Hybrid models of molecular machines and the no-pumping theorem

TL;DR

This paper extends the theoretical modeling of molecular machines to include diffusive transition processes and confirms that the no-pumping theorem still applies in this more realistic setting.

Contribution

It introduces a detailed class of models with finite-time, diffusive transitions and demonstrates the no-pumping theorem's validity within this framework.

Findings

No-pumping theorem holds for diffusive transition models.

Finite-time, diffusive models are more realistic for molecular machines.

Directed motion cannot be generated by periodic external parameter variation in these models.

Abstract

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.