As first proposed more than 200 years ago by Grotthuss, the transport of protons is activated by a mechanism of breaking and creation of chemical bonds by jumps of protons via networks of water or “wires”, often contained in confined systems such as protein channels or nanotubes. Here, concepts from graph theory are used in order to define a continuously differentiable collective variable for the connectivity of water wires and the easy transport of protons. As such, water connectivity can be explicitly quantified via free energy sampling to describe both qualitatively and quantitatively the thermodynamics and kinetics of water-facilitated proton transport via the Grotthuss jump – 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 which fluctuate in the confined pathways provide the environment and medium for the migration of excess hydrated protons via the Grotthuss shuttle. However, a definitive collective variable (CV) that precisely couples the hydration and connectivity of the proton wire with the proton translocation has remained elusive. To address this important challenge – and thus define a quantitative paradigm for the easy transport of protons in confined spaces – a CV is derived in this work from graph theory, which is verified to accurately describe the formation and breaking of wires. of water coupled with the translocation of protons into carbon. nanotubes and Cl–/ H+ anti-carrier protein, ClC-ec1. Significant alterations in the conformations and thermodynamics of water strands are discovered after having introduced an excess of proton. Large barriers in the proton translocation free energy profiles are found when the water wires are defined as being disconnected according to the new CV, even though the relevant confined space is still reasonably well hydrated and – by simple measurement from the mere existence of a structure – the transport of protons would have been predicted to be easy via this simplistic measurement. In this paradigm, however, the mere presence of water is not sufficient to infer the translocation of protons, since an excess of the proton itself is able to conduct hydration, and furthermore, the water molecules themselves. they must be properly connected to facilitate any successful proton transport.