Maximum likelihood and the single receptor

TL;DR

This paper derives a fundamental physical limit on chemical sensing accuracy in cells using maximum likelihood estimation, highlighting how optimal receptor strategies can improve sensing beyond traditional bounds.

Contribution

It introduces a new lower limit on sensing accuracy based on maximum likelihood, focusing on unoccupied receptor intervals, and suggests biological implementation strategies.

Findings

Maximum likelihood improves sensing accuracy by focusing on unoccupied intervals.

Receptors minimizing bound time intervals achieve optimal sensing.

Proposed biological mechanisms for implementing optimal sensing strategies.

Abstract

Biological cells are able to accurately sense chemicals with receptors at their surfaces, allowing cells to move towards sources of attractant and away from sources of repellent. The accuracy of sensing chemical concentration is ultimately limited by the random arrival of particles at the receptors by diffusion. This fundamental physical limit is generally considered to be the Berg & Purcell limit [H.C. Berg and E.M. Purcell, Biophys. J. {\bf 20}, 193 (1977)]. Here we derive a lower limit by applying maximum likelihood to the time series of receptor occupancy. The increased accuracy stems from solely considering the unoccupied time intervals - disregarding the occupied time intervals as these do not contain any information about the external particle concentration, and only decrease the accuracy of the concentration estimate. Receptors which minimize the bound time intervals achieve the highest possible accuracy. We discuss how a cell could implement such an optimal sensing strategy by absorbing or degrading bound particles.