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

Area of Science:

• Systems Biology
• Computational Biology
• Biophysics

Background:

• Excitable gene circuits can exhibit noise-induced oscillations.
• Ordinary differential equations (ODEs) models are commonly used to describe gene circuit dynamics.
• Stochastic simulation models capture inherent randomness in biological systems.

Purpose of the Study:

• To investigate the relationship between stochastic simulation and ODE models for excitable gene circuits.
• To analyze how gene copy number influences system behavior near bifurcation points.
• To understand the limitations of ODE models in small systems.

Main Methods:

• Developed and compared a stochastic simulation model with an ODE model.
• Analyzed the dynamics of an excitable gene circuit exhibiting noise-induced oscillations.
• Investigated the impact of varying gene copy numbers on model predictions.

Main Results:

• Stochastic simulations showed significantly different behavior compared to ODE predictions near bifurcation points.
• System dynamics were highly dependent on gene copy number.
• Very slow convergence to the large number limit was observed near the bifurcation point.

Conclusions:

• ODE models may inaccurately predict gene circuit dynamics in regions of low copy number or near bifurcations.
• Stochastic effects are crucial for understanding the behavior of excitable gene circuits with few constituents.
• Findings have implications for birth-death dynamical systems with limited components.