Microscopic reversibility and reciprocal relations for Brownian molecular machines

Chemists have made great progress in synthesizing molecules that emulate in part the remarkable properties of biological molecular motors, most especially the ability to use chemical energy to drive directed motion and do mechanical work. Here the mechanism of a molecular motor is treated as a renewal process in which the motor molecule fluctuates away from, and then returns to some arbitrary initial configurational state. During this excursion, some number of fuel molecules will have been catalytically converted to product, and the motor will have undergone some number of mechanical cycles in which work is done on the environment. The dependences of the number of catalytic and mechanical processes per renewal obey reciprocal relations for arbitrarily strong load force and chemical driving force. These relations characterize the behavior of the system far from thermodynamic equilibrium in the same way that the Onsager reciprocal relations characterize the system close to thermodynamic equilibrium.

Triangle reaction scheme for a three-ring catenane and topology for using this molecule as a machine.