Stochastic model of elongation-shortening-switching kinetics of a polymeric filament: Critical slowing down of first-passage and finite-size regularization
Abstract
Several filamentous biopolymers exhibit unusual polymerization-depolymerization kinetics where continued elongation (shortening) is possible only in an `active' (`inactive') state while occasional random transition (switching) between the active and inactive states takes place. Here, we present a minimal stochastic model capturing only the key features of random elongation-shortening-switching kinetics of a generic filament. The structure and/or function of the filament ends when its length hits a critical value during its shortening; the time to reach this critical length can be formulated as a first-passage time (FPT) and for its calculation the critical length is treated as an absorbing boundary. Moreover, the lengths of the filaments that inspire our model are constrained to a finite maximum value 𝒩; therefore, in our model we impose a reflecting boundary beyond which the filament cannot grow. We determined the distribution of the FPT and derived its first two moments. We identify a critical point where the drift of the tip of the filament vanishes making its movement purely diffusive; at this critical point, in the limit 𝒩 → ∞, the fluctuations in the FPT diverges and MFPT becomes infinite indicating `critical slowing down'. Our analytical results will serve as the testing ground for the accuracy of the approximate theoretical results of more realistic models for polymerization-depolymerization kinetics of specific bio-filaments.
Versions
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BibTeX
@misc{singh2026stochastic,
title = {{Stochastic model of elongation-shortening-switching kinetics of a polymeric filament: Critical slowing down of first-passage and finite-size regularization}},
author = {Manvendra Singh and Ashok Garai and Debashish Chowdhury},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29270},
eprint = {2610.29270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29270},
}
RIS
TY - UNPB
TI - Stochastic model of elongation-shortening-switching kinetics of a polymeric filament: Critical slowing down of first-passage and finite-size regularization
AU - Manvendra Singh
AU - Ashok Garai
AU - Debashish Chowdhury
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29270
UR - https://arxiv.org/abs/2610.29270
AB - Several filamentous biopolymers exhibit unusual polymerization-depolymerization kinetics where continued elongation (shortening) is possible only in an `active' (`inactive') state while occasional random transition (switching) between the active and inactive states takes place. Here, we present a minimal stochastic model capturing only the key features of random elongation-shortening-switching kinetics of a generic filament. The structure and/or function of the filament ends when its length hits a critical value during its shortening; the time to reach this critical length can be formulated as a first-passage time (FPT) and for its calculation the critical length is treated as an absorbing boundary. Moreover, the lengths of the filaments that inspire our model are constrained to a finite maximum value 𝒩; therefore, in our model we impose a reflecting boundary beyond which the filament cannot grow. We determined the distribution of the FPT and derived its first two moments. We identify a critical point where the drift of the tip of the filament vanishes making its movement purely diffusive; at this critical point, in the limit 𝒩 → ∞, the fluctuations in the FPT diverges and MFPT becomes infinite indicating `critical slowing down'. Our analytical results will serve as the testing ground for the accuracy of the approximate theoretical results of more realistic models for polymerization-depolymerization kinetics of specific bio-filaments.
ER -