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

Source: [Fluctuations in first passage times and utility of resetting protocol in biochemical systems with two-state toggling](<https://www.sota2.com/research/paper/68fa4c601e209131ce94c98b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T10:31:27.820Z

Authors: Hillol Kumar Barman, Pathik Das, Syed Yunus Ali

Published: 2025-10-21T05:39:33.000Z

## Abstract

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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2510.18309>)

[PDF](<https://arxiv.org/pdf/2510.18309.pdf>)