Logistic models

What function to use: fit_50

Logistic models are implemented in the traditional sigmoid form. This model could be used broadly for any dose-response curve, where x corresponds to dose and y corresponds to response. In the context of BindCurve, x will commonly correspond to the total concentration of the titrated ligand. By fixing the slope in these models to a constant value (e.g. 1 for activation and -1 for inhibition), this four-parameter model is reduced to a three-parameter model.

Fitting midpoint

Model name: IC50

\(\text{IC}_{50}\) is fitted using the following equation:

\[ y = ymin + (ymax - ymin) \frac{1}{1 + \left(\frac{\text{IC}_{50}}{x}\right)^{\text{slope}}} \]

where x is the dose, usually the total concentration of the titrated ligand

\[ x = [L]_T \]

Fitting midpoint from log-transformed data

Model name: logIC50

Analogically, \(\text{logIC}_{50}\) is fitted using:

\[ y = ymin + (ymax - ymin) \frac{1}{1 + 10^{\text{slope}(\text{logIC}_{50} - x)}} \]

where x is log transformed dose

\[ x = \log([L]_T) \]

Note

Once you have \(\text{logIC}_{50}\) value, it can easily be converted to \(\text{pIC}_{50}\) by multiplying with -1.