Non-Markovian processes in gene regulation

Dmitri A. Bratsun; Dmitri N. Volfson; Jeff Hasty; Lev S. Tsimring

doi:10.1117/12.609707

23 May 2005 Non-Markovian processes in gene regulation (Keynote Address)

Dmitri A. Bratsun, Dmitri N. Volfson, Jeff Hasty, Lev S. Tsimring

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Proceedings Volume 5845, Noise in Complex Systems and Stochastic Dynamics III; (2005) https://doi.org/10.1117/12.609707
Event: SPIE Third International Symposium on Fluctuations and Noise, 2005, Austin, Texas, United States

Abstract

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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Dmitri A. Bratsun, Dmitri N. Volfson, Jeff Hasty, and Lev S. Tsimring "Non-Markovian processes in gene regulation (Keynote Address)", Proc. SPIE 5845, Noise in Complex Systems and Stochastic Dynamics III, (23 May 2005); https://doi.org/10.1117/12.609707

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KEYWORDS

Stochastic processes

Proteins

Correlation function

Systems modeling

Molecules

Chemical analysis

Genetics

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