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
\[ x = \log([L]_T) \]
Once you have \(\text{logIC}_{50}\) value, it can easily be converted to \(\text{pIC}_{50}\) by multiplying with -1.