{
  "abstract": "Kinetic models of protein aggregation describe populations by size, not by spatial organization or morphology. We extend Lumry-Eyring nucleated polymerization to a model in which the monomer is a density field and each aggregate is a region bounded by a level set. Growth is a flux condition on the available sites of a surface. Condensation is a reaction between the bonding sites of two surfaces in contact, at a rate set by the bond rate and the contact geometry. The availability of those sites is a field on the interface, and its equilibrium value follows from Wertheim's perturbation theory. The collision efficiency and the Fuchs stability ratio are therefore computed, not fitted. In a well-mixed limit the model's spatial averages satisfy the rate equations term by term; the monomer fraction agrees to eight parts in ten thousand, a difference that arises from equating aggregate size with volume. The condensation kernel's exponent is $0.5806\\pm0.0013$ against the $0.600\\pm0.010$ fitted to a monoclonal antibody. The computed stability ratio reproduces thirteen of fourteen published conditions at twelve $k_BT$, but only with the bond rate at the top of its range. In a many-body box, aggregates merge at $2.2$ to $3.8$ times the two-body rate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27185",
  "author_total": 1,
  "authors": [
    {
      "name": "Pouria A. Mistani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9hrbzk5yrj4t1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27185",
  "fulltext_url": null,
  "id": "9hrbzk5yrj4t1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27185",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "physics.bio-ph"
    ],
    [
      "arxiv",
      "q-bio.BM"
    ],
    [
      "openalex",
      "1312|Protein purification and stability"
    ]
  ],
  "openalex": "W7214170052",
  "pdf_url": "https://arxiv.org/pdf/2609.27185",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hrbzk5yrj4t1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27185",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27185"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "arxiv:q-bio.BM",
      "subfield": "biophysics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.bio-ph",
      "subfield": "biological-medical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Spatially Resolved Nucleated Polymerization: A Free-Boundary Model of Protein Aggregation in Concentrated Solutions",
  "title_text": "Spatially Resolved Nucleated Polymerization: A Free-Boundary Model of Protein Aggregation in Concentrated Solutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:01Z",
  "url": "https://research.draconitic.com/paper/9hrbzk5yrj4t1",
  "venue": "arXiv",
  "versions": []
}