Limitations on concentration measurements and gradient discerning times in cellular systems

TL;DR

This paper revisits the Berg and Purcell limit on cellular concentration measurement error, showing it remains unchanged when measuring from contact, and derives a new lower bound on gradient sensing time based on ligand detachment rates.

Contribution

It provides a revised analysis of measurement error at contact and establishes a fundamental lower bound on gradient sensing time independent of diffusion or concentration.

Findings

Measurement error at contact matches Berg and Purcell's original bound.

Lower bound on gradient sensing time depends on ligand-receptor detachment rate.

Results may explain experimental observations of cellular sensing limitations.

Abstract

This work reports on two results. At first we revisit the Berg and Purcell calculation that provides a lower bound to the error in concentration measurement by cells, by considering the realistic case when the cell starts measuring the moment it comes in contact with the chemoattractants, instead of measuring after equilibrating with the chemotactic concentration as done in the classic Berg and Purcell paper. We find that the error in concentration measurement is still the same as evaluated by Berg and Purcell. We next derive a lower bound on measurement time below which it is not possible for the cell to discern extra-cellular chemotactic gradients through spatial sensing mechanisms. This bound is independent of diffusion rate and concentration of the chemoattracts and is instead set by detachment rate of ligands from the cell receptors. The result could help explain experimental observations.