Noise Effects in Nonlinear Biochemical Signaling

TL;DR

This paper investigates the limitations of Gaussian noise models in biochemical signaling, demonstrating potential unphysical results and proposing methods to regularize or approximate the stochastic effects in nonlinear reaction networks.

Contribution

It reveals the issues with Gaussian noise assumptions in biochemical models and introduces analytical and regularization techniques to address these limitations.

Findings

Gaussian models can produce unphysical results in biochemical signaling.

Time scale separation allows for an approximate, solvable model.

Cutoff procedures can regularize Gaussian noise results.

Abstract

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it is a priori obvious that this approximation can violate physical constraints, such as the positivity of chemical concentrations. Here, we show that even when such nonphysical fluctuations are rare, an exact solution of the Gaussian model shows that the model can yield unphysical results. This is done in the context of a simple incoherent-feedforward model which exhibits perfect adaptation in the deterministic limit. We show how one can use the natural separation of time scales in this model to yield an approximate model, that is analytically solvable, including its dynamical response to an environmental change. Alternatively, one can employ a cutoff procedure to regularize the Gaussian result.