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The dynamics of molecular motors which occasionally detach from aheterogeneous track like DNA or RNA is considered. Motivated by recent singlemolecule experiments, we study a simple model for a motor moving along adisordered track using chemical energy while an external force opposes itsmotion. The motors also have finite processivity, i.e., they can leave thetrack with a position dependent rate. We show that the response of the systemto disorder in the hopping off rate depends on the value of the external force.For most values of the external force, strong disorder causes the motors whichsurvive for long times on the track to be localized at preferred positions.However, near the stall force, localization occurs for any amount of disorder.Existence of localized states near the top of the band implies a stretchedexponential contribution to the decay of the survival probability. To obtainthese results, we study the complex eigenvalue spectrum of the time evolutionoperator. A similar spectral analysis also provides a very efficient method forstudying the dynamics of motors with infinite processivity.Comment: 19 Pages, 21 Figure

Dynamics of molecular motors with finite processivity on heterogeneous tracks