Asymmetric potentials and motor effect: a large deviation approach

Benoît Perthame (1) , Panagiotis E. Souganidis (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 Department of Mathematics and Statistics [Texas Tech]

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).

Mots clés: Hamilton-Jacobi equations; molecular motors; Fokker-Planck equations

Domaines: Equations aux dérivées partielles [math.AP]

Benoît Perthame, Panagiotis E. Souganidis. Asymmetric potentials and motor effect: a large deviation approach. 2007. ⟨hal-00147705⟩