XLSTAT: Competitive Inhibition Using Nonlinear Regression in Excel

 

Background

Nonlinear regression is suited for modeling complex relationships that linear models can't capture—such as enzyme inhibition types (competitive, non-competitive, uncompetitive, mixed).

This guide focuses on competitive inhibition and outlines how to estimate and interpret key parameters (Vmax, Km, Ki). A sample dataset with fictitious data is provided for practice.

Enzymes accelerate reactions by lowering activation energy. Competitive inhibitors block substrates from binding to enzymes, slowing or stopping the reaction. The enzyme kinetics are modeled by:

v=Vmax⋅SKm⋅(1+IKi)+S

Where:

• v: reaction speed

• Vmax: maximum reaction speed

• S: substrate concentration

• Km: Michaelis constant

• Ki: inhibitor constant

• I: inhibitor concentration (varies per curve)

Using the example, we will estimate shared parameters (Vmax, Km, Ki) across curves via global nonlinear regression. Results appear in two sheets:

• Data: selected input variables

• Nonlinear Regression: estimated parameters and model fit results.

 

Setting Up

• Open XLSTAT.

• Click on the Modeling data menu and select the Nonlinear regression feature.

• Once the button is clicked, the dialog box pops up.

In the General tab:

• Enter the dependent variables which correspond to the Y columns which are all the curves, and the explanatory variable which in this case is the substrate concentration.

In the Functions tab:

• Choose the formulas for competitive inhibition (enzymatic kinetics / competitive inhibition), and enter the different concentrations of the inhibitor, one concentration for each of the curves.

• You can add starting values, limits and labels for the parameters. 

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

Following the descriptive statistics of variables, and the goodness of fit coefficients, a third table provides details on the parameters of the model. Since the parameters are the same for each of the curves (only the inhibitor concentration varies), we only display the first ones of the table.

These values ​​are the ones that best estimate the parameters of the model. We can then see, with the graph of the curves speed as a function of the substrate, that the estimated parameters allow to obtain a very good fit of the data.

These four curves, which each represent one of the dependent columns, are lower and lower as the inhibitor concentration increases.

Finally, we can see that in the case of competitive inhibition, the nonlinear regression allows to measure the speed curves as a function of the substrate concentration in the presence of several inhibitor concentrations. XLSTAT also proposes to do this for non-competitive inhibition, uncompetitive inhibition and mixed inhibition.