Phase Behavior of Correlated Random Copolymers.

In this work, we calculate Flory-Huggins phase diagrams for correlated random copolymers. We achieve it in two steps. At first, we derive a distribution function of two-letter A, B copolymer chains depending on the fraction of A-segments and AB-duplets. Then, we use the method of moments, which was developed by Sollich and Cates [Phys. Rev. Lett.80, 1998, 1365-1368] for polydisperse systems, to reduce the number of degrees of freedom of the computational problem and calculate phase diagrams. We explore how the location of transition points and composition of coexisting phases depends on the fractions of A-segments and AB-duplets in a sequence and the degree of polymerization. The proposed approach allows taking into account fractionation, which was shown to affect the appearance of the phase diagrams of statistical copolymers.

Identifying hydrophobic protein patches to inform protein interaction interfaces.

Interactions between proteins lie at the heart of numerous biological processes and are essential for the proper functioning of the cell. Although the importance of hydrophobic residues in driving protein interactions is universally accepted, a characterization of protein hydrophobicity, which informs its interactions, has remained elusive. The challenge lies in capturing the collective response of the protein hydration waters to the nanoscale chemical and topographical protein patterns, which determine protein hydrophobicity. To address this challenge, here, we employ specialized molecular simulations wherein water molecules are systematically displaced from the protein hydration shell; by identifying protein regions that relinquish their waters more readily than others, we are then able to uncover the most hydrophobic protein patches. Surprisingly, such patches contain a large fraction of polar/charged atoms and have chemical compositions that are similar to the more hydrophilic protein patches. Importantly, we also find a striking correspondence between the most hydrophobic protein patches and regions that mediate protein interactions. Our work thus establishes a computational framework for characterizing the emergent hydrophobicity of amphiphilic solutes, such as proteins, which display nanoscale heterogeneity, and for uncovering their interaction interfaces.

Protein Hydration Waters Are Susceptible to Unfavorable Perturbations.

The interactions of a protein, its phase behavior, and, ultimately, its ability to function are all influenced by the interactions between the protein and its hydration waters. Here, we study proteins with a variety of sizes, shapes, chemistries, and biological functions and characterize their interactions with their hydration waters using molecular simulations and enhanced sampling techniques. We find that, akin to extended hydrophobic surfaces, proteins situate their hydration waters at the edge of a dewetting transition, making them susceptible to unfavorable perturbations. We also find that the strength of the unfavorable potential needed to trigger dewetting is roughly the same for all proteins studied here and depends primarily on the width of the hydration shell being perturbed. Our findings establish a framework for systematically classifying protein patches according to how favorably they interact with water.

Protein Hydration Thermodynamics: The Influence of Flexibility and Salt on Hydrophobin II Hydration.

The solubility of proteins and other macromolecular solutes plays an important role in numerous biological, chemical, and medicinal processes. An important determinant of protein solubility is the solvation free energy of the protein, which quantifies the overall strength of the interactions between the protein and the aqueous solution that surrounds it. Here we present an all-atom explicit-solvent computational framework for the rapid estimation of protein solvation free energies. Using this framework, we estimate the hydration free energy of hydrophobin II, an amphiphilic fungal protein, in a computationally efficient manner. We further explore how the protein hydration free energy is influenced by enhancing flexibility and by the addition of sodium chloride, and find that it increases in both cases, making protein hydration less favorable.

Hydrophobicity of proteins and nanostructured solutes is governed by topographical and chemical context.

Hydrophobic interactions drive many important biomolecular self-assembly phenomena. However, characterizing hydrophobicity at the nanoscale has remained a challenge due to its nontrivial dependence on the chemistry and topography of biomolecular surfaces. Here we use molecular simulations coupled with enhanced sampling methods to systematically displace water molecules from the hydration shells of nanostructured solutes and calculate the free energetics of interfacial water density fluctuations, which quantify the extent of solute-water adhesion, and therefore solute hydrophobicity. In particular, we characterize the hydrophobicity of curved graphene sheets, self-assembled monolayers (SAMs) with chemical patterns, and mutants of the protein hydrophobin-II. We find that water density fluctuations are enhanced near concave nonpolar surfaces compared with those near flat or convex ones, suggesting that concave surfaces are more hydrophobic. We also find that patterned SAMs and protein mutants, having the same number of nonpolar and polar sites but different geometrical arrangements, can display significantly different strengths of adhesion with water. Specifically, hydroxyl groups reduce the hydrophobicity of methyl-terminated SAMs most effectively not when they are clustered together but when they are separated by one methyl group. Hydrophobin-II mutants show that a charged amino acid reduces the hydrophobicity of a large nonpolar patch when placed at its center, rather than at its edge. Our results highlight the power of water density fluctuations-based measures to characterize the hydrophobicity of nanoscale surfaces and caution against the use of additive approximations, such as the commonly used surface area models or hydropathy scales for characterizing biomolecular hydrophobicity and the associated driving forces of assembly.

Spontaneous recovery of superhydrophobicity on nanotextured surfaces.

Rough or textured hydrophobic surfaces are dubbed "superhydrophobic" due to their numerous desirable properties, such as water repellency and interfacial slip. Superhydrophobicity stems from an aversion of water for the hydrophobic surface texture, so that a water droplet in the superhydrophobic "Cassie state" contacts only the tips of the rough surface. However, superhydrophobicity is remarkably fragile and can break down due to the wetting of the surface texture to yield the "Wenzel state" under various conditions, such as elevated pressures or droplet impact. Moreover, due to large energetic barriers that impede the reverse transition (dewetting), this breakdown in superhydrophobicity is widely believed to be irreversible. Using molecular simulations in conjunction with enhanced sampling techniques, here we show that on surfaces with nanoscale texture, water density fluctuations can lead to a reduction in the free energetic barriers to dewetting by circumventing the classical dewetting pathways. In particular, the fluctuation-mediated dewetting pathway involves a number of transitions between distinct dewetted morphologies, with each transition lowering the resistance to dewetting. Importantly, an understanding of the mechanistic pathways to dewetting and their dependence on pressure allows us to augment the surface texture design, so that the barriers to dewetting are eliminated altogether and the Wenzel state becomes unstable at ambient conditions. Such robust surfaces, which defy classical expectations and can spontaneously recover their superhydrophobicity, could have widespread importance, from underwater operation to phase-change heat transfer applications.

Sparse Sampling of Water Density Fluctuations in Interfacial Environments.

The free energetics of water density fluctuations near a surface, and the rare low-density fluctuations in particular, serve as reliable indicators of surface hydrophobicity; the easier it is to displace the interfacial waters, the more hydrophobic the underlying surface is. However, characterizing the free energetics of such rare fluctuations requires computationally expensive, non-Boltzmann sampling methods like umbrella sampling. This inherent computational expense associated with umbrella sampling makes it challenging to investigate the role of polarizability or electronic structure effects in influencing interfacial fluctuations. Importantly, it also limits the size of the volume, which can be used to probe interfacial fluctuations. The latter can be particularly important in characterizing the hydrophobicity of large surfaces with molecular-level heterogeneities, such as those presented by proteins. To overcome these challenges, here we present a method for the sparse sampling of water density fluctuations, which is roughly 2 orders of magnitude more efficient than umbrella sampling. We employ thermodynamic integration to estimate the free energy differences between biased ensembles, thereby circumventing the umbrella sampling requirement of overlap between adjacent biased distributions. Further, a judicious choice of the biasing potential allows such free energy differences to be estimated using short simulations, so that the free energetics of water density fluctuations are obtained using only a few, short simulations. Leveraging the efficiency of the method, we characterize water density fluctuations in the entire hydration shell of the protein, ubiquitin, a large volume containing an average of more than 600 waters.

Pathways to dewetting in hydrophobic confinement.

Liquid water can become metastable with respect to its vapor in hydrophobic confinement. The resulting dewetting transitions are often impeded by large kinetic barriers. According to macroscopic theory, such barriers arise from the free energy required to nucleate a critical vapor tube that spans the region between two hydrophobic surfaces--tubes with smaller radii collapse, whereas larger ones grow to dry the entire confined region. Using extensive molecular simulations of water between two nanoscopic hydrophobic surfaces, in conjunction with advanced sampling techniques, here we show that for intersurface separations that thermodynamically favor dewetting, the barrier to dewetting does not correspond to the formation of a (classical) critical vapor tube. Instead, it corresponds to an abrupt transition from an isolated cavity adjacent to one of the confining surfaces to a gap-spanning vapor tube that is already larger than the critical vapor tube anticipated by macroscopic theory. Correspondingly, the barrier to dewetting is also smaller than the classical expectation. We show that the peculiar nature of water density fluctuations adjacent to extended hydrophobic surfaces--namely, the enhanced likelihood of observing low-density fluctuations relative to Gaussian statistics--facilitates this nonclassical behavior. By stabilizing isolated cavities relative to vapor tubes, enhanced water density fluctuations thus stabilize novel pathways, which circumvent the classical barriers and offer diminished resistance to dewetting. Our results thus suggest a key role for fluctuations in speeding up the kinetics of numerous phenomena ranging from Cassie-Wenzel transitions on superhydrophobic surfaces, to hydrophobically driven biomolecular folding and assembly.