Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911924122288128 |
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| author | Barbet, Gaetan MacLaurin, James Silverstein, Moshe |
| author_facet | Barbet, Gaetan MacLaurin, James Silverstein, Moshe |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_12493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves Barbet, Gaetan MacLaurin, James Silverstein, Moshe Probability Subcellular Processes 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. |
| title | Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves |
| topic | Probability Subcellular Processes |
| url | https://arxiv.org/abs/2406.12493 |