  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).
