{
  "abstract": "Introduction\n\nReaction-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 Ca²⁺ buffering. Previous models have primarily focused on stationary Ca²⁺ nanodomains while neglecting diffusion and saturation of intracellular Ca²⁺ buffers and sensors.Results\n\nWe derive analytical solutions using WKBJ ansatz and demonstrate that sustained Ca²⁺ source produces continuously expanding distributions of free Ca²⁺, whereas the concentration of Ca²⁺-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 Ca²⁺ currents.Discussion\n\nThe 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": [
    "Institute of Neuro- and Sensory Physiology, Georg-August-University, Göttingen, Germany."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Sergej L Mironov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5bmh5h2pejxd5.bib",
  "cited_by": 0,
  "doi": "10.3389/fncel.2026.1925214",
  "fulltext_url": "https://europepmc.org/articles/PMC13679644",
  "id": "5bmh5h2pejxd5",
  "issns": [
    "1662-5102"
  ],
  "landing_url": "https://europepmc.org/article/MED/42898928",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1312|Ion channel regulation and function"
    ]
  ],
  "openalex": "W7220357101",
  "pdf_url": "https://europepmc.org/articles/PMC13679644?pdf=render",
  "pmcid": "PMC13679644",
  "pmid": "42898928",
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5bmh5h2pejxd5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:37Z",
      "native_id": "MED:42898928",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42898928"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "openalex:1312|Ion channel regulation and function",
      "subfield": "molecular-biology"
    }
  ],
  "title": "Long-range diffusion of bound Ca²⁺: time-dependent WKBJ solutions in one- and two-dimensional imaging.",
  "title_text": "Long-range diffusion of bound Ca²⁺: time-dependent WKBJ solutions in one- and two-dimensional imaging.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:19:37Z",
  "url": "https://research.draconitic.com/paper/5bmh5h2pejxd5",
  "venue": "Frontiers in cellular neuroscience",
  "versions": [
    {
      "doi": "10.64898/2026.07.06.735233",
      "pid": "7zghq1xrgmch2",
      "relation": "preprint",
      "title": "Fast Diffusion of Bound Ca: Analytical and Experimental Characterization of One- and Two-Dimensional Traveling Waves",
      "venue": "bioRxiv"
    }
  ]
}