menten relationship are better recommended, such as the Eadie-Hofstee plot. An Eadie-Hofstee plot doesn’t take the reciprocal of the measured rates, and since direct values for V_{o} are used on both the axes, gives all measurements equal weight in the linear fit. Another common linear transformation of the Michaelis-Menten relationship is the Direct Linear plot. This is an entirely graphical analysis that requires no math to be done.