Fluctuations in reactive networks subject to extrinsic noise studied in the framework of the Chemical Langevin Equation

TL;DR

This paper investigates how extrinsic noise influences fluctuations in reactive networks at non-equilibrium steady states, deriving a Chemical Langevin Equation to analyze correlation functions and the fluctuation-dissipation theorem's applicability.

Contribution

It introduces a generic model incorporating extrinsic noise into the Chemical Langevin framework for reactive networks, analyzing fluctuation-response relations.

Findings

Correlation functions are derived for noisy reactive networks.

The deviation from the fluctuation-dissipation theorem is quantified.

Conditions for defining an effective temperature are identified.

Abstract

Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and how they relate to the response of the reactive network to a perturbation. Answers to these questions are of prime importance to extract meaningful parameters from the in vivo fluorescence correlation spectroscopy data. In this paper we study the fluctuations of the concentration of a reactive species involved in a cyclic network that is in a non-equilibrium steady state perturbed by a noisy force, taking into account both the breaking of detailed balance and extrinsic noises. Using a generic model for the network and the extrinsic noise, we derive a Chemical Langevin Equation that describes the dynamics of the system, we determine the expressions of the correlation functions of the concentrations, estimate the deviation of the fluctuation-dissipation theorem and the range of parameters in which an effective temperature can be defined.