Tug of war in motility assay experiments

The dynamics of two groups of molecular motors pulling in opposite directions on a rigid filament is studied theoretically. To this end we first consider the behavior of one set of motors pulling in a single direction against an external force using a new mean-field approach. Based on these results we analyze a similar setup with two sets of motors pulling in opposite directions in a tug of war in the presence of an external force. In both cases we find that the interplay of fluid friction and protein friction leads to a complex phase diagram where the force-velocity relations can exhibit regions of bistability and spontaneous symmetry breaking. Finally, motivated by recent work, we turn to the case of motility assay experiments where motors bound to a surface push on a bundle of filaments. We find that, depending on the absence or the presence of bistability in the force-velocity curve at zero force, the bundle exhibits anomalous or biased diffusion on long-time and large-length scales.