Hill coefficients of a polymodal Monod-Wyman-Changeux model for ion channel gating

Allosteric transitions of ion channels can be driven by multiple sources of free energies. One class of model for describing such transitions is the multistimulus Monod-Wyman-Changeux model, in which each stimulus interacts with a specific sensor on the protein and activation of the sensor is allosterically coupled to conformational changes of the protein. In general, when a protein is stressed by multiple stimuli, one stimulus can influence the response to another, which can result in both a shift of the midpoint of the dose-response curve and a change of the slope of the curve. Here I show that, for a Monod-Wyman-Changeux model with independent sensors, the different dose-response curves of open probability for one stimulus have the same slope at the same agonist concentration. In the other words, the slope of the dose-response curve for one stimulus is an intrinsic property of the sensors for that stimulus; it is independent of other stimuli or their sensor properties. As the dose-response curve for many receptors can be fit to a Boltzmann or Hill equation, this property provides a practical, usable test for applicability of such models.