Eur. Phys. J. B 75, 381-387 (2010)
https://doi.org/10.1140/epjb/e2010-00138-x

Nanoscale swimmers: hydrodynamic interactions and propulsion of molecular machines

¹ Department of Physics, Kyushu University 33, 812-8581 Fukuoka, Japan
² PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama, 332-0012, Japan
³ Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, M5S 3H6, Canada
⁴ Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany

Corresponding author: ^a sakaue@phys.kyushu-u.ac.jp

Received: 25 June 2009
Revised: 19 November 2009
Published online: 6 May 2010

Abstract

Molecular machines execute nearly regular cyclic conformational changes as a result of ligand binding and product release. This cyclic conformational dynamics is generally non-reciprocal so that under time reversal a different sequence of machine conformations is visited. Since such changes occur in a solvent, coupling to solvent hydrodynamic modes will generally result in self-propulsion of the molecular machine. These effects are investigated for a class of coarse grained models of protein machines consisting of a set of beads interacting through pair-wise additive potentials. Hydrodynamic effects are incorporated through a configuration-dependent mobility tensor, and expressions for the propulsion linear and angular velocities, as well as the stall force, are obtained. In the limit where conformational changes are small so that linear response theory is applicable, it is shown that propulsion is exponentially small; thus, propulsion is nonlinear phenomenon. The results are illustrated by computations on a simple model molecular machine.