{
  "id": "2406.12493",
  "version": "v1",
  "published": "2024-06-18T10:56:02.000Z",
  "updated": "2024-06-18T10:56:02.000Z",
  "title": "Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves",
  "authors": [
    "Gaetan Barbet",
    "James MacLaurin",
    "Moshe Silverstein"
  ],
  "categories": [
    "math.PR",
    "q-bio.SC"
  ],
  "abstract": "We prove a Large Deviation Principle for Piecewise Deterministic Markov Processes (PDMPs). This is an asymptotic estimate for the probability of a trajectory in the large size limit. Explicit Euler-Lagrange equations are determined for computing optimal first-hitting-time trajectories. The results are applied to a model of stochastic calcium dynamics. It is widely conjectured that the mechanism of calcium puff generation is a multiscale process: with microscopic stochastic fluctuations in the opening and closing of individual channels generating cell-wide waves via the diffusion of calcium and other signaling molecules. We model this system as a PDMP, with $N \\gg 1$ stochastic calcium channels that are coupled via the ambient calcium concentration. We employ the Large Deviations theory to estimate the probability of cell-wide calcium waves being produced through microscopic stochasticity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-18T10:56:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation",
      "stochastic calcium waves",
      "individual channels generating cell-wide waves",
      "piecewise-deterministic-markov-processes",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}