Intrinsic fluctuations in stochastic delay systems: theoretical description and application to a simple model of gene regulation

TL;DR

This paper develops a theoretical framework to analyze intrinsic noise effects in stochastic delay systems, revealing noise-induced oscillations and applying it to a gene regulation model relevant to biological processes.

Contribution

It introduces an analytical approach to describe noise-induced oscillations in stochastic delay systems, demonstrated on a gene regulation model with biological significance.

Findings

Intrinsic noise can induce oscillations where deterministic models do not predict them.

The power spectra of stochastic oscillations are computed analytically and match simulations.

The approach is applicable to biological systems with small molecule numbers, like gene regulation.

Abstract

The effects of intrinsic noise on stochastic delay systems is studied within an expansion in the inverse system size. We show that the stochastic nature of the underlying dynamics may induce oscillatory behaviour in parameter ranges where the deterministic system does not sustain cycles, and compute the power spectra of these stochastic oscillations analytically, in good agreement with simulations. The theory is developed in the context of a simple one-dimensional toy model, but is applicable more generally. Gene regulatory systems in particular often contain only a small number of molecules, leading to significant fluctuations in mRNA and protein concentrations. As an application we therefore study a minimalistic model of the expression levels of hes1 mRNA and Hes1 protein, representing the simple motif of an auto-inhibitory feedback loop and motivated by its relevance to somite segmentation.