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.

通过密闭空间的水辅助质子传输影响生物分子和纳米材料系统中的许多现象。在这种情况下，在受限路径中波动的水分子为水合过量质子通过 Grotthuss 穿梭迁移提供了环境和介质。然而，将质子线的水合作用和连通性与质子易位准确耦合的确定性集体变量 (CV) 仍然难以捉摸。为了应对这一重要挑战——并因此定义在密闭空间中轻松传输质子的定量范式——在这项工作中从图论推导出了一个 CV，该 CV 被证实可以准确描述与碳中质子易位耦合的水线形成和断裂纳米管和 Cl ^- /H ⁺逆向转运蛋白，ClC-ec1。在将过量的质子引入水线后，水线的构象和热力学发生了显着变化。当根据新的 CV 将水线定义为断开连接时，在质子易位自由能剖面中发现了大的障碍，即使相关的密闭空间仍然具有相当良好的水合，并且——通过仅存在水的简单测量结构——通过这种过于简单的测量方法，预计质子传输会很容易。然而，在这个范例中，水的简单存在不足以推断质子易位，因为过量的质子本身能够驱动水合作用，此外，水分子本身必须充分连接以促进任何成功的质子传输。