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Main Authors: Barman, Hillol Kumar, Das, Pathik, Ali, Syed Yunus
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2510.18309
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author Barman, Hillol Kumar
Das, Pathik
Ali, Syed Yunus
author_facet Barman, Hillol Kumar
Das, Pathik
Ali, Syed Yunus
contents Interesting theoretical problems of target search or threshold crossing, formally known as {\it 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 {\it 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 {\it non-monotonic} in all these cases, with increasing strength of bias towards the target. We also study suitable {\it 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_18309
institution arXiv
publishDate 2025
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spellingShingle Fluctuations in first passage times and utility of resetting protocol in biochemical systems with two-state toggling
Barman, Hillol Kumar
Das, Pathik
Ali, Syed Yunus
Statistical Mechanics
Interesting theoretical problems of target search or threshold crossing, formally known as {\it 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 {\it 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 {\it non-monotonic} in all these cases, with increasing strength of bias towards the target. We also study suitable {\it 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.
title Fluctuations in first passage times and utility of resetting protocol in biochemical systems with two-state toggling
topic Statistical Mechanics
url https://arxiv.org/abs/2510.18309