University of California, San Diego

Delay- Induced Stochastic Oscillations in Gene Regulation

Lev S. Tsimring

Abstract:  We study the stochastic properties of gene regulation taking into
account the non-Markovian character of gene transcription and
translation. The time delay in protein production or degradation may
change the behavior of the system from stationary to oscillatory even
when a deterministic counterpart of the stochastic system exhibits no
oscillations. Assuming significant decorrelation on the time scale of
gene transcription,  we deduce a truncated master equation of the
reactive system and derive an analytical expression for the
autocorrelation function of the protein concentration. For weak feedback
the theory agrees well with numerical simulations based on the modified
direct Gillespie method.