Non-Markovian gene expression

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• Michael Assaf (Hebrew University of Jerusalem)
• Thursday 09 November 2023, 15:00-15:30
• Seminar Room 1, Newton Institute.

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MMVW04 - Modelling non-Markov Movement Processes

We study two non-Markovian gene-expression models in which protein production is a stochastic process with a fat-tailed non-exponential distribution of waiting times. 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 of the dynamics, from which the system can only exit via a non-exponential reaction. At times shorter than the MFPT the dynamics are stationary and ergodic while at times longer than the MFPT the dynamics are nonstationary and nonergodic. The MFP Tto the ground state is shown to directly affect the average population sizes and we postulate that the transition to nonergodicity is a universal feature of models with a non-Markovian state.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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