(253q) Sparse Sampling of Water Density Fluctuations

Water density fluctuations play an important role in understanding hydrophobic hydration and interactions. The rare low-density water density fluctuations at a solid-water surface have also been shown as a robust measure of surface hydrophobicity. However, characterizing the free energetics of such rare fluctuations requires computationally expensive, non-Boltzmann sampling methods like umbrella sampling, which limits the size of the volume in which the density fluctuations are characterized. Here we present a method that enables the sparse sampling of water density fluctuations, making it roughly 2 orders of magnitude more efficient than umbrella sampling. We circumvent the umbrella sampling requirement of overlap between adjacent biased distributions, by employing thermodynamic integration to estimate the free energy differences between biased ensembles. Leveraging the efficiency of the method, we are able to characterize water density fluctuations in the entire hydration shell of the protein, ubiquitin, a large volume containing an average of more than 600 waters, as well as enormous spherical volumes in bulk water containing up to 30,000 waters on average.