The interplay of intrinsic and extrinsic bounded noises in genetic networks

TL;DR

This paper explores how bounded extrinsic and intrinsic noises jointly influence genetic networks, revealing that bounded extrinsic noise can induce new behaviors and modes in biochemical systems, expanding modeling capabilities.

Contribution

It introduces a novel stochastic modeling framework incorporating bounded extrinsic noise into Gillespie-like models of genetic networks, and analyzes its effects on biochemical dynamics.

Findings

Bounded extrinsic noise affects enzymatic reaction approximations.

Extrinsic noise induces new modes in probability densities.

Bounded noise can qualitatively alter genetic switch behavior.

Abstract

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises.