2023/08/12 by Ohad Vilk, Ralf Metzler, Vilk, Ohad +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Gene Regulatory Network Analysis #Diffusion and Search Dynamics #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2308.06538
We study two non-Markovian gene-expression models in which protein production is a stochastic process with a fat-tailed non-exponential 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 non-exponential 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.