Effect of subcritical excitation of oscillations in stochastic systems with time delay. Part I. Regulation of gene expression

Abstract

We study excitation of oscillations in the stochastic gene systems with time-delayed feedback loop during transcription. The oscillations arise due to interaction noise and time delay even when deterministic counterpart of the system exhibits stationary behaviour. This effect becomes important when degree-of-freedom of a system is not high, and role of fluctuations becomes principal. The analytical solution of master-equation is obtained. The results of numerical simulations are presented.

Keywords

• time-delay
• stochastic systems
• oscillations
• gene regulation