Dynamic Instabilities in Assemblies of Molecular Motors with Finite Stiffness

We propose a two-state "soft-motor" model for the collective behavior of molecular motors which takes into account both the internal motor stiffness and the periodic interaction with the filament. As in the Prandtl-Tomlinson model of tribology, the important parameter of the model is the pinning parameter, which compares the stiffness of the motors to the stiffness of the potential. The model predicts dynamic instabilities in two disconnected regions of parameter space. These parameter ranges correspond to two existing theories of motor assemblies, the rigid two-state model and the crossbridge model. The model also predicts a discontinuity of the slope of the force-velocity relation at small velocities.