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 Equation: Noncompetitive inhibition

## Terminology

Copeland suggests not using this equation, which is simplistic. Instead he suggests using the equation we call mixed-model inhibition (but he calls noncompetitive inhibition).

## Introduction

A noncompetitive inhibitor reversibly binds to both the enzyme-substrate complex, and the enzyme itself. This means that the effective Vmax decreases with inhibition but the Km does not change. You can determine the Ki of a competitive inhibitor by measuring substrate-velocity curves in the presence of several concentrations of inhibitor.

The term 'noncompetitive' is used inconsistently. It is usually used as defined above, when the inhibitor binds with identical affinity to the free enzyme and the enzyme-substrate complex. Sometimes, however, the term 'noncompetitive' is used more generally, when the two binding affinities differ, which is more often called mixed-model inhibition.

## Step by step

Create an XY data table. Enter substrate concentration into the X column, and enzyme activity into the Y columns. Each data set (Y column) represents data collected in the presence of a different concentration of inhibitor, starting at zero. Enter these concentrations into the column titles. Be sure to enter concentrations, not logarithms of concentration.

After entering data, click Analyze, choose nonlinear regression, choose the panel of enzyme kinetics equations, and choose Noncompetitive enzyme inhibition.

## The model

Vmaxinh=Vmax/(1+I/Ki)

Y=Vmaxinh*X/(Km+X)

The constant I is the concentration of inhibitor, a value you enter into each column title. This is constrained to be a data set constant.

The parameters Vmax, Km and Ki are shared, so Prism fits one best-fit value for the entire set of data.

## Interpreting the parameters

Vmax is the maximum enzyme velocity in the absence of inhibitor, expressed in the same units as Y.

Km is the Michaelis-Menten constant (in the absence of inhibitor), expressed in the same units as X. It describes the interaction of substrate and enzyme in the absence of inhibitor.

Ki is the inhibition constant, expressed in the same units as I, which you entered.

If the data don't fit the model well, consider instead fitting to a competitive or uncompetitive model. Or fit to the more general equation for mixed-model inhibition.

## Reference

Equation 3.4 in: RA Copeland, Evaluation of Enzyme Inhibitors in Drug Discovery, Second edition, Wiley 2013. IBSN: 978-1-118-48813-3.