Noise Propagation in Biological and Chemical Reaction Networks

TL;DR

This paper analyzes how noise propagates through biological and chemical reaction networks, examining the effects of network topology, cycles, and crosstalk on output variance and system stability.

Contribution

It introduces a mathematical framework for quantifying noise propagation in reaction networks, highlighting the impact of network structure and correlations on variance and steady states.

Findings

Cycles increase output variance due to correlations.

Long cycles limit the effect of feedforward and feedback on noise.

Crosstalk reduces noise but slows network response.

Abstract

We describe how noise propagates through a network by calculating the variance of the outputs. Using stochastic calculus and dynamical systems theory, we study the network topologies that accentuate or alleviate the effect of random variance in the network for both directed and undirected graphs. Given a linear tree network, the variance in the output is a convex function of the poles of the individual nodes. Cycles create correlations which in turn increase the variance in the output. Feedforward and feedback have a limited effect on noise propagation when the respective cycles is sufficiently long. Crosstalk between the elements of different pathways helps reduce the output noise, but makes the network slower. Next, we study the differences between disturbances in the inputs and disturbances in the network parameters, and how they propagate to the outputs. Finally, we show how noise correlations can affect the steady state of the system in chemical reaction networks with reactions of two or more reactants, each of which may be affected by independent or correlated noise sources.