Fundamental Limits on Sensing Chemical Concentrations with Linear Biochemical Networks

TL;DR

This paper investigates the fundamental limits of how accurately living cells can measure chemical concentrations using linear biochemical networks, revealing conditions under which they can surpass traditional sensing limits.

Contribution

It derives the optimal time-averaging strategy for linear networks and establishes the fundamental measurement limits for both stationary and nonstationary signals.

Findings

Linear networks reach the Berg-Purcell limit for long stationary signals.

Non-uniform time-averaging allows surpassing the Berg-Purcell limit for short or nonstationary signals.

Optimal weighting functions for time averaging are derived for improved sensing accuracy.

Abstract

Living cells often need to extract information from biochemical signals that are noisy. We study how accurately cells can measure chemical concentrations with signaling networks that are linear. For stationary signals of long duration, they can reach, but not beat, the Berg-Purcell limit, which relies on uniformly averaging in time the fluctuations in the input signal. For short times or nonstationary signals, however, they can beat the Berg-Purcell limit, by non-uniformly time-averaging the input. We derive the optimal weighting function for time averaging and use it to provide the fundamental limit of measuring chemical concentrations with linear signaling networks.