Effects of geometry and chemistry on hydrophobic solvation

Mechanical Regulation of Polymer Gels

The mechanical properties of polymer gels devote to emerging devices and machines in fields such as biomedical engineering, flexible bioelectronics, biomimetic actuators, and energy harvesters. Coupling network architectures and interactions has been explored to regulate supportive mechanical characteristics of polymer gels; however, systematic reviews correlating mechanics to interaction forces at the molecular and structural levels remain absent in the field. This review highlights the molecular engineering and structural engineering of polymer gel mechanics and a comprehensive mechanistic understanding of mechanical regulation. Molecular engineering alters molecular architecture and manipulates functional groups/moieties at the molecular level, introducing various interactions and permanent or reversible dynamic bonds as the dissipative energy. Molecular engineering usually uses monomers, cross-linkers, chains, and other additives. Structural engineering utilizes casting methods, solvent phase regulation, mechanochemistry, macromolecule chemical reactions, and biomanufacturing technology to construct and tailor the topological network structures, or heterogeneous modulus compositions. We envision that the perfect combination of molecular and structural engineering may provide a fresh view to extend exciting new perspectives of this burgeoning field. This review also summarizes recent representative applications of polymer gels with excellent mechanical properties. Conclusions and perspectives are also provided from five aspects of concise summary, mechanical mechanism, biofabrication methods, upgraded applications, and synergistic methodology.

A classical density functional theory for solvation across length scales

A central aim of multiscale modeling is to use results from the Schrödinger equation to predict phenomenology on length scales that far exceed those of typical molecular correlations. In this work, we present a new approach rooted in classical density functional theory (cDFT) that allows us to accurately describe the solvation of apolar solutes across length scales. Our approach builds on the Lum-Chandler-Weeks (LCW) theory of hydrophobicity [K. Lum et al., J. Phys. Chem. B 103, 4570 (1999)] by constructing a free energy functional that uses a slowly varying component of the density field as a reference. From a practical viewpoint, the theory we present is numerically simpler and generalizes to solutes with soft-core repulsion more easily than LCW theory. Furthermore, by assessing the local compressibility and its critical scaling behavior, we demonstrate that our LCW-style cDFT approach contains the physics of critical drying, which has been emphasized as an essential aspect of hydrophobicity by recent theories. As our approach is parameterized on the two-body direct correlation function of the uniform fluid and the liquid-vapor surface tension, it straightforwardly captures the temperature dependence of solvation. Moreover, we use our theory to describe solvation at a first-principles level on length scales that vastly exceed what is accessible to molecular simulations.

Relationships between Water's Structure and Solute Affinity at Polypeptoid Brush Surfaces

Excellent antifouling surfaces are generally thought to create a tightly bound layer of water that resists solute adsorption, and highly hydrophilic surfaces such as those with zwitterionic functionalities are of significant current interest as antifoulant strategies. However, despite significant proofs-of-concept, we still lack a fundamental understanding of how the nanoscopic structure of this hydration layer translates to reduced fouling, how surface chemistry can be tuned to achieve antifouling through hydration water, and why, in particular, zwitterionic surfaces seem so promising. Here, we use molecular dynamics simulations and free energy calculations to investigate the molecular relationships among surface chemistry, hydration water structure, and surface-solute affinity across a variety of surface-decorated chemistries. Specifically, we consider polypeptoid-decorated surfaces that display well-known experimental antifouling capabilities and that can be synthesized sequence specifically, with precise backbone positioning of, e.g., charged groups. Through simulations, we calculate the affinities of a range of small solutes to polypeptoid brush surfaces of varied side-chain chemistries. We then demonstrate that measures of the structure of surface hydration water in response to a particular surface chemistry signal solute-surface affinity; specifically, we find that zwitterionic chemistries produce solute-surface repulsion through highly coordinated hydration water while suppressing tetrahedral structuring around the solute, in contrast to uncharged surfaces that show solute-surface affinity. Based on the relationship of this structural perturbation to the affinity of small-molecule solutes, we propose a molecular mechanism by which zwitterionic surface chemistries enhance solute repulsion, with broader implications for the design of antifouling surfaces.

A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model

Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.

Solvation thermodynamics from cavity shapes of amino acids

According to common physical chemistry wisdom, the solvent cavities hosting a solute are tightly sewn around it, practically coinciding with its van der Waals surface. Solvation entropy is primarily determined by the surface and the volume of the cavity while enthalpy is determined by the solute-solvent interaction. In this work, we challenge this picture, demonstrating by molecular dynamics simulations that the cavities surrounding the 20 amino acids deviate significantly from the molecular surface. Strikingly, the shape of the cavity alone can be used to predict the solvation free energy, entropy, enthalpy, and hydrophobicity. Solute-solvent interactions involving the different chemical moieties of the amino acid, determine indirectly the cavity shape, and the properties of the branches but do not have to be taken explicitly into account in the prediction model.

Heterogeneous and Allosteric Role of Surface Hydration for Protein-Ligand Binding

Atomistic-level understanding of surface hydration mediating protein-protein interactions and ligand binding has been a challenge due to the dynamic nature of water molecules near the surface. We develop a computational method to evaluate the solvation free energy based on the density map of the first hydration shell constructed from all-atom molecular dynamics simulation and use it to examine the binding of two intrinsically disordered ligands to their target protein domain. One ligand is from the human protein, and the other is from the 1918 Spanish flu virus. We find that the viral ligand incurs a 6.9 kcal/mol lower desolvation penalty upon binding to the target, which is consistent with its stronger binding affinity. The difference arises from the spatially fragmented and nonuniform water density profiles of the first hydration shell. In particular, residues that are distal from the ligand-binding site contribute to a varying extent to the desolvation penalty, among which the "entropy hotspot" residues contribute significantly. Thus, ligand binding alters hydration on remote sites in addition to affecting the binding interface. The nonlocal effect disappears when the conformational motion of the protein is suppressed. The present results elucidate the interplay between protein conformational dynamics and surface hydration. Our approach of measuring the solvation free energy based on the water density of the first hydration shell is tolerant of the conformational fluctuation of protein, and we expect it to be applicable to investigating a broad range of biomolecular interfaces.

Structural features of interfacial water predict the hydrophobicity of chemically heterogeneous surfaces

The hydrophobicity of an interface determines the magnitude of hydrophobic interactions that drive numerous biological and industrial processes. Chemically heterogeneous interfaces are abundant in these contexts; examples include the surfaces of proteins, functionalized nanomaterials, and polymeric materials. While the hydrophobicity of nonpolar solutes can be predicted and related to the structure of interfacial water molecules, predicting the hydrophobicity of chemically heterogeneous interfaces remains a challenge because of the complex, non-additive contributions to hydrophobicity that depend on the chemical identity and nanoscale spatial arrangements of polar and nonpolar groups. In this work, we utilize atomistic molecular dynamics simulations in conjunction with enhanced sampling and data-centric analysis techniques to quantitatively relate changes in interfacial water structure to the hydration free energy (a thermodynamically well-defined descriptor of hydrophobicity) of chemically heterogeneous interfaces. We analyze a large data set of 58 self-assembled monolayers (SAMs) composed of ligands with nonpolar and polar end groups of different chemical identity (amine, amide, and hydroxyl) in five mole fractions, two spatial patterns, and with scaled partial charges. We find that only five features of interfacial water structure are required to accurately predict hydration free energies. Examination of these features reveals mechanistic insights into the interfacial hydrogen bonding behaviors that distinguish different surface compositions and patterns. This analysis also identifies the probability of highly coordinated water structures as a unique signature of hydrophobicity. These insights provide a physical basis to understand the hydrophobicity of chemically heterogeneous interfaces and connect hydrophobicity to experimentally accessible perturbations of interfacial water structure.

Nanocellulosics in Transient Technology

Envisage a world where discarded electrical/electronic devices and single-use consumables can dematerialize and lapse into the environment after the end-of-useful life without constituting health and environmental burdens. As available resources are consumed and human activities build up wastes, there is an urgency for the consolidation of efforts and strategies in meeting current materials needs while assuaging the concomitant negative impacts of conventional materials exploration, usage, and disposal. Hence, the emerging field of transient technology (Green Technology), rooted in eco-design and closing the material loop toward a friendlier and sustainable materials system, holds enormous possibilities for assuaging current challenges in materials usage and disposability. The core requirements for transient materials are anchored on meeting multicomponent functionality, low-cost production, simplicity in disposability, flexibility in materials fabrication and design, biodegradability, biocompatibility, and environmental benignity. In this regard, biorenewables such as cellulose-based materials have demonstrated capacity as promising platforms to fabricate scalable, renewable, greener, and efficient materials and devices such as membranes, sensors, display units (for example, OLEDs), and so on. This work critically reviews the recent progress of nanocellulosic materials in transient technologies toward mitigating current environmental challenges resulting from traditional material exploration, usage, and disposal. While spotlighting important fundamental properties and functions in the material selection toward practicability and identifying current difficulties, we propose crucial research directions in advancing transient technology and cellulose-based materials in closing the loop for conventional materials and sustainability.

Learning the relationship between nanoscale chemical patterning and hydrophobicity

The hydrophobicity of proteins and similar surfaces, which display chemical heterogeneity at the nanoscale, drives countless aqueous interactions and assemblies. However, predicting how surface chemical patterning influences hydrophobicity remains a challenge. Here, we address this challenge by using molecular simulations and machine learning to characterize and model the hydrophobicity of a diverse library of patterned surfaces, spanning a wide range of sizes, shapes, and chemical compositions. We find that simple models, based only on polar content, are inaccurate, whereas complex neural network models are accurate but challenging to interpret. However, by systematically incorporating chemical correlations between surface groups into our models, we are able to construct a series of minimal models of hydrophobicity, which are both accurate and interpretable. Our models highlight that the number of proximal polar groups is a key determinant of hydrophobicity and that polar neighbors enhance hydrophobicity. Although our minimal models are trained on particular patch size and shape, their interpretability enables us to generalize them to rectangular patches of all shapes and sizes. We also demonstrate how our models can be used to predict hot-spot locations with the largest marginal contributions to hydrophobicity and to design chemical patterns that have a fixed polar content but vary widely in their hydrophobicity. Our data-driven models and the principles they furnish for modulating hydrophobicity could facilitate the design of novel materials and engineered proteins with stronger interactions or enhanced solubilities.

Hydration of Linear Alkanes is Governed by the Small Length-Scale Hydrophobic Effect

Length-scale dependence of the hydrophobic effect is well understood for apolar spherical solutes: for small solutes (diameter, d ≲ 0.8 nm), the hydration free energy is entropically driven, while for larger solutes (d ≳ 2 nm), it is enthalpically driven. The nature of the hydrophobic effect in the case of anisotropic molecules such as linear alkanes is not understood yet. In this work, we have calculated the hydration free energy of linear alkanes going from methane to octadecane and of a spherical decane droplet of d ≈ 3 nm using molecular simulations. We show that the hydration free energies of alkanes, irrespective of their size, are governed by the small length-scale hydrophobic effect. That is, unlike the case of large spherical solutes, the hydration free energies of linear alkanes are entropically driven.

How Far Is "Bulk Water" from Interfaces? Depends on the Nature of the Surface and What We Measure

Using systematic molecular dynamics (MD) simulations, we revisit the question: At what distance from an interface do the properties of "bulk water" get recovered? We have considered three different kinds of interfaces: nonpolar (hydrophobic; isooctane-water interface), charged (negative; AOT bilayer), and polar (zwitterionic; POPC bilayer). In order to interrogate the extent of perturbation of the interfacial water molecules as a function of the distance from the interface, we utilize a diverse range of structural and dynamical parameters. To capture the structural perturbations, we look into local density (translational order), local tetrahedral order parameter, and dipolar orientation of the water molecules. We also explore the anisotropic diffusion of the water molecules in the direction perpendicular to the interface as well as the planar diffusion parallel to the interface in a distance dependent manner. In addition, the orientational time correlation functions have been computed to understand the extent of slowdown in the rotational dynamics. As expected, the electrostatic field emanating from the charged AOT interface seems to have the highest long-range effect on the orientational order and dynamics of the water molecules, whereas specific interactions like hydrogen bonding and electrostatic interaction lead to significant trapping and kinetic slowdown for both AOT and POPC (zwitterionic) very close to the interface. Our analysis highlights that not only the length-scale of perturbation depends on the nature of the interfaces and specific interactions but also the type of water property that we measure/calculate. Different water properties seem to have widely different length-scale of perturbation. Orientational order parameters seem to be perturbed to a much longer length-scale as compared to translational order parameters. The global orientational order of water can be perturbed even up to ∼4-5 nm near the negatively charged AOT surface in the absence of any extra electrolyte. This observation has significant implication toward the interpretation of experimental measurements as well since different spectroscopic techniques would probe different parameters or water properties with possible mutual disagreement and inconsistency between different types of measurements. Thus, our study provides a broader and unifying perspective toward the aspect of "context dependent" structural and dynamical perturbation of "interfacial water".

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.

Quantitative description of a contractile macromolecular machine

Contractile injection systems (CISs) [type VI secretion system (T6SS), phage tails, and tailocins] use a contractile sheath-rigid tube machinery to breach cell walls and lipid membranes. The structures of the pre- and postcontraction states of several CISs are known, but the mechanism of contraction remains poorly understood. Combining structural information of the end states of the 12-megadalton R-type pyocin sheath-tube complex with thermodynamic and force spectroscopy analyses and an original modeling procedure, we describe the mechanism of pyocin contraction. We show that this nanomachine has an activation energy of 160 kilocalories/mole (kcal/mol), and it releases 2160 kcal/mol of heat and develops a force greater than 500 piconewtons. Our combined approach provides a quantitative and experimental description of the membrane penetration process by a CIS.

Implicit Solvents for the Polarizable Atomic Multipole AMOEBA Force Field

Computational protein design, ab initio protein/RNA folding, and protein-ligand screening can be too computationally demanding for explicit treatment of solvent. For these applications, implicit solvent offers a compelling alternative, which we describe here for the polarizable atomic multipole AMOEBA force field based on three treatments of continuum electrostatics: numerical solutions to the nonlinear and linearized versions of the Poisson-Boltzmann equation (PBE), the domain-decomposition conductor-like screening model (ddCOSMO) approximation to the PBE, and the analytic generalized Kirkwood (GK) approximation. The continuum electrostatics models are combined with a nonpolar estimator based on novel cavitation and dispersion terms. Electrostatic model parameters are numerically optimized using a least-squares style target function based on a library of 103 small-molecule solvation free energy differences. Mean signed errors for the adaptive Poisson-Boltzmann solver (APBS), ddCOSMO, and GK models are 0.05, 0.00, and 0.00 kcal/mol, respectively, while the mean unsigned errors are 0.70, 0.63, and 0.58 kcal/mol, respectively. Validation of the electrostatic response of the resulting implicit solvents, which are available in the Tinker (or Tinker-HP), OpenMM, and Force Field X software packages, is based on comparisons to explicit solvent simulations for a series of proteins and nucleic acids. Overall, the emergence of performative implicit solvent models for polarizable force fields opens the door to their use for folding and design applications.

How the Shape and Chemistry of Molecular Penetrants Control Responsive Hydrogel Permeability

The permeability of hydrogels for the selective transport of molecular penetrants (drugs, toxins, reactants, etc.) is a central property in the design of soft functional materials, for instance in biomedical, pharmaceutical, and nanocatalysis applications. However, the permeation of dense and hydrated polymer membranes is a complex multifaceted molecular-level phenomenon, and our understanding of the underlying physicochemical principles is still very limited. Here, we uncover the molecular principles of permeability and selectivity in hydrogel permeation. We combine the solution-diffusion model for permeability with comprehensive atomistic simulations of molecules of various shapes and polarities in a responsive hydrogel in different hydration states. We find in particular that dense collapsed states are extremely selective, owing to a delicate balance between the partitioning and diffusivity of the penetrants. These properties are sensitively tuned by the penetrant size, shape, and chemistry, leading to vast cancellation effects, which nontrivially contribute to the permeability. The gained insights enable us to formulate semiempirical rules to quantify and extrapolate the permeability categorized by classes of molecules. They can be used as approximate guiding ("rule-of-thumb") principles to optimize penetrant or membrane physicochemical properties for a desired permeability and membrane functionality.

Affinity of small-molecule solutes to hydrophobic, hydrophilic, and chemically patterned interfaces in aqueous solution

Performance of membranes for water purification is highly influenced by the interactions of solvated species with membrane surfaces, including surface adsorption of solutes upon fouling. Current efforts toward fouling-resistant membranes often pursue surface hydrophilization, frequently motivated by macroscopic measures of hydrophilicity, because hydrophobicity is thought to increase solute-surface affinity. While this heuristic has driven diverse membrane functionalization strategies, here we build on advances in the theory of hydrophobicity to critically examine the relevance of macroscopic characterizations of solute-surface affinity. Specifically, we use molecular simulations to quantify the affinities to model hydroxyl- and methyl-functionalized surfaces of small, chemically diverse, charge-neutral solutes represented in produced water. We show that surface affinities correlate poorly with two conventional measures of solute hydrophobicity, gas-phase water solubility and oil-water partitioning. Moreover, we find that all solutes show attraction to the hydrophobic surface and most to the hydrophilic one, in contrast to macroscopically based hydrophobicity heuristics. We explain these results by decomposing affinities into direct solute interaction energies (which dominate on hydroxyl surfaces) and water restructuring penalties (which dominate on methyl surfaces). Finally, we use an inverse design algorithm to show how heterogeneous surfaces, with multiple functional groups, can be patterned to manipulate solute affinity and selectivity. These findings, importantly based on a range of solute and surface chemistries, illustrate that conventional macroscopic hydrophobicity metrics can fail to predict solute-surface affinity, and that molecular-scale surface chemical patterning significantly influences affinity-suggesting design opportunities for water purification membranes and other engineered interfaces involving aqueous solute-surface interactions.

Cavity Particle in Aqueous Solution with a Hydrophobic Solute: Structure, Energetics, and Functionals

Endpoints density functional theory (DFT) provides a framework for calculating the excess chemical potential of a solute in solution using solvent distribution functions obtained from both physical endpoints of a hypothetical charging process which transforms the solvent density from that of the pure liquid to the solution state. In this work, the endpoints DFT equations are formulated in terms of the indirect (solvent-mediated) contribution ω(x) to the solute-solvent potential of mean force, and their connections are established with the conventional DFT expressions which are based on the use of direct correlation functions. ω actually corresponds to the free-energy cost to move a cavity particle (a tagged solvent molecule which interacts with the other solvent molecules but not the solute) from the bulk to the configuration x of a solvent molecule relative to the solute and is a suitable variable to describe the solvent effects on the solute-solvent interactions. HNC and PY type approximations are then used to integrate the DFT charging integral involved in the exact expression for the excess chemical potential. With these approximations, molecular simulations are to be performed at the two endpoints of solute insertion: pure solvent without the solute and the solution system with the fully coupled solute-solvent interaction. An endpoints method thus utilizes the ensembles of intermolecular configurations of physical interest, which are often readily accessible with MD simulations given the present computational power. To illustrate properties of the formulation, we perform simulations of model systems consisting of a cavity particle in an aqueous solution containing a spherical hydrophobic solute of three different sizes from which ω(x) and the solute chemical potential can be calculated using endpoints DFT expressions. These are compared with corresponding results obtained using the approximations needed in order to evaluate the endpoints DFT charging integral when cavity particle simulation data is not available. We analyze a new approximation (two-points quadratic HNC) to the DFT charging integral which captures the correct behavior of the cavity distributions at both endpoints of the solute insertion. The behavior of the cavity particle in simple and complex liquids plays an important role in various theoretical treatments of the solute chemical potential. For pure Lennard-Jones fluids, the free energy to bring a cavity particle from the bulk to the center of a fluid particle is negative. However, for solutes of varying size, this is not generally true for Lennard-Jones fluids or the systems studied in this work. We carry out energetic and structural analyses of the cavity particle in aqueous solution with hydrophobic solutes of varying size and discuss the results in the context of the hydrophobic effect.

Spatially Heterogeneous Water Properties at Disordered Surfaces Decrease the Hydrophobicity of Nonpolar Self-Assembled Monolayers

Understanding the relationship between hydrophobicity and the properties of functionalized surfaces is vital to the design of materials that interact in aqueous environments. In this Letter, we use atomistic molecular dynamics simulations to investigate the effects of surface order on the hydrophobicity of self-assembled monolayers (SAMs) containing nonpolar ligands. We find that the interfacial hydrophobicity is highly correlated with SAM order and, strikingly, poorly correlated with the solvent-accessible surface area, which typically has been related to interfacial hydrophobicity. Analysis of spatial variations in both SAM and water properties reveals that the SAM-water interface is pinned near regions of disordered SAM surfaces with increased free volume, decreasing the overall interfacial hydrophobicity. Spatial variations in ligand end group positions at disordered SAM surfaces thus translate to spatial variations in hydrophobicity, yielding heterogeneous surface properties. These findings provide new insights into how surface order can alter the hydrophobicity of chemically uniform surfaces.

Hydration-Shell Vibrational Spectroscopy

Hydration-shell vibrational spectroscopy provides an experimental window into solute-induced water structure changes that mediate aqueous folding, binding, and self-assembly. Decomposition of measured Raman and infrared (IR) spectra of aqueous solutions using multivariate curve resolution (MCR) and related methods may be used to obtain solute-correlated spectra revealing solute-induced perturbations of water structure, such as changes in water hydrogen-bond strength, tetrahedral order, and the presence of dangling (non-hydrogen-bonded) OH groups. More generally, vibrational-MCR may be applied to both aqueous and nonaqueous solutions, including multicomponent mixtures, to quantify solvent-mediated interactions between oily, polar, and ionic solutes, in both dilute and crowded fluids. Combining vibrational-MCR with emerging theoretical modeling strategies promises synergetic advances in the predictive understanding of multiscale self-assembly processes of both biological and technological interest.

Free Energy Calculations Based on Coupling Proximal Distribution Functions and Thermodynamic Cycles

Techniques to calculate the free energy changes of a system are very useful in the study of biophysical and biochemical properties. In practice, free energy changes can be described with thermodynamic cycles, and the free energy change of an individual process can be computed by sufficiently sampling the corresponding configurations. However, this is still time-consuming especially for large biomolecular systems. Previously, we have shown that by utilizing precomputed solute-solvent correlations, so-called proximal distribution functions (pDF), we are capable of reconstructing the solvent environment near solute atoms, thus estimating the solute-solvent interactions and solvation free energies of molecules. In this contribution, we apply the technique of pDF-reconstructions to calculate chemical potentials and use this information in thermodynamic cycles. This illustrates how free energy changes of nontrivial chemical processes in aqueous solution systems can be rapidly estimated.

Heterogeneity of water structure and dynamics at the protein-water interface

In this molecular dynamics simulation study, we analyze the local structural and dynamic properties of water hydrating the protein ubiquitin on a spatial grid with 1 Å resolution. This allows for insights into the spatial distribution of water number densities, molecular orientations, translations, and rotations as a function of distance from the protein surface. Water molecule orientations follow a heterogeneous distribution with preferred local orientations of water dipoles and O-H bond vectors up to 10-15 Å distances from the protein, while local variations of the water number density converge to homogeneous bulk-like values within less than 8 Å. Interestingly, we find that the long-ranged orientational structure of water does not impact either the translational or rotational dynamics of water. Instead, heterogeneous distributions of local dynamical parameters and averaged dynamical retardation factors are only found close to the protein surface and follow a distance dependence comparable to heterogeneities in the local water number density. This study shows that the formation of nanodomains of preferred water orientations far from the protein does not significantly impact dynamical processes probed as a non-local average in most experiments.

Does a pair of methane molecules aggregate in water?

Molecular dynamics (MD) simulations of methane-water mixtures were performed using ab initio force fields for the CH₄-H₂O, H₂O-H₂O, and CH₄-CH₄ interactions. Both methane and water molecules were polarizable. From these calculations, the potential of mean force (PMF) between two methane molecules was extracted. Our results are compared with PMFs from a density-functional-theory (DFT) based Born-Oppenheimer type MD (BOMD) simulation, from a Monte Carlo (MC) simulation with ab initio-based force fields, and from MD simulations with empirical force fields. Our PMF is qualitatively similar to that obtained from the simulations with empirical force fields but differs significantly from those resulting from the DFT-BOMD and MC simulations. The depth of the PMF global minimum obtained in the present work is in a much better agreement with the experimental estimate than the result of the DFT-BOMD simulation, possibly due to the inability of DFT to describe the dispersion interactions and the lack of extensive sampling in the BOMD simulations. Our work indicates that, for a pair of methane molecules, there are configurations where the solvent increases the attraction between the solutes, but there are also conformations in which the solvent causes a weak net repulsion. On average, the methane molecules are more likely to be in the configuration where they are separated by a water molecule than in the one in which they are in contact even though the minimum of the PMF at the latter configuration is deeper than that at the former. Finally, we found that the water structure around methane solutes does not show a greater tetrahedral ordering than in neat bulk water.

Characterizing Solvent Density Fluctuations in Dynamical Observation Volumes

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 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 dynamical 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.

Molecular Order Affects Interfacial Water Structure and Temperature-Dependent Hydrophobic Interactions between Nonpolar Self-Assembled Monolayers

Understanding how material properties affect hydrophobic interactions-the water-mediated interactions that drive the association of nonpolar materials-is vital to the design of materials in contact with water. Conventionally, the magnitude of the hydrophobic interactions between extended interfaces is attributed to interfacial chemical properties, such as the amount of nonpolar solvent-exposed surface area. However, recent experiments have demonstrated that the hydrophobic interactions between uniformly nonpolar self-assembled monolayers (SAMs) also depend on molecular-level SAM order. In this work, we use atomistic molecular dynamics simulations to investigate the relationship between SAM order, water structure, and hydrophobic interactions to explain these experimental observations. The SAM-SAM hydrophobic interactions calculated from the simulations increase in magnitude as SAM order increases, matching experimental observations. We explain this trend by showing that the molecular-level order of the SAM impacts the nanoscale structure of interfacial water molecules, leading to an increase in water structure near disordered SAMs. These findings are consistent with a decrease in the solvation entropy of disordered SAMs, which is confirmed by measuring the temperature dependence of hydrophobic interactions using both simulations and experiments. This study elucidates how hydrophobic interactions can be influenced by an interfacial physical property, which may guide the design of synthetic materials with fine-tuned interfacial hydrophobicity.

Characterizing surface wetting and interfacial properties using enhanced sampling (SWIPES)

We introduce an accurate and efficient method for characterizing surface wetting and interfacial properties, such as the contact angle made by a liquid droplet on a solid surface, and the vapor-liquid surface tension of a fluid. The method makes use of molecular simulations in conjunction with the indirect umbrella sampling technique to systematically wet the surface and estimate the corresponding free energy. To illustrate the method, we study the wetting of a family of Lennard-Jones surfaces by water. For surfaces with a wide range of attractions for water, we estimate contact angles using our method, and compare them with contact angles obtained using droplet shapes. Notably, our method is able to capture the transition from partial to complete wetting as surface-water attractions are increased. Moreover, the method is straightforward to implement and is computationally efficient, providing accurate contact angle estimates in roughly 5 nanoseconds of simulation time.

Combining the polarizable Drude force field with a continuum electrostatic Poisson-Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson-Boltzmann/solvent-accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self-consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well-experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas-phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute-solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non-polar solvation effects. © 2018 Wiley Periodicals, Inc.

Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies

The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ G_el) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ G_el estimates varies widely between different GB models and also across different types of biomolecular complexes, with R² correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R² = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ G_el. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.

Implicit Solvation Using the Superposition Approximation (IS-SPA): An Implicit Treatment of the Nonpolar Component to Solvation for Simulating Molecular Aggregation

Nonpolar solute-solvent interactions are the driving force for aggregation in important chemical and biological phenomena including protein folding, peptide self-assembly, and oil-water emulsion formation. Currently, the most accurate and computationally efficient description of these processes requires an explicit treatment of all solvent and solute atoms. Previous computationally feasible implicit solvent models, such as solute surface area approaches, are unsuccessful at capturing aggregation features including both structural and energetic trends while more theoretically rigorous approaches, such as Reference Interaction Site Model (RISM), are accurate but extremely computationally demanding. Our approach, denoted Implicit Solvation using the Superposition Approximation (IS-SPA), builds on previous theory utilizing the Kirkwood superposition approximation to approximate the mean force of the solvent from solute parameters. We introduce and verify a parabolic first solvation shell truncation of atomic solvation, fitting water distributions around a molecule, and a Monte Carlo integration of the mean solvent force. These extensions allow this method to be implemented as an efficient nonpolar implicit solvent model for molecular simulation. The approximations in IS-SPA are first explored and justified for the homodimerization of an array of different sized Lennard-Jones spheres. The accuracy and transferability of the approach are demonstrated by its ability to capture the position and relative energies of the desolvation barrier and free energy minimum of alkane homodimers. The model is then shown to reproduce the phase separation and solubility of cyclohexane and water. These promising results, coupled with 2 orders of magnitude speed-up for dilute systems as compared to explicit solvent simulations, demonstrate that IS-SPA is an appealing approach to boost the time- and length-scale of molecular aggregation simulations.

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.

Intramolecular Interactions Overcome Hydration to Drive the Collapse Transition of Gly15

Simulations and experiments show oligo-glycines, polypeptides lacking any side chains, can collapse in water. We assess the hydration thermodynamics of this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here taken as the end-to-end distance (r) in the chain. To examine the role of the various conformations for a given r, we study the conditional distribution, P(R_g|r), of the radius of gyration for a given value of r. The free energy change versus R_g, -k_BT ln P(R_g|r), is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this observation within a multistate generalization of the potential distribution theorem, we calculate a tight upper bound for the hydration free energy of the peptide for a given r. On this basis, we find that peptide hydration greatly favors the expanded state of the chain, despite primitive hydrophobic effects favoring chain collapse. The net free energy of collapse is seen to be a delicate balance between opposing intrapeptide and hydration effects, with intrapeptide contributions favoring collapse.

Solvation Thermodynamics of Oligoglycine with Respect to Chain Length and Flexibility

Oligoglycine is a backbone mimic for all proteins and is prevalent in the sequences of intrinsically disordered proteins. We have computed the absolute chemical potential of glycine oligomers at infinite dilution by simulation with the CHARMM36 and Amber ff12SB force fields. We performed a thermodynamic decomposition of the solvation free energy (ΔG(sol)) of Gly2-5 into enthalpic (ΔH(sol)) and entropic (ΔS(sol)) components as well as their van der Waals and electrostatic contributions. Gly2-5 was either constrained to a rigid/extended conformation or allowed to be completely flexible during simulations to assess the effects of flexibility on these thermodynamic quantities. For both rigid and flexible oligoglycine models, the decrease in ΔG(sol) with chain length is enthalpically driven with only weak entropic compensation. However, the apparent rates of decrease of ΔG(sol), ΔH(sol), ΔS(sol), and their elec and vdw components differ for the rigid and flexible models. Thus, we find solvation entropy does not drive aggregation for this system and may not explain the collapse of long oligoglycines. Additionally, both force fields yield very similar thermodynamic scaling relationships with respect to chain length despite both force fields generating different conformational ensembles of various oligoglycine chains.

Real-time monitoring of hydrophobic aggregation reveals a critical role of cooperativity in hydrophobic effect

The hydrophobic interaction drives nonpolar solutes to aggregate in aqueous solution, and hence plays a critical role in many fundamental processes in nature. An important property intrinsic to hydrophobic interaction is its cooperative nature, which is originated from the collective motions of water hydrogen bond networks surrounding hydrophobic solutes. This property is widely believed to enhance the formation of hydrophobic core in proteins. However, cooperativity in hydrophobic interactions has not been successfully characterized by experiments. Here, we quantify cooperativity in hydrophobic interactions by real-time monitoring the aggregation of hydrophobic solute (hexaphenylsilole, HPS) in a microfluidic mixer. We show that association of a HPS molecule to its aggregate in water occurs at sub-microsecond, and the free energy change is −5.8 to −13.6 kcal mol⁻¹. Most strikingly, we discover that cooperativity constitutes up to 40% of this free energy. Our results provide quantitative evidence for the critical role of cooperativity in hydrophobic interactions.

Hydrophobic interactions occur between nonpolar molecules in water and their experimental quantification can help the understanding of biological self-assembly. Here Jiang et al. examine the kinetics and thermodynamics of hydrophobic aggregation in a bulk environment and characterize its cooperativity.

Approaches for calculating solvation free energies and enthalpies demonstrated with an update of the FreeSolv database

Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here, we briefly review "alchemical" approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations, and illustrate by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a non-physical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version, rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies, as well as electrostatic and nonpolar components of solvation free energies.

Nonpolar Solvation Free Energy from Proximal Distribution Functions

Using precomputed near neighbor or proximal distribution functions (pDFs) that approximate solvent density about atoms in a chemically bonded context one can estimate the solvation structures around complex solutes and the corresponding solute-solvent energetics. In this contribution, we extend this technique to calculate the solvation free energies (ΔG) of a variety of solutes. In particular we use pDFs computed for small peptide molecules to estimate ΔG for larger peptide systems. We separately compute the non polar (ΔG_vdW) and electrostatic (ΔG_elec) components of the underlying potential model. Here we show how the former can be estimated by thermodynamic integration using pDF-reconstructed solute-solvent interaction energy. The electrostatic component can be approximated with Linear Response theory as half of the electrostatic solute-solvent interaction energy. We test the method by calculating the solvation free energies of butane, propanol, polyalanine, and polyglycine and by comparing with traditional free energy simulations. Results indicate that the pDF-reconstruction algorithm approximately reproduces ΔG_vdW calculated by benchmark free energy simulations to within ∼ kcal/mol accuracy. The use of transferable pDFs for each solute atom allows for a rapid estimation of ΔG for arbitrary molecular systems.

A driving force for polypeptide and protein collapse

Polypeptide collapse is driven by the solvent-excluded volume decrease, the presence of nonpolar side chains is not so important.

On the Role of Nonspherical Cavities in Short Length-Scale Density Fluctuations in Water

Density fluctuations in liquid water are at the heart of numerous phenomena associated with hydrophobic effects such as protein folding and the interaction between biomolecules. One of the most fundamental processes in this regard is the solvation of hydrophobic solutes in water. The vast majority of theoretical and numerical studies examine density fluctuations at the short length scale focusing exclusively on spherical cavities. In this work, we use both first-principles and classical molecular dynamics simulations to demonstrate that density fluctuations in liquid water can deviate significantly from the canonical spherical shapes. We show that regions of empty space are frequently characterized by exotic, highly asymmetric shapes that can be quite delocalized over the hydrogen bond network. Interestingly, density fluctuations of these shapes are characterized by Gaussian statistics with larger fluctuations. An important consequence of this is that the work required to create non spherical cavities can be substantially smaller than that of spheres. This feature is also qualitatively captured by the Lum-Chandler-Weeks theory. The scaling behavior of the free energy as a function of the volume at short length scales is qualitatively different for the nonspherical entities. We also demonstrate that nonspherical density fluctuations are important for accommodating the hydrophobic amino acid alanine and are thus likely to have significant implications when it comes to solvating highly asymmetrical species such as alkanes, polymers, or biomolecules.

Universal Repulsive Contribution to the Solvent-Induced Interaction Between Sizable, Curved Hydrophobes

In addition to the direct attraction, sizable hydrophobes in water experience an attractive force mediated by interfacial water. Using simple geometric arguments, we identify the conditions at which the water-induced interaction between curved hydrocarbon surfaces becomes repulsive. The repulsive contribution arises from the thermodynamic penalty due to the emergence of the liquid/vapor boundary created as water gets expelled between curved hydrophobes. By augmenting the mean field approach with atomistic simulations of pristine and alkyl-coated graphitic nanoparticles in three distinct geometries, spherical, cylindrical and planar, immersed in water, we show the macroscopic thermodynamics remarkably works down to the molecular scale. The new insights improve the prediction and control of wetting and dispersion properties for a broad class of nonpolar nanoparticles.

Problems of robustness in Poisson-Boltzmann binding free energies

Although models based on the Poisson–Boltzmann (PB) equation have been fairly successful at predicting some experimental quantities, such as solvation free energies (ΔG), these models have not been consistently successful at predicting binding free energies (ΔΔG). Here we found that ranking a set of protein–protein complexes by the electrostatic component (ΔΔGel) of ΔΔG was more difficult than ranking the same molecules by the electrostatic component (ΔGel) of ΔG. This finding was unexpected because ΔΔGel can be calculated by combining estimates of ΔGel for the complex and its components with estimates of the ΔΔGel in vacuum. One might therefore expect that if a theory gave reliable estimates of ΔGel, then its estimates of ΔΔGel would be reliable. However, ΔΔGel for these complexes were orders of magnitude smaller than ΔGel, so although estimates of ΔGel obtained with different force fields and surface definitions were highly correlated, similar estimates of ΔΔGel were often not correlated.

Solute-Solvent Energetics Based on Proximal Distribution Functions

We consider the hydration structure and thermodynamic energetics of solutes in aqueous solution. On the basis of the dominant local correlation between the solvent and the chemical nature of the solute atoms, proximal distribution functions (pDF) can be used to quantitatively estimate the hydration pattern of the macromolecules. We extended this technique to study the solute-solvent energetics including the van der Waals terms representing excluded volume and tested the method with butane and propanol. Our results indicate that the pDF-reconstruction algorithm can reproduce van der Waals solute-solvent interaction energies to useful kilocalorie per mole accuracy. We subsequently computed polyalanine-water interaction energies for a variety of conformers, which also showed agreement with the simulated values.

Solvation thermodynamics of amino acid side chains on a short peptide backbone

The hydration process of side chain analogue molecules differs from that of the actual amino acid side chains in peptides and proteins owing to the effects of the peptide backbone on the aqueous solvent environment. A recent molecular simulation study has provided evidence that all nonpolar side chains, attached to a short peptide backbone, are considerably less hydrophobic than the free side chain analogue molecules. In contrast to this, the hydrophilicity of the polar side chains is hardly affected by the backbone. To analyze the origin of these observations, we here present a molecular simulation study on temperature dependent solvation free energies of nonpolar and polar side chains attached to a short peptide backbone. The estimated solvation entropies and enthalpies of the various amino acid side chains are compared with existing side chain analogue data. The solvation entropies and enthalpies of the polar side chains are negative, but in absolute magnitude smaller compared with the corresponding analogue data. The observed differences are large; however, owing to a nearly perfect enthalpy-entropy compensation, the solvation free energies of polar side chains remain largely unaffected by the peptide backbone. We find that a similar compensation does not apply to the nonpolar side chains; while the backbone greatly reduces the unfavorable solvation entropies, the solvation enthalpies are either more favorable or only marginally affected. This results in a very small unfavorable free energy cost, or even free energy gain, of solvating the nonpolar side chains in strong contrast to solvation of small hydrophobic or nonpolar molecules in bulk water. The solvation free energies of nonpolar side chains have been furthermore decomposed into a repulsive cavity formation contribution and an attractive dispersion free energy contribution. We find that cavity formation next to the peptide backbone is entropically favored over formation of similar sized nonpolar side chain cavities in bulk water, in agreement with earlier work in the literature on analysis of cavity fluctuations at nonpolar molecular surfaces. The cavity and dispersion interaction contributions correlate quite well with the solvent accessible surface area of the nonpolar side chains attached to the backbone. This correlation however is weak for the overall solvation free energies owing to the fact that the cavity and dispersion free energy contributions are almost exactly cancelling each other.

Reconciling the understanding of 'hydrophobicity' with physics-based models of proteins

The idea that a 'hydrophobic energy' drives protein folding, aggregation, and binding by favoring the sequestration of bulky residues from water into the protein interior is widespread. The solvation free energies (ΔGsolv) of small nonpolar solutes increase with surface area (A), and the free energies of creating macroscopic cavities in water increase linearly with A. These observations seem to imply that there is a hydrophobic component (ΔGhyd) of ΔGsolv that increases linearly with A, and this assumption is widely used in implicit solvent models. However, some explicit-solvent molecular dynamics studies appear to contradict these ideas. For example, one definition (ΔG(LJ)) of ΔGhyd is that it is the free energy of turning on the Lennard-Jones (LJ) interactions between the solute and solvent. However, ΔG(LJ) decreases with A for alanine and glycine peptides. Here we argue that these apparent contradictions can be reconciled by defining ΔGhyd to be a near hard core insertion energy (ΔGrep), as in the partitioning proposed by Weeks, Chandler, and Andersen. However, recent results have shown that ΔGrep is not a simple function of geometric properties of the molecule, such as A and the molecular volume, and that the free energy of turning on the attractive part of the LJ potential cannot be computed from first-order perturbation theory for proteins. The theories that have been developed from these assumptions to predict ΔGhyd are therefore inadequate for proteins.