Non-Markovian gene expression

Ohad Vilk, Ralf Metzler, Michael Assaf

Research output: Contribution to journalArticlepeer-review


We study two non-Markovian gene-expression models in which protein production is a stochastic process with a fat-tailed nonexponential waiting time distribution (WTD). For both models, we find two distinct scaling regimes separated by an exponentially long time, proportional to the mean first passage time (MFPT) to a ground state (with zero proteins) of the dynamics, from which the system can only exit via a nonexponential reaction. At times shorter than the MFPT the dynamics are stationary and ergodic, entailing similarity across different realizations of the same process, with an increased Fano factor of the protein distribution, even when the WTD has a finite cutoff. Notably, at times longer than the MFPT the dynamics are nonstationary and nonergodic, entailing significant variability across different realizations. The MFPT to the ground state is shown to directly affect the average population sizes and we postulate that the transition to nonergodicity is universal in such non-Markovian models.

Original languageAmerican English
Article numberL022026
JournalPhysical Review Research
Issue number2
StatePublished - Apr 2024

Bibliographical note

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© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.


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