{
  "abstract": "Planar cell polarity is preceded by the clustering of polarity proteins into discrete, low-turnover membrane subdomains (puncta), yet the minimal interactions that nucleate puncta, set their number, and segregate opposite orientations remain unclear. We address these questions with a mass-conserving reaction-diffusion model in which two diffusible monomers bind reversibly across a cell-cell junction into trans-complexes of two orientations, with feedback entering only through concentration-dependent rates. Above a critical density, the uniform state undergoes a long-wavelength mass-redistribution instability rather than a finite-wavelength Turing bifurcation. The form of the feedback then selects between two morphologies: broad mesas fixed by a Maxwell construction under saturating feedback, and narrow mass-limited spikes under unbounded feedback. For spikes we obtain closed-form expressions exhibiting a clean separation of amplitude (mass and feedback), width (the complex diffusion length), and spacing (the monomer screening length). Within a fast-monomer reduction we prove, for any number and arrangement of puncta, that like-oriented arrays coarsen, so multiplicity is metastable and kinetically determined. The second monomer reservoir introduces a second screening length that rate-limits competition by the harmonic mean of the monomer diffusivities, and the spectrum of a punctum remains free of oscillatory (\"blinking\") instabilities throughout. Finally, sign-definite cross-modulation of turnover converts clustering into orientation sorting - the mutual exclusion of orientations along a single contact: mass redistribution sets puncta number, and the sign of the cross-coupling determines whether orientations segregate. Puncta number and orientation sorting are thus governed by mathematically separable ingredients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29679",
  "author_total": 4,
  "authors": [
    {
      "name": "Sk Raj Hossein"
    },
    {
      "name": "Eman Alwani"
    },
    {
      "name": "Andreas Buttenschön"
    },
    {
      "name": "Alexander G. Fletcher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/db8e24qfvbajp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29679",
  "fulltext_url": null,
  "id": "db8e24qfvbajp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29679",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "q-bio.SC"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7204904112",
  "pdf_url": "https://arxiv.org/pdf/2608.29679",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/db8e24qfvbajp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29679",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29679"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.SC",
      "subfield": "cell-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Clustering versus sorting: a mass-conserving reaction-diffusion model of planar polarity puncta",
  "title_text": "Clustering versus sorting: a mass-conserving reaction-diffusion model of planar polarity puncta",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:49Z",
  "url": "https://research.draconitic.com/paper/db8e24qfvbajp",
  "venue": "arXiv",
  "versions": []
}