Averaging and large deviation principles for fully-coupled piecewise deterministic Markov processes and applications to molecular motors

TL;DR

This paper analyzes fully-coupled piecewise deterministic Markov processes with applications to molecular motors, establishing laws of large numbers, large deviation principles, and convergence results for different jump regimes, relevant for understanding mechanochemical cycles.

Contribution

It introduces a comprehensive analysis of fully-coupled PDMPs with both fast and slow jumps, including new convergence and large deviation results, applied to molecular motor models.

Findings

Proved law of large numbers for PDMPs with fast jumps.

Established large deviation principles for PDMPs.

Demonstrated convergence to effective PDMPs in mixed jump regimes.

Abstract

We consider Piecewise Deterministic Markov Processes (PDMPs) with a finite set of discrete states. In the regime of fast jumps between discrete states, we prove a law of large number and a large deviation principle. In the regime of fast and slow jumps, we analyze a coarse-grained process associated to the original one and prove its convergence to a new PDMP with effective force fields and jump rates. In all the above cases, the continuous variables evolve slowly according to ODEs. Finally, we discuss some applications related to the mechanochemical cycle of macromolecules, including strained--dependent power--stroke molecular motors. Our analysis covers the case of fully--coupled slow and fast motions.