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We consider random walks on quasi one dimensional lattices, as introduced in\cite{FS}. This mathematical setting covers a large class of discrete kineticmodels for non-cooperative molecular motors on periodic tracks. We derivegeneral formulas for the asymptotic velocity and diffusion coefficient, and weshow how to reduce their computation to suitable linear systems of the samedegree of a single fundamental cell, with possible linear chain removals. Weapply the above results to special families of kinetic models, also catchingsome errors in the biophysics literature.

Discrete kinetic models for molecular motors: asymptotic velocity and gaussian fluctuations