{
  "abstract": "Reaction–diffusion (RD) systems play a fundamental role in numerous biochemical and biophysical processes. Here, we present a novel analytical framework for solving RD equations by applying the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) formalism to Ca 2+ buffering. Previous models have primarily focused on stationary Ca 2+ nanodomains while neglecting diffusion and saturation of intracellular Ca 2+ buffers and sensors. We derive analytical solutions using WKBJ ansatz and demonstrate that sustained Ca 2+ source produces continuously expanding distributions of free Ca 2+ , whereas the concentration of Ca 2+ -bound buffers develops at much slower timescale. These predictions are supported experimentally by measurements of one-dimensional fluorescence profiles produced by single-channel activity and two-dimensional profiles generated by whole-cell Ca 2+ currents. The analytical framework developed here extends Michaelis–Menten-type kinetics to reaction–diffusion systems and may therefore be broadly applicable to biochemical and biophysical processes in which diffusion cannot be neglected.",
  "abstract_shown": true,
  "affiliations": [
    "Georg-August-University"
  ],
  "article_type": "New results",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "S. Mironov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zghq1xrgmch2.bib",
  "cited_by": 0,
  "doi": "10.64898/2026.07.06.735233",
  "fulltext_url": "https://www.biorxiv.org/content/10.64898/2026.07.06.735233v2.full",
  "id": "7zghq1xrgmch2",
  "issns": [],
  "landing_url": "https://www.biorxiv.org/content/10.64898/2026.07.06.735233v2",
  "language": null,
  "licence": "PDM-1.0",
  "licence_label": "Public domain",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/publicdomain/mark/1.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "biorxiv",
      "biophysics"
    ],
    [
      "openalex",
      "1312|Ion channel regulation and function"
    ]
  ],
  "openalex": "W7167912259",
  "pdf_url": "https://www.biorxiv.org/content/10.64898/2026.07.06.735233v2.full.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zghq1xrgmch2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:52Z",
      "native_id": "10.64898/2026.07.06.735233",
      "source": "biorxiv",
      "url": "https://www.biorxiv.org/content/10.64898/2026.07.06.735233v2"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "biorxiv:biophysics",
      "subfield": "biophysics"
    }
  ],
  "title": "Fast Diffusion of Bound Ca: Analytical and Experimental Characterization of One- and Two-Dimensional Traveling Waves",
  "title_text": "Fast Diffusion of Bound Ca: Analytical and Experimental Characterization of One- and Two-Dimensional Traveling Waves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:52Z",
  "url": "https://research.draconitic.com/paper/7zghq1xrgmch2",
  "venue": "bioRxiv",
  "versions": [
    {
      "doi": "10.3389/fncel.2026.1925214",
      "pid": "5bmh5h2pejxd5",
      "relation": "published-as",
      "title": "Long-range diffusion of bound Ca²⁺: time-dependent WKBJ solutions in one- and two-dimensional imaging.",
      "venue": "Frontiers in cellular neuroscience"
    }
  ]
}