{
  "abstract": "The quest for the origin of life, especially in the metabolism-first scenario inspired by the celebrated Miller-Urey experiment, has triggered a research program dedicated to studying the emergence of complex dynamical behaviors in large chemical mixtures. Though autocatalysis, understood as the capacity of a reaction network to grow exponentially, has been recognized as a potential driver of instability and multistability, no quantitative theory has yet emerged, partly because of the lack of available kinetic data. We introduce a computational tool for large chemical reaction networks based on a scale-splitting algorithm inspired by Wilson's renormalization group. We focus on dilute regimes, where species of interest have low concentration, non-unimolecular reactions may be neglected, and the dynamics is close to linear. Depending on parameter thresholds, such networks can exhibit autocatalytic behavior. Our algorithm takes as input a network structure and outputs (1) a simplified effective graph containing the dominant reaction pathways, obtained through recursive coarse-graining; and (2) analytical formulas for the dynamics in terms of kinetic rates, called hierarchical formulas. These formulas are approximate but interpretable, accurate when scale separation is effective, and provide a reliable multiscale description of the dynamics. Their domains of validity define kinetic phases, each typically associated with a distinct pattern of chemical composition. We show on a simple example that this approach enables fast and reliable inference of kinetic rates from concentration time series. Hierarchical formulas have been implemented as a Python package and are illustrated on a simplified model of the formose reaction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.24246",
  "author_total": 3,
  "authors": [
    {
      "name": "Jeremie Unterberger"
    },
    {
      "name": "Ulysse Herbach"
    },
    {
      "name": "Roxane Cellier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pqvfnvm4dhd8.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "8pqvfnvm4dhd8",
  "issns": [],
  "landing_url": "https://hal.science/hal-05783234v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.chim"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.chim.theo"
    ],
    [
      "hal",
      "1.math.math-st"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05783234/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pqvfnvm4dhd8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:50Z",
      "native_id": "hal-05783234",
      "source": "hal",
      "url": "https://hal.science/hal-05783234v1"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "hal:1.chim.theo",
      "subfield": "theoretical"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-st",
      "subfield": "statistics"
    }
  ],
  "title": "Hierarchical models for large chemical reaction networks",
  "title_text": "Hierarchical models for large chemical reaction networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:50Z",
  "url": "https://research.draconitic.com/paper/8pqvfnvm4dhd8",
  "venue": "HAL",
  "versions": []
}