Work

Large deviations of piecewise-deterministic Markov processes with application to stochastic calcium waves

Year: 2026

Type: article

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 $$N\gg 1$$ N ≫ 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.

Source: Journal of Mathematical Biology

DOI: 10.1007/s00285-026-02446-7

Authors: Gaetan Barbet, James MacLaurin, Moshe Silverstein, Pedro Vilanova

Institutions: Rutgers, The State University of New Jersey, New Jersey Institute of Technology, Stevens Institute of Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: National Science Foundation