Brownian motors in a ring and type IV pilus retraction

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 exceed 100 pN (Maier, B., Potter, L., So, M., Seifert, H. S. and Sheetz, M. P., PNAS 99:16012 (2002)). In this paper we formulate a theoretical model for the retraction motor, whose features are suggested by recent experiments. We consider a molecular motor model that consists of several motor units coupled together in a ring-shaped geometry, supported by crystallographic data. The model describes the motor units in terms of elastically coupled particles in a time dependent motor-filament binding potential (flashing ratchet potential), corresponding to the ATP hydrolysis cycle. Compared with a single particle flashing ratchet model, we find higher efficiency and qualitatively different forcevelocity relationships. The model captures several of the qualitative features obtained in recent experiments on pilus retraction forces, such as a plateau in velocity at low loads and insensitivity in the stall force to changes in ATP concentration.