# Ligand-concentration sensitivity of a multi-state receptor

## TL;DR

This paper investigates the sensitivity of ligand concentration detection in biological receptors operating out of equilibrium, deriving a universal formula that confirms the Berg-Purcell limit applies broadly.

## Contribution

It provides a general formula for maximum receptor sensitivity, demonstrating the Berg-Purcell limit's universality across equilibrium and non-equilibrium states.

## Key findings

- Sensitivity is universally limited by the Berg-Purcell limit.
- Derived a general formula for maximum sensitivity.
- Sensitivity bounds hold regardless of receptor equilibrium state.

## Abstract

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.