This function is applicable for a wide variety of ligand-receptor interactions and provides the theoretical basis for standard dose-response analysis. Ligand doses are usually expressed as log(dose) and receptor binding or biological effect is normally plotted on a linear scale. Empirical data conforming to this theoretically derived function have particularly strong intrinsic validity. Notable exceptions to this model include allosteric receptor binding and certain pharmacodynamic drug interactions.
The following simulation assumes a simple bimolecular model. In cases
where efficacy = 1, the biological response should directly follow the
binding function. Compare the figure generated by this function with the
shape of a typical dose-response curve.
| K = 0.003 | Concentration (A) =
0.3 log unit increments |
| A * rt
Xe = ------- A + K |
Receptors (rt) = 100 |
| Ligand
Concentration |
%
Maximum
Binding |
| 0.0001 | 3.2 |
| 0.0002 | 6.3 |
| 0.0004 | 11.8 |
| 0.0008 | 21.1 |
| 0.0016 | 34.8 |
| 0.0032 | 51.6 |
| 0.0064 | 68.1 |
| 0.0128 | 81.0 |
| 0.0256 | 89.5 |
| 0.0512 | 94.5 |
| 0.1024 | 97.2 |
| 0.2048 | 98.6 |
| 0.4096 | 99.3 |
| 0.8192 | 99.6 |
The data are plotted in the following graph. The ligand concentration
is expressed on a log scale, but the listed values are misleading (i.e.,
they represent successive log[dose]-increments not actual log[dose]). Note
that the portion of the curve between 20% (A20) and 80% (A80)
of the maximum binding is linear.