{
  "abstract": "Tau-amyloid-$β$ cross-seeding creates a spatial paradox. Bioavailable tau can promote A$β$42 nucleation, thereby increasing local fibril number and catalytic-site burden; yet the same fibrils consume the free A$β$ monomer required for homotypic secondary nucleation. The region containing the most tau or fibrillar material therefore need not be the region with the highest secondary-nucleation rate. We test this idea with a reaction-diffusion model that tracks a propagating effective tau catalyst, free A$β$ monomer, elongation-competent fibrils, fibril mass, and the catalytic sites exposed to monomer. The model reduces the spatial competition to two quantities: accessible catalytic sites and free monomer. Their balance yields an exact condition for an interior kinetic maximum: the logarithmic decrease in accessible catalytic sites must equal twice the logarithmic increase in free monomer. Two Damkohler numbers then separate the relevant competitions-elongation versus clearance, and elongation versus diffusive redistribution-while a monomer screening length sets the physical scale over which depletion can persist. Independent transport and turnover estimates place this length near 0.44-0.54 mm. Simulations show that tau first raises secondary nucleation near its source; continued fibril growth then produces a monomer-depleted wake, and the maximum shifts to a region with fewer catalytic sites but more available monomer. Oligomer transport and sustained reversible exchange can weaken or eliminate this contrast, whereas growth-history-dependent site density can strengthen it. The robust prediction is therefore a spatial separation among tau burden, fibril-mass growth, and instantaneous A$β$ secondary-nucleation activity, rather than a universal hotspot speed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33981",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrey V. Kuznetsov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dn73fq9w1dgr7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33981",
  "fulltext_url": null,
  "id": "dn73fq9w1dgr7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33981",
  "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",
      "q-bio.SC"
    ],
    [
      "openalex",
      "2737|Alzheimer's disease research and treatments"
    ]
  ],
  "openalex": "W7223948977",
  "pdf_url": "https://arxiv.org/pdf/2610.33981",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dn73fq9w1dgr7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:44Z",
      "native_id": "2610.33981",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33981"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.SC",
      "subfield": "cell-biology"
    }
  ],
  "title": "Tau creates spatially moving hotspots of amyloid-$β$ secondary nucleation: a reaction-diffusion model",
  "title_text": "Tau creates spatially moving hotspots of amyloid-β secondary nucleation: a reaction-diffusion model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:44Z",
  "url": "https://research.draconitic.com/paper/dn73fq9w1dgr7",
  "venue": "arXiv",
  "versions": []
}