Chemical event chain model of coupled genetic oscillators

TL;DR

This paper presents a stochastic model for coupled genetic oscillators using Poisson processes, analyzing their steady states, synchronization, and optimal conditions as biological pacemakers, with insights into stochastic effects and delay-coupled phase oscillators.

Contribution

It introduces a novel stochastic framework for genetic oscillator coupling, linking chemical event chains to oscillator dynamics and effective phase models.

Findings

Steady states characterized by frequency, quality factor, and cross correlation.

Coupling induces stochastic transitions between modes.

Optimal pacemaker behavior occurs in specific parameter regions.

Abstract

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.