A quantitative paradigm for water-assisted proton transport through proteins and other confined spaces

Significance As first proposed more than 200 y ago by Grotthuss, proton transport is enabled by a chemical bond-breaking and bond-making proton-hopping mechanism through water networks or “wires,” often contained within confined systems such as protein channels or nanotubes. Herein, concepts from graph theory are utilized in order to define a continuously differentiable collective variable for water wire connectivity and facile proton transport. As such, the water connectivity can be explicitly quantified via free-energy sampling to both qualitatively and quantitatively describe the thermodynamics and kinetics of water-facilitated proton transport via Grotthuss hopping—something that has been lacking since the first conceptual identification of this key chemical process in nature. Water-assisted proton transport through confined spaces influences many phenomena in biomolecular and nanomaterial systems. In such cases, the water molecules that fluctuate in the confined pathways provide the environment and the medium for the hydrated excess proton migration via Grotthuss shuttling. However, a definitive collective variable (CV) that accurately couples the hydration and the connectivity of the proton wire with the proton translocation has remained elusive. To address this important challenge—and thus to define a quantitative paradigm for facile proton transport in confined spaces—a CV is derived in this work from graph theory, which is verified to accurately describe water wire formation and breakage coupled to the proton translocation in carbon nanotubes and the Cl−/H+ antiporter protein, ClC-ec1. Significant alterations in the conformations and thermodynamics of water wires are uncovered after introducing an excess proton into them. Large barriers in the proton translocation free-energy profiles are found when water wires are defined to be disconnected according to the new CV, even though the pertinent confined space is still reasonably well hydrated and—by the simple measure of the mere existence of a water structure—the proton transport would have been predicted to be facile via that oversimplified measure. In this paradigm, however, the simple presence of water is not sufficient for inferring proton translocation, since an excess proton itself is able to drive hydration, and additionally, the water molecules themselves must be adequately connected to facilitate any successful proton transport.