  The motility of certain gram-negative bacteria is mediated by retraction of
type IV pili surface filaments, which are essential for infectivity. The
retraction is powered by a strong molecular motor protein, PilT, producing very
high forces that can exceed 150 pN. The molecular details of the motor
mechanism are still largely unknown, while other features have been identified,
such as the ring-shaped protein structure of the PilT motor. The surprisingly
high forces generated by the PilT system motivate a model investigation of the
generation of large forces in molecular motors. We propose a simple model,
involving a small ensemble of motor subunits interacting through the
deformations on a circular backbone with finite stiffness. The model describes
the motor subunits in terms of diffusing particles in an asymmetric,
time-dependent binding potential (flashing ratchet potential), roughly
corresponding to the ATP hydrolysis cycle. We compute force-velocity relations
in a subset of the parameter space and explore how the maximum force (stall
force) is determined by stiffness, binding strength, ensemble size, and degree
of asymmetry. We identify two qualitatively different regimes of operation
depending on the relation between ensemble size and asymmetry. In the
transition between these two regimes, the stall force depends nonlinearly on
the number of motor subunits. Compared to its constituents without
interactions, we find higher efficiency and qualitatively different
force-velocity relations. The model captures several of the qualitative
features obtained in experiments on pilus retraction forces, such as roughly
constant velocity at low applied forces and insensitivity in the stall force to
changes in the ATP concentration.
