{
  "abstract": "Moment-closure methods provide a widely used approach for approximating low-order statistics of stochastic biochemical reaction networks, but the resulting closed equations may exhibit physically meaningless dynamics. Here, we systematically investigate the stability of second-order moment-closure approximations for a bursty gene expression model with nonlinear protein degradation. We consider the Gaussian, log-normal, and negative-binomial closures. By analyzing the resulting dynamical systems, we show that the Gaussian closure fails the proposed stability criterion for all parameter values, whereas both the log-normal and negative-binomial closures possess a unique physically accessible fixed point and are stable if and only if kB(1 + 2B) [≥] 1, where B is the mean burst size and k is the dimensionless protein synthesis rate. Moreover, this condition is automatically satisfied when the steady-state mean protein copy number is at least one, suggesting that it is mild in biologically relevant regimes. Numerical comparisons over a broad parameter range further show that the negative-binomial closure is the most accurate, while the Gaussian closure is the least accurate. We further develop higher-order negative-binomial moment-closure schemes and demonstrate that increasing the closure order substantially improves predictive accuracy. These results highlight the importance of considering dynamical stability, in addition to numerical accuracy, when assessing moment-closure approximations.",
  "abstract_shown": true,
  "affiliations": [
    "Harbin Institute of Technology"
  ],
  "article_type": "New results",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "M. Zhou"
    },
    {
      "affs": [
        0
      ],
      "name": "C. Jia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2rqa1k15zaftn.bib",
  "cited_by": 0,
  "doi": "10.64898/2026.09.30.755644",
  "fulltext_url": "https://www.biorxiv.org/content/10.64898/2026.09.30.755644v1.full",
  "id": "2rqa1k15zaftn",
  "issns": [],
  "landing_url": "https://www.biorxiv.org/content/10.64898/2026.09.30.755644v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "biorxiv",
      "systems biology"
    ],
    [
      "openalex",
      "1312|Gene Regulatory Network Analysis"
    ]
  ],
  "openalex": "W7215056180",
  "pdf_url": "https://www.biorxiv.org/content/10.64898/2026.09.30.755644v1.full.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2rqa1k15zaftn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:37Z",
      "native_id": "10.64898/2026.09.30.755644",
      "source": "biorxiv",
      "url": "https://www.biorxiv.org/content/10.64898/2026.09.30.755644v1"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "biorxiv:systems biology",
      "subfield": "systems-synthetic"
    }
  ],
  "title": "Dynamical stability and accuracy of moment closure approximations for bursty gene expression with nonlinear degradation",
  "title_text": "Dynamical stability and accuracy of moment closure approximations for bursty gene expression with nonlinear degradation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:37Z",
  "url": "https://research.draconitic.com/paper/2rqa1k15zaftn",
  "venue": "bioRxiv",
  "versions": []
}