  We consider the context of molecular motors modelled by a diffusion process
driven by the gradient of a weakly periodic potential that depends on an
internal degree of freedom. The switch of the internal state, that can freely
be interpreted as a molecular switch, is modelled as a Markov jump process that
depends on the location of the motor. Rescaling space and time, the limit of
the trajectory of the diffusion process homogenizes over the periodic potential
as well as over the internal degree of freedom. Around the homogenized limit,
we prove the large deviation principle of trajectories with a method developed
by Feng and Kurtz based on the analysis of an associated
Hamilton--Jacobi--Bellman equation with an Hamiltonian that here, as an
innovative fact, depends on both position and momenta.
