Macroscopic fluctuation-response theory and its use for gene regulatory networks

TL;DR

This paper develops a macroscopic fluctuation-response theory for nonequilibrium systems, deriving relations that connect fluctuations to responses, and applies it to gene regulatory networks to analyze noise characteristics.

Contribution

It introduces exact fluctuation-response relations for nonequilibrium steady states and demonstrates their application to gene regulatory networks with feedback.

Findings

Derived explicit fluctuation-response relations linking spectral density and response.

Provided a method to reconstruct dynamics and noise features from experimental data.

Applied theory to gene networks, including noise decomposition and cross-correlation analysis.

Abstract

Gaussian macroscopic fluctuation theory underpins the understanding of noise in a broad class of nonequilibrium systems. We derive exact fluctuation-response relations linking the power spectral density of stationary fluctuations to the linear response of stable nonequilibrium steady states. Both of these can be determined experimentally and used to reconstruct the kernel of the linearized dynamics and the diffusion matrix, and thus any features of the Gaussian theory. We apply our theory to gene regulatory networks with negative feedback, and derive an explicit internal-external noise decomposition of the power spectral density for any networks, including cross-correlations.