Barman, H. K. | Search bioRxiv

bioRxiv2026

Distributions of threshold crossing times of messenger RNA

Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid (mRNA) and present an exact probability distribution of first passage times in Laplace space. The function furnishes moments of any order and also predicts the characteristic time of the exponential tail of the distribution, which we match against Gillespie simulations. We find that all the measures of relative fluctuations of the threshold crossing times show U-shapes within this simple model of mRNA, as was found earlier in more mathematically involved models of threshold crossing time statistics of proteins. Furthermore, we extend the exact formula to include the phenomenon of DNA duplication and the corresponding doubling of transcription rate. As expected, the distribution varies considerably depending on the onset of the duplication stage within the cell cycle.

biophysics↗

bioRxiv2025

Fluctuations in first passage times and utility of resetting protocol in biochemical systems with two-state toggling

Interesting theoretical problems of target search or threshold crossing, formally known as first passage, often arise in both diffusive transport problems as well as problems of chemical reaction kinetics. We study three systems following different chemical kinetics, and are special as they toggle between two states: (i) a population dynamics of cells with auto-catalytic birth and intermittent toxic chemical-induced forced death, (ii) a bond cluster model representing membrane adhesion to extracellular matrix under a fluctuating load, and (iii) a model of gene transcription with a regulated promoter switching between active and inactive states. Each of these systems has a target state to attain, which defines a first passage problem - namely, population becoming extinct, complete membrane detachment, or mRNA count crossing a threshold. We study the fluctuations in first passage time and show that it is interestingly non-monotonic in all these cases, with increasing strength of bias towards the target. We also study suitable stochastic resetting protocols to expedite first passage for these systems, and show that there is a re-entrant transition of the efficacy of this protocol in all the three cases, as a function of the bias. The exact analytical condition for these transitions predicted in earlier literature is verified here through simulations.

biophysics↗