Optimal inference strategies and their implications for the linear noise approximation

TL;DR

This paper investigates the information loss in time-averaging inference strategies for binary sensors measuring weak signals, identifying conditions under which full information is retained or lost, with implications for the linear noise approximation.

Contribution

It derives a condition based on local detailed balance that predicts when time integration captures all information, linking it to the linear noise approximation's limitations.

Findings

Information loss can be up to 0.5 bits per measurement.

Symmetric energy distribution ensures full information capture.

Linear noise approximation inherently involves information loss.

Abstract

We study the information loss of a class of inference strategies that is solely based on time averaging. For an array of independent binary sensors (e.g., receptors, single electron transistors) measuring a weak random signal (e.g., ligand concentration, gate voltage) this information loss is up to 0.5 bit per measurement irrespective of the number of sensors. We derive a condition related to the local detailed balance relation that determines whether or not such a loss of information occurs. Specifically, if the free energy difference arising from the signal is symmetrically distributed among the forward and backward rates, time integration mechanisms will capture the full information about the signal. As an implication, for the linear noise approximation, we can identify the same loss of information, arising from its inherent simplification of the dynamics.