Before revision:  We construct a lattice model based on a Fokker Planck description of the two-state system, and study it using a kinetic Monte Carlo method . We compute transport properties such as the average velocity and the effective diffusivity of the MCC.
After revision:  We construct a lattice model based on a Fokker Planck description of the two-state system, and study it using a kinetic Monte Carlo method and compare our numerical results with analytical expressions for a mean field limit. We find that the effect of confinement strongly depends on the bound velocity and the effective diffusivity of the MCC.