Necessity of capillary modes in a minimal model of nanoscale hydrophobic solvation

Abstract

Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing the importance of interfaces in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of such nanoscale interfaces requires careful attention to the statistics of capillary waves, with significant quantitative implications for the calculation of solvation thermodynamics. Here, we show that a coarse-grained lattice model like that of Chandler [Chandler D (2005) Nature 437(7059):640-647], when informed by this understanding, can capture a broad range of hydrophobic behaviors with striking accuracy. Specifically, we calculate probability distributions for microscopic density fluctuations that agree very well with results of atomistic simulations, even many SDs from the mean and even for probe volumes in highly heterogeneous environments. This accuracy is achieved without adjustment of free parameters, because the model is fully specified by well-known properties of liquid water. As examples of its utility, we compute the free-energy profile for a solute crossing the air-water interface, as well as the thermodynamic cost of evacuating the space between extended nanoscale surfaces. These calculations suggest that a highly reduced model for aqueous solvation can enable efficient multiscale modeling of spatial organization driven by hydrophobic and interfacial forces.hydrophobic effect | self-assembly | coarse-grained model | lattice models H ydrophobic forces play a crucial role in biological self-assembly, protein folding, ion channel gating, and lipid membrane dynamics (1-9). The origin and strength of these forces are well understood at extreme length scales, based on the recognition that accommodating an ideal volume-excluding hydrophobe in water carries the same thermodynamic cost as evacuating solvent from the corresponding volume. On the scale of a small molecule like methane, density fluctuations that enable such evacuation are Gaussian-distributed to a very good approximation, even far from the mean (10). Linear response theories, such as Pratt-Chandler theory, can thus be quite accurate for assessing solvation of individual small hydrophobic species.Solvation at much larger scales is, by contrast, dominated by water's proximity to liquid-vapor coexistence. Hydrophobic forces involving extended substrates are shaped by the physics of interfaces and are quantified by macroscopic parameters like surface tension. In between these extremes, a rich variety of hydrophobic effects results from the combined importance of nearby phase coexistence and details of intermolecular structure. Capturing this interplay, for instance, near a biological macromolecule, presents a significant challenge for theory.Lum-Chandler-Weeks (LCW) theory represents the modern understanding of hydrophobic solvation, providing a conceptual and mathematical framework to couple interfacial forces with the short-wavelength density fluctuations that determine solvation of small molecules (10, 11). The theory's physical pers...

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