Molecular motors and nonuniform ratchets

Dimeric kinesin presumably moves in a "hand-over-hand" fashion via alternating steps of its two heads, which can cooperate in various ways. This motion is discussed in the framework of nonuniform ratchet models in which the molecular motor is described by M internal states and undergoes transitions at K spatial locations within the period of the molecular force potentials. Two subclasses of models with (M, K)=(3, 2) and (M, K)=(2, 2) are studied which correspond to weakly and strongly cooperative heads, respectively. Both subclasses lead to the same universal relationship between the motor velocity and the unbinding rate constant of the motor heads which is reminiscent of, but distinct from, Michaelis-Menten kinetics.