The dynamics of molecular motors moving on a heterogeneous track, like DNA or RNA will be discussed. Motivated by recent single molecule experiments, a setup in which the molecular motor is using chemical energy to move along the substrate while an external force opposes its motion will be considered.

First, the case of infinite processivity, in which the motor is assumed to remain bound to the track, will be considered. It will be shown that near the stall force the heterogeneous track causes the dynamics of the motor to be anomalous. Second, the effect of finite processivity, where motor occasionally detach from the track will be considered. It will be shown that motors which remain on the track for long times can become localized at preferred positions along the track. The conditions for localization will be discussed.

Institut Curie