Hybrid models of molecular machines and the no-pumping theorem

Synthetic nanoscale complexes capable of mechanical movement are often studied theoretically using discrete-state models that involve instantaneous transitions between metastable states. A number of general results have been derived within this framework, including a "no-pumping theorem" that restricts the possibility of generating directed motion by the periodic variation of external parameters. Motivated by recent experiments using time-resolved vibrational spectroscopy [Panman et al., Science 328, 1255 (2010)], we introduce a more detailed and realistic class of models in which transitions between metastable states occur by finite-time, diffusive processes rather than sudden jumps. We show that the no-pumping theorem remains valid within this framework.