Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves
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 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.
Cite
@article{arxiv.2406.12493,
title = {Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves},
author = {Gaetan Barbet and James MacLaurin and Moshe Silverstein},
journal= {arXiv preprint arXiv:2406.12493},
year = {2024}
}