Overdamped thermal ratchets in one and more dimensions. Kinesin transport and protein folding

The overdamped thermal ratchet driven by an external (Orstein–Uhlenbeck) noise is revisited. The ratchet we consider is unbounded in space and not necessarily periodic. We briefly discuss the conditions under which current is obtained by analyzing the corresponding Fokker–Planck equation and its lack of stationary states. Next, two examples in more than one dimension and related to biological systems are presented. First, a two-dimensional model of a “kinesin protein” on a “microtubule” is analyzed and, second, we suggest that a ratchet mechanism may be behind the folding of proteins; the latter is elaborated with a multidimensional ratchet model.