Limits of sensing temporal concentration changes by single cells

TL;DR

This paper extends classical limits of single-cell concentration sensing to dynamic ramps, comparing measurement strategies and exploring biological implementations, revealing that maximum likelihood estimation can significantly improve sensing accuracy.

Contribution

It generalizes sensing limits to concentration ramps, compares linear regression and maximum likelihood strategies, and suggests biological signatures of optimal estimation methods.

Findings

Maximum likelihood estimation can be twice as accurate as linear regression.

Lower bounds on ramp sensing uncertainty are derived for different measurement devices.

Biological systems may implement maximum likelihood strategies, as indicated by specific signatures.

Abstract

Berg and Purcell [Biophys. J. 20, 193 (1977)] calculated how the accuracy of concentration sensing by single-celled organisms is limited by noise from the small number of counted molecules. Here we generalize their results to the sensing of concentration ramps, which is often the biologically relevant situation (e.g. during bacterial chemotaxis). We calculate lower bounds on the uncertainty of ramp sensing by three measurement devices: a single receptor, an absorbing sphere, and a monitoring sphere. We contrast two strategies, simple linear regression of the input signal versus maximum likelihood estimation, and show that the latter can be twice as accurate as the former. Finally, we consider biological implementations of these two strategies, and identify possible signatures that maximum likelihood estimation is implemented by real biological systems.