Statistics of optimal information flow in ensembles of regulatory motifs

TL;DR

This paper uses statistical field theory to analyze the distribution of maximal mutual information in ensembles of regulatory motifs, revealing variability in regulatory effectiveness due to parameter heterogeneity.

Contribution

It introduces a novel analytical approach to quantify the statistics of information capacity in regulatory motifs with random parameters.

Findings

Mean capacity and distribution accurately predicted by theory.

Heterogeneity in kinetic parameters causes variability in regulatory effectiveness.

Analytical results match numerical simulations for large N.

Abstract

Genetic regulatory circuits universally cope with different sources of noise that limit their ability to coordinate input and output signals. In many cases, optimal regulatory performance can be thought to correspond to configurations of variables and parameters that maximize the mutual information between inputs and outputs. Such optima have been well characterized in several biologically relevant cases over the past decade. Here we use methods of statistical field theory to calculate the statistics of the maximal mutual information (the `capacity') achievable by tuning the input variable only in an ensemble of regulatory motifs, such that a single controller regulates N targets. Assuming (i) sufficiently large N, (ii) quenched random kinetic parameters, and (iii) small noise affecting the input-output channels, we can accurately reproduce numerical simulations both for the mean capacity and for the whole distribution. Our results provide insight into the inherent variability in effectiveness occurring in regulatory systems with heterogeneous kinetic parameters.