Non-Markovian processes in gene regulation (Keynote Address)

We study the stochastic properties of gene regulation taking into account the non-Markovian character of gene transcription and translation. We show that 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 with numerical simulations based on the modified direct Gillespie method.

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