Free energy profiles for H+ conduction along hydrogen-bonded chains of water molecules

The molecular mechanism for proton conduction along hydrogen-bonded chains, or "proton wires," is studied with free energy simulations. The complete transport of a charge along a proton wire requires two complementary processes: 1) translocation of an excess proton (propagation of an ionic defect), and 2) reorientation of the hydrogen-bonded chain (propagation of a bonding defect). The potential of mean force profile for these two steps is computed in model systems comprising a single-file chain of nine dissociable and polarizable water molecules represented by the PM6 model of Stillinger and co-workers. Results of molecular dynamics simulations with umbrella sampling indicate that the unprotonated chain is preferably polarized, and that the inversion of its total dipole moment involves an activation free energy of 8 kcal/mol. In contrast, the rapid translocation of an excess H+ across a chain extending between two spherical solvent droplets is an activationless process. These results suggest that the propagation of a bonding defect constitutes a limiting step for the passage of several protons along single-file chains of water molecules, whereas the ionic translocation may be fast enough to occur within the lifetime of transient hydrogen-bonded water chains in biological membranes.