Role of protein flexibility in molecular motor function: coupled diffusion in a tilted periodic potential

Biomolecular motors are tiny engines that transport material at the microscopic level within biological cells. It has been proposed that many such motors operate, at least in part, by a Brownian ratchet mechanism. Since biomolecular motors typically transport cargo that are much larger than themselves, one would expect the speed of such a motor to be severely limited by the small diffusion coefficient of its enormous cargo. It has been suggested by Berg and Kahn [Mobility and Recognition in Cell Biology, H. Suns and C. Veeger, eds., de Gruyter, Berlin, 1983, pp. 485-497] and Meister, Caplan, and Berg [Biophys. J., 55 (1989), pp. 905-914] that this limitation can be overcome if the tether that connects the motor to its cargo is sufficiently elastic. This paper evaluates the influence of the elasticity of the tether on the speed of an imperfect Brownian ratchet. This is done in two limiting cases: (1) large diffusion coefficient of the motor and (2) large potential barrier against reverse motion at each ratchet site. In both cases, the speed of the motor is an increasing function of the elasticity of the tether.