The transition between stochastic and deterministic behavior in an excitable gene circuit

TL;DR

This paper investigates how stochastic and deterministic models of an excitable gene circuit differ near bifurcation points, highlighting the impact of gene copy number on system behavior and convergence.

Contribution

It provides a detailed analysis of the transition from stochastic to deterministic behavior in gene circuits, especially near bifurcations, emphasizing slow convergence at low copy numbers.

Findings

Behavior near bifurcation points differs significantly between models.

Slow convergence to the large number limit near bifurcations.

Gene copy number critically influences noise-induced oscillations.

Abstract

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.