{
  "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 $\\mathcal{N}$; 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 $\\mathcal{N} \\to \\infty$, 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Physical Review E 114, 045404 (2026)",
  "arxiv": "2610.29270",
  "author_total": 3,
  "authors": [
    {
      "name": "Manvendra Singh"
    },
    {
      "name": "Ashok Garai"
    },
    {
      "name": "Debashish Chowdhury"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9epbb3bnygydd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29270",
  "fulltext_url": null,
  "id": "9epbb3bnygydd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29270",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "physics.bio-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.29270",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9epbb3bnygydd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.29270",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29270"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.bio-ph",
      "subfield": "biological-medical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Stochastic model of elongation-shortening-switching kinetics of a polymeric filament: Critical slowing down of first-passage and finite-size regularization",
  "title_text": "Stochastic model of elongation-shortening-switching kinetics of a polymeric filament: Critical slowing down of first-passage and finite-size regularization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:19Z",
  "url": "https://research.draconitic.com/paper/9epbb3bnygydd",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/gr8t-t7gr",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}