Protein flexibility and the correlation ratchet

Biomolecular motors are tiny engines that transport material at the microscopic level within biological cells. 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. Sund and C. Veeger, eds., De Gruyter, Berlin, 1983] 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. In a recent article the effects of the elastic properties of the tether on the speed of the motor were investigated when the driving mechanism was a Brownian ratchet [SIAM J. Appl. Math., 60 (2000), pp. 842-867]. Here we extend that work to include the correlation ratchet [C. Peskin, G. Ermentrout, and G. Oster, in Mechanics and Cellular Engineering, V. Mow et al., eds., Springer, New York, 1994; Phys. Rev. Lett., 72 (1994), pp. 2652-2655; Phys. Rev. Lett., 72 (1994), pp. 1766-1769]. In contrast to the Brownian ratchet, it is shown that in the limit of a large motor diffusion coefficient the average velocity increases monotonically as the stiffness of the tether is increased. However, Monte-Carlo simulations reveal that for any finite diffusion coefficient of the motor there is an optimal stiffness at which the motor travels fastest.