Ligand-concentration sensitivity of a multi-state receptor

Biological sensory systems generally operate out of equilibrium, which often leads to their improved performance. Here, we study the sensitivity of ligand concentration for a general receptor model, which is generally in the non-equilibrium stationary state, in the framework of a stochastic diffusion equation. We derived a general formula of the maximum sensitivity. Specifically, the sensitivity is limited universally by the Berg-Purcell limit [Biophys. J ., 1977], regardless of whether the receptor is in an equilibrium or non-equilibrium state.