  Hydrophobic effects drive diverse aqueous assemblies, such as micelle
formation or protein folding, wherein the solvent plays an important role.
Consequently, characterizing the free energetics of solvent density
fluctuations can lead to important insights into these processes. Although
techniques such as the indirect umbrella sampling (INDUS) method (Patel et al.
J. Stat. Phys. 2011, 145, 265-275) can be used to characterize solvent
fluctuations in static observation volumes of various sizes and shapes,
characterizing how the solvent mediates inherently dynamic processes, such as
self-assembly or conformational change, remains a challenge. In this work, we
generalize the INDUS method to facilitate the enhanced sampling of solvent
fluctuations in dynamical observation volumes, whose positions and shapes can
evolve. We illustrate the usefulness of this generalization by characterizing
water density fluctuations in dynamic volumes pertaining to the hydration of
flexible solutes, the assembly of small hydrophobes, and conformational
transitions in a model peptide. We also use the method to probe the dynamics of
hard spheres.
