Asymmetric potentials and motor effect: a large deviation approach

TL;DR

This paper analyzes how asymmetric potentials influence the concentration phenomena in a Fokker-Planck system modeling motor proteins, using a large deviation approach and Hamilton-Jacobi equations.

Contribution

It introduces a mathematical framework for understanding protein conformations in motor systems via large deviation principles and Hamilton-Jacobi equations.

Findings

Concentrations of solutions form Dirac masses under certain conditions.

Different classes of conformation transition coefficients are considered.

The analysis provides insights into the zero diffusion limit behavior.

Abstract

We provide a mathematical analysis of appearance of the concentrations (as Dirac masses) of the solution to a Fokker-Planck system with asymmetric potentials. This problem has been proposed as a model to describe motor proteins moving along molecular filaments. The components of the system describe the densities of the different conformations of the proteins. Our results are based on the study of a Hamilton-Jacobi equation arising, at the zero diffusion limit, after an exponential transformation change of the phase function that rises a Hamilton-Jacobi equation. We consider different classes of conformation transitions coefficients (bounded, unbounded and locally vanishing).