Journal of Statistical Physics, Vol. 110, Nos. 3–6, March 2003, p. 1141-1167.
Molecular motor cycles are studied in the framework of stochastic ratchets in which the motor moves along a 1-dimensional track, can attain M internal states, and can undergo transitions between these levels at K spatial positions. These ratchets can be mapped onto a stochastic network of KM discrete states. The network is governed by a Master equation, fulfills a vertex rule, and satisfies detailed balance in the absence of enzymatic activity and external force. Any pathway of the motor cycle which leads to a forward or backward step of the motor corresponds to a certain sequence of transitions spanning this network. The dependence of the motor velocity on the transition rates can be determined for arbitrary values of K and M and exhibits some simple and universal features.