Deciphering noise amplification and reduction in open chemical reaction networks

TL;DR

This paper analyzes how noise is amplified or reduced in open chemical reaction networks using stochastic differential equations, revealing that flux direction influences noise levels, with implications for biological and synthetic systems.

Contribution

It provides a theoretical framework linking network deficiency, flux direction, and noise modulation in chemical reaction networks, extending understanding beyond detailed-balanced systems.

Findings

Zero deficiency systems have uncorrelated species with Poisson noise.

Flux direction determines noise amplification or reduction in deficiency one systems.

The relation between flux and noise is generalized to higher deficiency systems.

Abstract

The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would allow rationally designing synthetic networks with controlled noise. Using the It\=o stochastic differential equation formalism, we performed both analytic and numerical analyses of several model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. These systems represent for example biomolecular oligomerization processes, complex-breakage reactions, signaling cascades or metabolic networks. For chemical reaction networks with zero deficiency values, which admit a detailed- or complex-balanced steady state, all molecular species are uncorrelated. The number of molecules of each species follow a Poisson distribution and their Fano factors, which measure the intrinsic noise, are equal to one. Systems with deficiency one have an unbalanced non-equilibrium steady state and a non-zero S-flux, defined as the flux flowing between the complexes multiplied by an adequate stoichiometric coefficient. In this case, the noise on each species is reduced if the flux flows from the species of lowest to highest complexity, and is amplified is the flux goes in the opposite direction. These results are generalized to systems of deficiency two, which possess two independent non-vanishing S-fluxes, and we conjecture that a similar relation holds for higher deficiency systems.