An information theory model of hydrophobic interactions

Structural and dynamical properties of aqueous NaCl brines confined in kaolinite nanopores

Quantifying thermodynamics, structural, and dynamical properties of brine confined in clay pores is critical for a variety of geo-energy applications, including underground hydrogen storage (UHS) and carbon capture and sequestration (CCS). Atomistic molecular dynamics simulations are applied here to study aqueous NaCl brines within 10-Å kaolinite slit pores. NaCl concentrations are chosen at 5, 10, 12.5, and 15 wt. %, all below the solubility limit and high enough to provide statistically relevant information. The distribution of the ions within the nanopores is found not to be homogeneous. Explicitly, Na+ cations, preferentially attracted to the siloxane surface, accumulate in regions with low water density, whereas Cl- anions, attracted to the gibbsite surface of kaolinite, are found within the hydration layers. Confinement affects the properties of ions, with ion pairing being more pronounced within the pore than in bulk aqueous solutions at similar temperatures, pressures, and compositions. Conversely, the ions affect the properties of confined water. For example, the lifetime of water-water hydrogen bonds in confinement is shortened within the hydration shells; increasing salinity from 5 to 12.5 wt. % reduces the likelihood of water density fluctuations near the kaolinite surfaces, although when the NaCl concentration rises from 12.5 to 15 wt. %, Cl- anions enhance the likelihood of density fluctuations for the hydration layer near the gibbsite surface. The simulated molecular trajectories are studied further to extract diffusion coefficients. While confinement in the kaolinite nanopore reduces the mobility of all species, non-monotonic trends are observed as a function of salt concentration. The trends seem associated with the likelihood of ion pairing. Furthermore, the diffusion coefficients for the cations are predicted to be higher than those for the anions, which is contrary to what is typically observed in bulk brines. Because density fluctuations are correlated with properties such as the solubility of gases in confined water, our observations may have important implications for geo-energy applications such as UHS and CCS.

Potential distribution theory of alchemical transfer

We present an analytical description of the Alchemical Transfer Method (ATM) for molecular binding using the Potential Distribution Theory (PDT) formalism. ATM models the binding free energy by mapping the bound and unbound states of the complex by translating the ligand coordinates. PDT relates the free energy and the probability densities of the perturbation energy along the alchemical path to the probability density at the initial state, which is the unbound state of the complex in the case of a binding process. Hence, the ATM probability density of the transfer energy at the unbound state is first related by a convolution operation of the probability densities for coupling the ligand to the solvent and coupling it to the solvated receptor-for which analytical descriptions are available-with parameters obtained from maximum likelihood analysis of data from double-decoupling alchemical calculations. PDT is then used to extend this analytical description along the alchemical transfer pathway. We tested the theory on the alchemical binding of five guests to the tetramethyl octa-acid host from the SAMPL8 benchmark set. In each case, the probability densities of the perturbation energy for transfer along the alchemical transfer pathway obtained from numerical calculations match those predicted from the theory and double-decoupling simulations. The work provides a solid theoretical foundation for alchemical transfer, offers physical insights on the form of the probability densities observed in alchemical transfer calculations, and confirms the conceptual and numerical equivalence between the alchemical transfer and double-decoupling processes.

Molecular Hydrophobicity Signature in Charged Bidimensional Clay Materials

The unraveling of the hydrophobicity/hydrophilicity molecular signature of nanometric bidimensional confined systems represents a challenging task with repercussions in environmental transport processes. Swelling clay minerals represent an ideal model system, as hydrophobicity can be modified during material synthesis by substituting hydroxyls by fluorine in the structure, without additional surface treatment. This following work presents a combined approach, integrating experimental inelastic neutron scattering spectroscopy and ab initio molecular dynamics simulations, with the objective of advancing our understanding of the role of surface hydroxylation/fluorination and the extent of confinement on water properties. From computed structures, the analysis of molecular hydrophobicity/hydrophilicity signature was investigated in detail through water-cation-surface interactions. The results elucidate the influence of fluorination on interlayer species, thereby tracing the impact of the surface on the diminished number of water molecules in such a sample. It is notable that the strong cation-water interaction can overcome the disruptive influence of fluorine, thereby maintaining comparable water hydration shells around cations and resulting in an almost identical bidimensional confinement geometry for both hydroxylated and fluorinated specimens. The analysis of the hydrogen-bond network revealed a significant reorganization of the water molecules due to fluorination. Our results suggest that a quantitative molecular signature of hydrophobicity/hydrophilicity can be derived from the analysis of the formation of cavities in the confined fluid. This new finding represents a robust approach for generalizing the hydrophobicity/hydrophilicity character for a wide variety of bidimensional systems while proposing a framework for the design of new materials with controlled water properties.

Hofmeister effect enhanced SiO2/gelatin-based hydrophobically associated hydrogels and their lubricating properties

In recent years, hydrogel materials with suitable energy dissipation mechanisms and excellent mechanical properties have attracted much attention in tissue engineering due to their ability to mimic the natural cartilage structure. However, in cartilage tissue's regeneration and repair process, hydrogel materials should also possess satisfactory lubrication properties and biocompatibility. Therefore, preparing biocompatible low friction, high toughness hydrogels remain a challenge. In this paper, a new strategy is proposed to use gelatin, acrylamide (AM), lauryl methacrylate (LMA) and SiO2 to construct hydrophobically associated hydrogels, where gelatin was used as an emulsifier and SiO2 was used to a nano-enhanced filler. Then the Hofmeister effect enhanced SiO2/gelatin-based hydrophobically associated hydrogels were prepared by one-step immersion in ammonium sulfate solution. The results showed that the strong "salting out" effect of ammonium sulfate solution on gelatin led to further enhancement of the hydrophobic interactions between gelatin molecular chains, which significantly improved the mechanical properties and lubrication ability of the hydrogels. Furthermore, Calcein AM-PI fluorescent staining and haemolysis assays showed that the hydrogel had low cytotoxicity and good haemocompatibility, and ELISA and scratch assays confirmed the positive regulatory effect of the hydrogel on normal cell growth. The Hofmeister effect-enhanced SiO2/gelatin-based hydrophobically associated hydrogels have potential applications in articular cartilage repair.

The role of the water contact layer on hydration and transport at solid/liquid interfaces

Understanding the structure in the nanoscopic region of water that is in direct contact with solid surfaces, so-called contact layer, is key to quantifying macroscopic properties that are of interest to e.g. catalysis, ice nucleation, nanofluidics, gas adsorption, and sensing. We explore the structure of the water contact layer on various technologically relevant solid surfaces, namely graphene, MoS[Formula: see text], Au(111), Au(100), Pt(111), and Pt(100), which have been previously hampered by time and length scale limitations of ab initio approaches or force field inaccuracies, by means of molecular dynamics simulations based on ab initio machine learning potentials built using an active learning scheme. Our results reveal that the in-plane intermolecular correlations of the water contact layer vary greatly among different systems: Whereas the contact layer on graphene and on Au(111) is predominantly homogeneous and isotropic, it is inhomogeneous and anisotropic on MoS[Formula: see text], on Au(100), and on the Pt surfaces, where it additionally forms two distinct sublayers. We apply hydrodynamics and the theory of the hydrophobic effect, to relate the energy corrugation and the characteristic length-scales of the contact layer with wetting, slippage, the hydration of small hydrophobic solutes and diffusio-osmotic transport. Thus, this work provides a microscopic picture of the water contact layer and links it to macroscopic properties of liquid/solid interfaces that are measured experimentally and that are relevant to wetting, hydrophobic solvation, nanofluidics, and osmotic transport.

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.

Slip Opacity and Fast Osmotic Transport of Hydrophobes at Aqueous Interfaces with Two-Dimensional Materials

We investigate the interfacial transport of water and hydrophobic solutes on van der Waals bilayers and heterostructures formed by stacking graphene, hBN, and MoS2 using extensive ab initio molecular dynamics simulations. We compute water slippage and the diffusio-osmotic transport coefficient of hydrophobic particles at the interface by combining hydrodynamics and the theory of the hydrophobic effect. We find that slippage is dominated by the layer that is in direct contact with water and only marginally altered by the second layer, leading to a so-called "slip opacity". The screening of the lateral forces, where the liquid does not feel the forces coming from the second nearest layer, is one of the factors leading to the "slip opacity" in our systems. The diffusio-osmotic transport of small hydrophobes (with a radius below 2.5 Å) is also affected by the slip opacity, being dramatically enhanced by slippage. Furthermore, the direction of diffusio-osmotic flow is controlled by the solute size, with the flow in the opposite direction of the concentration gradient for smaller hydrophobes, and vice versa for larger ones. We connect our findings to the wetting properties of two-dimensional materials, and we propose that slippage and wetting can be controlled separately: whereas the slippage is mostly determined by the layer in closer proximity to water, wetting can be finely tuned by stacking different two-dimensional materials. Our study advances the computational design of two-dimensional materials and van der Waals heterostructures, enabling precise control over wetting and slippage properties for applications in coatings and water purification membranes.

Molecular Density Fluctuations Control Solubility and Diffusion for Confined Aqueous Hydrogen

Hydrogen's contribution to a sustainable energy transformation requires intermittent storage technologies, e.g., underground hydrogen storage (UHS). Toward designing UHS sites, atomistic molecular dynamics (MD) simulations are used here to quantify thermodynamic and transport properties for confined aqueous H2. Slit-shaped pores of width 10 and 20 Å are carved out of kaolinite. Within these pores, water yields pronounced hydration layers. Molecular H2 distributes along these hydration layers, yielding solubilities up to ∼25 times those in the bulk. Hydrogen accumulates near the siloxane surface, where water density fluctuates significantly. On the contrary, a dense hydration layer forms on the gibbsite surface, which is, for the most part, depleted of H2. Although confinement reduces water mobility, the diffusion of aqueous H2 increases as the kaolinite pore width decreases, also a consequence of water density fluctuations. These results relate to H2 permeability in underground hydrogen storage sites.

Molecular-Scale Liquid Density Fluctuations and Cavity Thermodynamics

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution. Computer simulations confirmed this prediction across various liquid models if the size of the observation volume is not large. The reversible work required to create a cavity and the chance of finding no molecules in a fixed observation volume are directly correlated. The Gaussian formula for the latter probability is scrutinized to derive the changes in enthalpy and entropy, which arise from the cavity creation. The reversible work of cavity creation has a purely entropic origin as a consequence of the solvent-excluded volume effect produced by the inaccessibility of a region of the configurational space. The consequent structural reorganization leads to a perfect compensation of enthalpy and entropy changes. Such results are coherent with those obtained from Lee in his direct statistical mechanical study.

Dynamic Transformation of High-Architectural Nanocrystal Superlattices upon Solvent Molecule Exposure

The cluster-based body-centered-cubic superlattice (cBCC SL) represents one of the most complicated structures among reported nanocrystal assemblies, comprised of 72 truncated tetrahedral quantum dots per unit cell. Our previous report revealed that truncated tetrahedral quantum dots within cBCC SLs possessed highly controlled translational and orientational order owing to an unusual energetic landscape based on the balancing of entropic and enthalpic contributions during the assembly process. However, the cBCC SL's structural transformability and mechanical properties, uniquely originating from such complicated nanostructures, have yet to be investigated. Herein, we report that cBCC SLs can undergo dynamic transformation to face-centered-cubic SLs in response to post-assembly molecular exposure. We monitored the dynamic transformation process using in situ synchrotron-based small-angle X-ray scattering, revealing a dynamic transformation involving multiple steps underpinned by interactions between incoming molecules and TTQDs' surface ligands. Furthermore, our mechanistic study demonstrated that the precise configuration of TTQDs' ligand molecules in cBCC SLs was key to their high structural transformability and unique jelly-like soft mechanical properties. While ligand molecular configurations in nanocrystal SLs are often considered minor features, our findings emphasize their significance in controlling weak van der Waals interactions between nanocrystals within assembled SLs, leading to previously unremarked superstructural transformability and unique mechanical properties. Our findings promote a facile route toward further creation of soft materials, nanorobotics, and out-of-equilibrium assemblies based on nanocrystal building blocks.

Gaussian and Non-Gaussian Solvent Density Fluctuations within Solute Cavities in a Water-like Solvent

We report a Monte Carlo simulation study of length-scale-dependent density fluctuations in cavities in the coarse-grained mW representation of water at ambient conditions. Specifically, we use a combination of test particle insertion and umbrella sampling techniques to examine the full range of water occupation states in spherical cavities up to 6.3 Å radius in water. As has previously been observed, water density fluctuations are found to be effectively Gaussian in nature for atomic-scale cavities, but as the cavities get larger, they exhibit a non-Gaussian "fat-tail" distribution for lower occupancy states. We introduce a new statistical thermodynamic approach to analyze non-Gaussian fluctuations based on the radial distribution of waters about cavities with varying numbers of waters within its boundaries. It is shown that the onset of these non-Gaussian fluctuations is a result of the formation of a bubble within the cavity as it is emptied, which is accompanied by the adsorption of waters onto its interior surface. We revisit a theoretical framework we previously introduced to describe Gaussian fluctuations within cavities to incorporate bubble formation by including surface tension contributions. This modified theory accurately describes density fluctuations within both atomic and meso-scale cavities. Moreover, the theory predicts the transition from Gaussian to non-Gaussian fluctuations at a specific cavity occupancy, in excellent agreement with simulation observations.

How do water-mediated interactions and osmotic second virial coefficients vary with particle size?

We examine quantitatively the solute-size dependences of the effective interactions between nonpolar solutes in water and in a simple liquid. The potential w(r) of mean force and the osmotic second virial coefficients B are calculated with high accuracy from molecular dynamics simulations. As the solute diameter increases from methane's to C60's with the solute-solute and solute-solvent attractive interaction parameters fixed to those for the methane-methane and methane-water interactions, the first minimum of w(r) lowers from -1.1 to -4.7 in units of the thermal energy kT. Correspondingly, the magnitude of B (<0) increases proportional to σα with some power close to 6 or 7, which reinforces the solute-size dependence of B found earlier for a smaller range of σ [H. Naito, R. Okamoto, T. Sumi and K. Koga, J. Chem. Phys., 2022, 156, 221104]. We also demonstrate that the strength of the attractive interactions between solute and solvent molecules can qualitatively change the characteristics of the effective pair interaction between solute particles, both in water and in a simple liquid. If the solute-solvent attractive force is set to be weaker (stronger) than a threshold, the effective interaction becomes increasingly attractive (repulsive) with increasing solute size.

Modulating hierarchical self-assembly in thermoresponsive intrinsically disordered proteins through high-temperature incubation time

The cornerstone of structural biology is the unique relationship between protein sequence and the 3D structure at equilibrium. Although intrinsically disordered proteins (IDPs) do not fold into a specific 3D structure, breaking this paradigm, some IDPs exhibit large-scale organization, such as liquid-liquid phase separation. In such cases, the structural plasticity has the potential to form numerous self-assembled structures out of thermal equilibrium. Here, we report that high-temperature incubation time is a defining parameter for micro and nanoscale self-assembly of resilin-like IDPs. Interestingly, high-resolution scanning electron microscopy micrographs reveal that an extended incubation time leads to the formation of micron-size rods and ellipsoids that depend on the amino acid sequence. More surprisingly, a prolonged incubation time also induces amino acid composition-dependent formation of short-range nanoscale order, such as periodic lamellar nanostructures. We, therefore, suggest that regulating the period of high-temperature incubation, in the one-phase regime, can serve as a unique method of controlling the hierarchical self-assembly mechanism of structurally disordered proteins.

Cavity formation at metal-water interfaces

The free energy cost of forming a cavity in a solvent is a fundamental concept in rationalizing the solvation of molecules and ions. A detailed understanding of the factors governing cavity formation in bulk solutions has inter alia enabled the formulation of models that account for this contribution in coarse-grained implicit solvation methods. Here, we employ classical molecular dynamics simulations and multistate Bennett acceptance ratio free energy sampling to systematically study cavity formation at a wide range of metal-water interfaces. We demonstrate that the obtained size- and position-dependence of cavitation energies can be fully rationalized by a geometric Gibbs model, which considers that the creation of the metal-cavity interface necessarily involves the removal of interfacial solvent. This so-called competitive adsorption effect introduces a substrate dependence to the interfacial cavity formation energy that is missed in existing bulk cavitation models. Using expressions from scaled particle theory, this substrate dependence is quantitatively reproduced by the Gibbs model through simple linear relations with the adsorption energy of a single water molecule. Besides providing a better general understanding of interfacial solvation, this paves the way for the derivation and efficient parametrization of more accurate interface-aware implicit solvation models needed for reliable high-throughput calculations toward improved electrocatalysts.

Anion-Specific Adsorption of Carboxymethyl Cellulose on Cellulose

Integration of fiber modification step with a modern pulp mill is a resource efficient way to produce functional fibers. Motivated by the need to integrate polymer adsorption with the current pulping system, anion-specific effects in carboxymethylcellulose (CMC) adsorption have been studied. The QCM-D adsorption experiments revealed that CMC adsorption to the cellulose model surface is prone to anion-specific effects. A correlation was observed between the adsorbed CMC and the degree of hydration of the co-ions present in the magnesium salts. The presence of a chaotropic co-ion such as nitrate increased the adsorption of CMC on cellulose compared to the presence of the kosmotropic sulfate co-ion. However, anion-specificity was not significant in the case of salts containing zinc cations. The hydration of anions determines the distribution of the ions at the interface. Chaotropic ions, such as nitrates, are likely to be distributed near the chaotropic cellulose surface, causing changes in the ordering of water molecules and resulting in greater entropy gain once released from the surface, thus increasing CMC adsorption.

Modulating Hierarchical Self-Assembly In Thermoresponsive Intrinsically Disordered Proteins Through High-Temperature Incubation Time

The cornerstone of structural biology is the unique relationship between protein sequence and the 3D structure at equilibrium. Although intrinsically disordered proteins (IDPs) do not fold into a specific 3D structure, breaking this paradigm, some IDPs exhibit large-scale organization, such as liquid-liquid phase separation. In such cases, the structural plasticity has the potential to form numerous self-assembled structures out of thermal equilibrium. Here, we report that high-temperature incubation time is a defining parameter for micro and nanoscale self-assembly of resilin-like IDPs. Interestingly, high-resolution scanning electron microscopy micrographs reveal that an extended incubation time leads to the formation of micron-size rods and ellipsoids that depend on the amino acid sequence. More surprisingly, a prolonged incubation time also induces amino acid composition-dependent formation of short-range nanoscale order, such as periodic lamellar nanostructures. We can correlate the lamellar structures to β-sheet formation and demonstrate similarities between the observed nanoscopic structural arrangement and spider silk. We, therefore, suggest that regulating the period of high-temperature incubation, in the one-phase regime, can serve as a unique method of controlling the hierarchical self-assembly mechanism of structurally disordered proteins.

Phenomenological description of the acidity of the citric acid and its deprotonated species: informational-theoretical study

CONTEXT

In spite of the fact that molecular acidity is a fundamental physicochemical property of molecular systems, the vast majority of theoretical studies have focused attention on monoprotic acids and on the prediction of pKa's. Polyprotic acids, represent a challenge for electronic structure calculations since the multiple acidic sites result in a vast group of species with different conformations and reactivities. In this work, Information-theoretic (IT) concepts of localizability, order and uniformity are applied to the Citric Acid and its deprotonated species through the one-electron density functionals: Shannon entropy (S), Fisher information (I) and Disequilibrium (D), respectively. We pursue the goal of characterizing the acidity of the aforementioned species with the aim to associate the IT concepts to chemical features such as the polarizability of the protonated/deprotonated species, the liability of the acidic sites, atomic electrostatic potentials, covalent bonding. IT analyses looks very promising for future studies on the acidity of specific deprotonation-sites of polyprotic acids.

METHODS

Density functional theory (DFT) calculations were performed with Gaussian 09 program. A sensitivity analysis of the IT-measures was performed for the citric acid and the citrate using B3LYP, B3PW91, BPW91, M05-2X, M06-2X and PBEPBE functionals with the 6-311++g(3df,2p), 6-311++g(d,p), 6.311+g(d,p) and aug-cc-pVDZ basis sets. The rest of the analysis was performed with the M05-2X/6-311+G(d,p) level of theory. Additionally, aqueous media was considered by use of the SMD solvent model. The IT-measures were calculated using a suite of programs developed in our laboratory jointly with the DGRID software package.

Machine learning assisted coarse-grained molecular dynamics modeling of meso-scale interfacial fluids

A hallmark of meso-scale interfacial fluids is the multi-faceted, scale-dependent interfacial energy, which often manifests different characteristics across the molecular and continuum scale. The multi-scale nature imposes a challenge to construct reliable coarse-grained (CG) models, where the CG potential function needs to faithfully encode the many-body interactions arising from the unresolved atomistic interactions and account for the heterogeneous density distributions across the interface. We construct the CG models of both single- and two-component polymeric fluid systems based on the recently developed deep coarse-grained potential [Zhang et al., J. Chem. Phys. 149, 034101 (2018)] scheme, where each polymer molecule is modeled as a CG particle. By only using the training samples of the instantaneous force under the thermal equilibrium state, the constructed CG models can accurately reproduce both the probability density function of the void formation in bulk and the spectrum of the capillary wave across the fluid interface. More importantly, the CG models accurately predict the volume-to-area scaling transition for the apolar solvation energy, illustrating the effectiveness to probe the meso-scale collective behaviors encoded with molecular-level fidelity.

MPCVD-Grown Nanodiamond Microelectrodes with Oxygen Plasma Activation for Neurochemical Applications

Nanodiamonds (NDs) are a carbon nanomaterial that has a diamond core with heteroatoms and defects at the surface. The large surface area, defect sites, and functional groups on NDs make them a promising material for electrochemical sensing. Previously, we dip-coated ND onto carbon-fiber microelectrodes (CFMEs) and found increases in sensitivity, but the coating was sparse. Here, we directly grew thin films of ND on niobium wires using microwave plasma chemical vapor deposition (MP-CVD) to provide full surface coverage. ND microelectrodes show a reliable performance in neurotransmitter detection with good antifouling properties. To improve sensitivity, we oxygen plasma etched ND films to activate the surface and intentionally add defects and oxygen surface functional groups. For fast-scan cyclic voltammetry detection of dopamine, oxygen plasma-etching increases the sensitivity from 21 nA/μM to 90 nA/μM after treatment. Fouling was tested by repeated injections of serotonin or tyramine, and both ND and plasma oxidized nanodiamond (NDO) microelectrodes maintain their currents better compared to CFMEs and therefore are more antifouling. A biofouling test in brain slices shows that ND microelectrodes barely have any current drop, while the more hydrophilic NDO microelectrodes decrease more, but still not as much as CFMEs. Overall, grown ND microelectrodes are promising in neurotransmitter detection with excellent fouling resistance, whereas oxygen plasma etching slightly lowers the fouling resistance but dramatically increases sensitivity.

Connecting Non-Gaussian Water Density Fluctuations to the Lengthscale Dependent Crossover in Hydrophobic Hydration

We connect density fluctuations in liquid water to lengthscale dependent crossover in hydrophobic hydration. Specifically, we employ indirect umbrella sampling (INDUS) simulations to characterize density fluctuations in observation volumes of various sizes and shapes in water and as a function of temperature and salt concentration. Consistent with previous observations, density fluctuations are Gaussian in small molecular scale volumes, but they display non-Gaussian "low-density fat tails" in larger volumes. These non-Gaussian tails are indicative of the proximity of water to its liquid to vapor phase transition and have implications on biomolecular interactions and function. We show that the onset of non-Gaussian fluctuations in large volumes is accompanied by the formation of a cavity in the observation volume. We develop a model that uses the physics of cavity-water interface formation as a key ingredient and show that it captures the nature of non-Gaussian density fluctuations over a broad region in water and in salt solutions. We discuss the limitations of this model in the very low density region of the distribution. Our calculations provide new insights into the origins of non-Gaussian density fluctuations in water and their connections to lengthscale dependent crossover in hydrophobic hydration.

Osmotic second virial coefficients for hydrophobic interactions as a function of solute size

To gain quantitative insight into how the overall strength of the hydrophobic interaction varies with the molecular size, we calculate osmotic second virial coefficients B for hydrophobic spherical molecules of different diameters σ in water based on molecular simulation with corrections to the finite-size and finite-concentration effects. It is shown that B (<0) changes by two orders of magnitude greater as σ increases twofold and its solute-size dependence is best fit by a power law B ∝ σ^α with the exponent α ≃ 6, which contrasts with the cubic power law that the second virial coefficients of gases obey. It is also found that values of B for the solutes in a nonpolar solvent are positive but they obey the same power law as in water. A thermodynamic identity for B derived earlier [K. Koga, V. Holten, and B. Widom, J. Phys. Chem. B 119, 13391 (2015)] indicates that if B is asymptotically proportional to a power of σ, the exponent α must be equal to or greater than 6.

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.

Grid inhomogeneous solvation theory for cross-solvation in rigid solvents

Grid Inhomogeneous Solvation Theory (GIST) has proven useful to calculate localized thermodynamic properties of water around a solute. Numerous studies have leveraged this information to enhance structure-based binding predictions. We have recently extended GIST toward chloroform as a solvent to allow the prediction of passive membrane permeability. Here, we further generalize the GIST algorithm toward all solvents that can be modeled as rigid molecules. This restriction is inherent to the method and is already present in the inhomogeneous solvation theory. Here, we show that our approach can be applied to various solvent molecules by comparing the results of GIST simulations with thermodynamic integration (TI) calculations and experimental results. Additionally, we analyze and compare a matrix consisting of 100 entries of ten different solvent molecules solvated within each other. We find that the GIST results are highly correlated with TI calculations as well as experiments. For some solvents, we find Pearson correlations of up to 0.99 to the true entropy, while others are affected by the first-order approximation more strongly. The enthalpy-entropy splitting provided by GIST allows us to extend a recently published approach, which estimates higher order entropies by a linear scaling of the first-order entropy, to solvents other than water. Furthermore, we investigate the convergence of GIST in different solvents. We conclude that our extension to GIST reliably calculates localized thermodynamic properties for different solvents and thereby significantly extends the applicability of this widely used method.

The behavior of methane-water mixtures under elevated pressures from simulations using many-body potentials

Non-polarizable empirical potentials have been proven to be incapable of capturing the mixing of methane-water mixtures at elevated pressures. Although density functional theory-based ab initio simulations may circumvent this discrepancy, they are limited in terms of the relevant time and length scales associated with mixing phenomena. Here, we show that the many-body MB-nrg potential, designed to reproduce methane-water interactions with coupled cluster accuracy, successfully captures this phenomenon up to 3 GPa and 500 K with varying methane concentrations. Two-phase simulations and long time scales that are required to fully capture the mixing, affordable due to the speed and accuracy of the MBX software, are assessed. Constructing the methane-water equation of state across the phase diagram shows that the stable mixtures are denser than the sum of their parts at a given pressure and temperature. We find that many-body polarization plays a central role, enhancing the induced dipole moments of methane by 0.20 D during mixing under pressure. Overall, the mixed system adopts a denser state, which involves a significant enthalpic driving force as elucidated by a systematic many-body energy decomposition analysis.

Temperature induced change of TMAO effects on hydrophobic hydration

The effect of trimethylamine-N-oxide (TMAO) on hydrophobic solvation and hydrophobic interactions of methane has been studied with Molecular Dynamics simulations in the temperature range between 280 and 370 K at 1 bar ambient pressure. We observe a temperature transition in the effect of TMAO on the aqueous solubility of methane. At low temperature (280 K), methane is preferentially hydrated, causing TMAO to reduce its solubility in water, while above 320 K, methane preferentially interacts with TMAO, causing TMAO to promote its solubility in water. Based on a statistical-mechanical analysis of the excess chemical potential of methane, we find that the reversible work of creating a repulsive methane cavity opposes the solubility of methane in TMAO/water solution more than in pure water. Below 320 K, this solvent-excluded volume effect overcompensates the contribution of methane–TMAO van der Waals interactions, which promote the solvation of methane and are observed at all temperatures. These van der Waals interactions with the methyl groups of TMAO tip the balance above 320 K where the effect of TMAO on solvent-excluded volume is smaller. We furthermore find that the effective attraction between dissolved methane solutes increases with the increasing TMAO concentration. This observation correlates with a reduction in the methane solubility below 320 K but with an increase in methane solubility at higher temperatures.

The Effects of Flexibility on dsDNA–dsDNA Interactions

A detailed understanding of the physical mechanism of ion-mediated dsDNA interactions is important in biological functions such as DNA packaging and homologous pairing. We report the potential of mean force (PMF) or the effective solvent mediated interactions between two parallel identical dsDNAs as a function of interhelical separation in 0.15 M NaCl solution. Here, we study the influence of flexibility of dsDNAs on the effective interactions by comparing PMFs between rigid models and flexible ones. The role of flexibility of dsDNA pairs in their association is elucidated by studying the energetic properties of Na⁺ ions as well as the fluctuations of ions around dsDNAs. The introduction of flexibility of dsDNAs softens the vdW contact wall and induces more counterion fluctuations around dsDNAs. In addition, flexibility facilitates the Na⁺ ions dynamics affecting their distribution. The results quantify the extent of attraction influenced by dsDNA flexibility and further emphasize the importance of non-continuum solvation approaches.

Nucleic acid folding simulations using a physics-based atomistic free energy model

Performing full-resolution atomistic simulations of nucleic acid folding has remained a challenge for biomolecular modeling. Understanding how nucleic acids fold and how they transition between different folded structures as they unfold and refold has important implications for biology. This paper reports a theoretical model and computer simulation of the ab initio folding of DNA inverted repeat sequences. The formulation is based on an all-atom conformational model of the sugar-phosphate backbone via chain closure, and it incorporates three major molecular-level driving forces-base stacking, counterion-induced backbone self-interactions, and base pairing-via separate analytical theories designed to capture and reproduce the effects of the solvent without requiring explicit water and ions in the simulation. To accelerate computational throughput, a mixed numerical/analytical algorithm for the calculation of the backbone conformational volume is incorporated into the Monte Carlo simulation, and special stochastic sampling techniques were employed to achieve the computational efficiency needed to fold nucleic acids from scratch. This paper describes implementation details, benchmark results, and the advantages and technical challenges with this approach.

The use of vector formalism in the analysis of hydrophobic and electric driving forces in biological assemblies

Hydrophobic forces are known to have a crucial part not only in the conformation of the three-dimensional structure of proteins, but also in the build-up of DNA–protein complexes. Electric forces also play an important role both in the tertiary as well in the quaternary structure of macromolecular associations. Sometimes both hydrophobic and electric interactions add up their strengths to accomplish these structures but in most cases they act in opposite directions. This fact, together with being overall interactions with different ranges, provides a nuanced equilibrium also modulated by the need to comply with steric hindrances and geometric frustration effects. This review focuses on the utility of using the hydrophobic and electrical dipole moment vectors to describe the interactions that give rise to the structures of biological macromolecules. Although different definitions of both electric dipole and hydrophobic moments have been described in the literature, results obtained in biological assemblies demonstrate the principle of the biological membrane model. According to this model, postulated by our group, biological macromolecules tend to associate by aligning their hydrophobic moments in a similar manner to phospholipids in a membrane. Examples of both closed and open structures are used to assess the predictability of our model. We seek agreement between our results with those described in the current literature. The review ends with possible future projections using this formalism.

Hydrophobic association and solvation of neopentane in urea, TMAO and urea-TMAO solutions

A detailed knowledge of hydrophobic association and solvation is crucial for understanding the con-formational stability of proteins and polymers in osmolyte solutions. Using molecular dynamics simulations, it is found that the hydrophobic association of neopentane molecules is greater in a mixed urea-TMAO-water solution in comparison to that in 8 M urea solution, 4 M TMAO solution and neat water. The neopentane association in urea solution is greater than that in TMAO solution or neat water. We find the association is even less in TMAO solution than pure water. From free energy calculations, it is revealed that the neopentane sized cavity creation in mixed urea-TMAO-water is most unfavorable and that causes the highest hydrophobic association. The cavity formation in urea solution is either more unfavorable or comparable to that in TMAO solution. Importantly, it is found that the population of neopentane-neopentane contact pair and the free energy contribution for the cavity formation step in TMAO solution are very sensitive towards the choice of TMAO force-fields. A careful construction of TMAO force-fields is important for studying the hydrophobic association. Interestingly it is observed that the total solute-solvent dispersion interaction energy contribution is always the most favorable in mixed urea-TMAO-water. The magnitude of this interaction energy is greater in urea solution relative to TMAO solution for two different force-fields of TMAO, whereas the lowest value is obtained in pure water. It is revealed that the extent of the overall hydrophobic association in osmolyte solutions is mainly governed by the cavity creation step and it nullifies the contribution coming from the solute-solvent interaction contribution.

Natural organic matter composition and nanomaterial surface coating determine the nature of platinum nanomaterial-natural organic matter corona

Natural organic matter corona (NOM corona) is an interfacial area between nanomaterials (NMs) and the surrounding environment, which gives rise to NMs' unique surface identity. While the importance of the formation of natural organic matter (NOM) corona on engineered nanomaterials (NMs) to NM behavior, fate, and toxicity has been well-established, the understanding of how NOM molecular properties affect NOM corona composition remains elusive due to the complexity and heterogeneity of NOM. This is further complicated by the variation of NOMs from different origins. Here we use eight NOM isolates of different molecular composition and ultrahigh resolution Fourier-transform ion cyclotron resonance-mass spectrometry (ESI-FT-ICR-MS) to determine the molecular composition of platinum NM-NOM corona as a function of NOM composition and NM surface coating. We observed that the composition of PtNM-NOM corona varied with the composition of the original NOM. The percentage of NOM formulas that formed PVP-PtNM-NOM corona was higher than those formed citrate-PtNM-NOM corona, due to increased sorption of NOM formulas, in particular condensed hydrocarbons, to the PVP coating. The relative abundance of heteroatom formulas (CHON, CHOS, and CHOP) was higher in the PVP-PtNM-NOM corona than in citrate-PtNM-corona which was in turn higher than those in the original NOM isolate, indicating preferential partitioning of heteroatom-rich molecules to NM surfaces. The relative abundance of CHO, CHON, CHOS, CHOP and condensed hydrocarbons in PtNM-NOM corona increased with their increase in NOM isolates. Furthermore, PtNM-NOM corona is rich with compounds with high molecular weight. This study demonstrates that the composition and properties of PtNM-NOM corona depend on NOM molecular properties and PtNM surface coating. The results here provide evidence of molecular interactions between NOM and NMs, which are critical to understanding NM colloidal properties (e.g., surface charge and stability), interaction forces (e.g., van der Waals and hydrophobic), environmental behaviors (e.g., aggregation, dissolution, sulfidation, etc.), and biological effects (e.g., uptake, bioaccumulation, and toxicity).

Explicit solvation thermodynamics in ionic solution: extending grid inhomogeneous solvation theory to solvation free energy of salt-water mixtures

Hydration thermodynamics play a fundamental role in fields ranging from the pharmaceutical industry to environmental research. Numerous methods exist to predict solvation thermodynamics of compounds ranging from small molecules to large biomolecules. Arguably the most precise methods are those based on molecular dynamics (MD) simulations in explicit solvent. One theory that has seen increased use is inhomogeneous solvation theory (IST). However, while many applications require accurate description of salt-water mixtures, no implementation of IST is currently able to estimate solvation properties involving more than one solvent species. Here, we present an extension to grid inhomogeneous solvation theory (GIST) that can take salt contributions into account. At the example of carbazole in 1 M NaCl solution, we compute the solvation energy as well as first and second order entropies. While the effect of the first order ion entropy is small, both the water-water and water-ion entropies contribute strongly. We show that the water-ion entropies are efficiently approximated using the Kirkwood superposition approximation. However, this approach cannot be applied to the water-water entropy. Furthermore, we test the quantitative validity of our method by computing salting-out coefficients and comparing them to experimental data. We find a good correlation to experimental salting-out constants, while the absolute values are overpredicted due to the approximate second order entropy. Since ions are frequently used in MD, either to neutralize the system or as a part of the investigated process, our method greatly extends the applicability of GIST. The use-cases range from biopharmaceuticals, where many assays require high salt concentrations, to environmental research, where solubility in sea water is important to model the fate of organic substances.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Healable, Adhesive, and Conductive Nanocomposite Hydrogels with Ultrastretchability for Flexible Sensors

In recent years, conductive hydrogels have generated tremendous attention in biomedicals and bioelectronics fields due to their excellent physiochemical properties. In this study, a physically cross-linked conducting hydrogel has been designed in combination with cellulose nanocrystalline (CNC), polyacrylic acid (PAA) chains, laurel methacrylate, and sodium dodecyl sulfate. The obtained result shows that the hydrogel prepared is ultrastretchable, mechanically robust, transparent, biocompatible, conductive, and self-healing. The mechanical property of the prepared hydrogel is optimized through variation of the CNC content. The optimal hydrogel (CNC-1/PAA) exhibits an impressive mechanics, including high stretchability (∼1800%) and compressibility, good elasticity, and fatigue resistance. Furthermore, the conductivity of the hydrogel enables tensile strain- and pressure-sensing capabilities. The CNC/PAA-based flexible sensors are successfully designed, which shows high sensitivity, fast response (290 ms), and excellent cycle stability as well as the pressure sensing capability. As a result, the designed hydrogel has the ability to sense and detect diverse human motion, including elbow/finger/wrist bending and speaking, which demonstrates that the designed self-healing conductive hydrogels have significant potential for applications in flexible electronics.

Generalizing Continuum Solvation in Crystal to Nonaqueous Solvents: Implementation, Parametrization, and Application to Molecules and Surfaces

We present an extension of a generalized finite-difference Poisson-Boltzmann (FDPB) continuum solvation model based on a self-consistent reaction field treatment to nonaqueous solvents. Implementation and reparametrization of the cavitation, dispersion, and structural (CDS) effects nonelectrostatic model are presented in CRYSTAL, with applications to both finite and infinite periodic systems. For neutral finite systems, computed errors with respect to available experimental data on free energies of solvation of 2523 solutes in 91 solvents, as well as 144 transfer energies from water to 14 organic solvents are on par with the reference SM12 solvation model for which the CDS parameters have been developed. Calculations performed on a TiO₂ anatase surface and compared to VASPsol data revealed an overall very good agreement of computed solvation energies, surface energies, as well as band structure changes upon solvation in three different solvents, validating the general applicability of the reparametrized FDPB approach to neutral nonperiodic and periodic solutes in aqueous and nonaqueous solvents. For ionic species, while the reparametrized CDS model led to large errors on free energies of solvation of anions, addition of a corrective term based on Abraham's acidity of the solvent significantly improved the accuracy of the proposed continuum solvation model, leading to errors on aqueous pK_a of a test set of 83 solutes divided by a factor of 4 compared to the reference solvation model based on density (SMD). Overall, therefore, these encouraging results demonstrate that the generalized FDPB continuum solvation model can be applied to a broad range of solutes in various solvents, ranging from finite neutral or charged solutes to extended periodic surfaces.

Effects of Salts on the Solvation of Hydrophobic Objects in Water

The solvation of large, hydrophobic objects in water is facilitated by the formation of a low-density region surrounding the solute that is separated from the bulk liquid by an interface, which has a structure that resembles that between a liquid and its vapor. We study the effect of dissolved sodium chloride on the thermodynamics of solvation and on the solvent structure surrounding hydrophobic solutes in the size regime where this interface is not yet fully formed. Using biased Molecular Dynamics computer simulations, we calculate solvation free energies and orientational distributions of water molecules at different salt concentrations and solute sizes. We find that while the effects of sodium chloride on thermodynamic properties are small, the ions' response to the presence of a hydrophobic solute differs significantly from that of the water. Our findings provide mechanistic insight into how our understanding of hydrophobic solvation in water can be extended to electrolyte solutions.

Efficient Alchemical Intermediate States in Free Energy Calculations Using λ-Enveloping Distribution Sampling

Alchemical free energy calculations generally require intermediate states along a coupling parameter λ to establish sufficient phase space overlap for obtaining converged results. Such intermediate states can also be engineered to lower the energy barriers and, consequently, reduce the required sampling time. The recently introduced λ-enveloping distribution sampling (λ-EDS) scheme combines the properties of the minimum variance pathway and the EDS methods to improve sampling and allow for larger steps along the alchemical pathway compared to conventional approaches. This scheme also eliminates the need for soft-core potentials and retains the behavior of conventional λ-intermediate states as a limiting case. In this study, an automated procedure is developed to select the parameters of λ-EDS for optimal performance. The underlying theory is illustrated based on simulations of simple test systems (bond length changes in harmonic oscillators, mutations of dihedral angles, and charge creation in water), as well as on the calculation of the absolute hydration free energies of 12 small organic molecules.

Bridging Gaussian Density Fluctuations from Microscopic to Macroscopic Volumes: Applications to Non-Polar Solute Hydration Thermodynamics

The hydration of hydrophobic solutes is intimately related to the spontaneous formation of cavities in water through ambient density fluctuations. Information theory-based modeling and simulations have shown that water density fluctuations in small volumes are approximately Gaussian. For limiting cases of microscopic and macroscopic volumes, water density fluctuations are known exactly and are rigorously related to the density and isothermal compressibility of water. Here, we develop a theory—interpolated gaussian fluctuation theory (IGFT)—that builds an analytical bridge to describe water density fluctuations from microscopic to molecular scales. This theory requires no detailed information about the water structure beyond the effective size of a water molecule and quantities that are readily obtained from water’s equation-of-state—namely, the density and compressibility. Using simulations, we show that IGFT provides a good description of density fluctuations near the mean, that is, it characterizes the variance of occupancy fluctuations over all solute sizes. Moreover, when combined with the information theory, IGFT reproduces the well-known signatures of hydrophobic hydration, such as entropy convergence and solubility minima, for atomic-scale solutes smaller than the crossover length scale beyond which the Gaussian assumption breaks down. We further show that near hydrophobic and hydrophilic self-assembled monolayer surfaces in contact with water, the normalized solvent density fluctuations within observation volumes depend similarly on size as observed in the bulk, suggesting the feasibility of a modified version of IGFT for interfacial systems. Our work highlights the utility of a density fluctuation-based approach toward understanding and quantifying the solvation of non-polar solutes in water and the forces that drive them toward surfaces with different hydrophobicities.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. II. Large Solvophovic Solutes

We use molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy as a function of temperature and pressure for hard-sphere solutes with diameters ranging from 4 to 36 Å in TIP4P/2005 and Jagla water-like solvents exhibiting unusual thermodynamics. An important piece of our discussion focuses on the nanometer-sized solutes, for which simulation results are found to be accounted for by the most basic classical thermodynamic treatment contemplating bulk and interfacial contributions to the solvation free energy. Thus, since water's liquid-vapor surface tension is only special inasmuch as it takes unusually large values, solvent's water-like unusual thermodynamics manifests through a term proportional to the pressure in the solvation free energy. As a result, such solvent's unusual thermodynamics is found to be relevant to the temperature and pressure dependence of the isochoric solvation energy and entropy as well as to the isothermal density derivative of the solvation free energy. This sharply contrasts with the findings of the first part of this series indicating that the solvation free energy of small hard spheres responds to temperature and pressure changes as solvent's density does, with such a contrasting picture embodying a "pressure-density dichotomy." As for the length-scale dependence, we find the zero nominal pressure and the solvent's temperature of the maximum density as singular conditions for cavity surface-area size scaling of large solutes to occur for all solvation quantities. We finally argue that the overall study undertaken in this series suggests that water's unusual thermodynamics may be relevant to the thermodynamic stability of clusters of solvophobic units in the temperature-pressure plane. Some comments on the role of solute-solvent attractive interactions are also depicted.

Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5 k_BT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.

Length-Scale Effects in Hydrophobic Polymer Collapse Transitions

The study of molecular mechanisms for cosolvent-driven hydrophobic polymer collapse transitions in water is of pivotal importance in the field of smart responsive materials. Computational studies together with complementary experimental data have led to the discovery and understanding of new phenomena in recent years. However, elementary mechanisms, generally contributing to polymer coil-globule transitions in different classes of cosolvent-water systems, remain elusive due to compensating energy-entropy effects. Herein, I discuss the role of length scales in polymer solubility problems. New ideas on surfactant mechanisms are discussed based on examples in which these mechanisms drive polymer swelling or collapse.

Characterizing the Interplay between Polymer Solvation and Conformation

Conformational transitions of flexible molecules, especially those driven by hydrophobic effects, tend to be hindered by desolvation barriers. For such transitions, it is thus important to characterize and understand the interplay between solvation and conformation. Using specialized molecular simulations, here we perform such a characterization for a hydrophobic polymer solvated in water. We find that an external potential, which unfavorably perturbs the polymer hydration waters, can trigger a coil-to-globule or collapse transition, and that the relative stabilities of the collapsed and extended states can be quantified by the strength of the requisite potential. Our results also provide mechanistic insights into the collapse transition, highlighting that the bottleneck to polymer collapse is the formation of a sufficiently large cluster, and the collective dewetting of such a cluster. We also study the collapse of the hydrophobic polymer in octane, a nonpolar solvent, and interestingly, we find that the mechanistic details of the transition are qualitatively similar to that in water.

Protein unfolded states populated at high and ambient pressure are similarly compact

The relationship between the dimensions of pressure-unfolded states of proteins compared with those at ambient pressure is controversial; resolving this issue is related directly to the mechanisms of pressure denaturation. Moreover, a significant pressure dependence of the compactness of unfolded states would complicate the interpretation of folding parameters from pressure perturbation and make comparison to those obtained using alternative perturbation approaches difficult. Here, we determined the compactness of the pressure-unfolded state of a small, cooperatively folding model protein, CTL9-I98A, as a function of temperature. This protein undergoes both thermal unfolding and cold denaturation, and the temperature dependence of the compactness at atmospheric pressure is known. High-pressure small angle x-ray scattering studies, yielding the radius of gyration and high-pressure diffusion ordered spectroscopy NMR experiments, yielding the hydrodynamic radius were carried out as a function of temperature at 250 MPa, a pressure at which the protein is unfolded. The radius of gyration values obtained at any given temperature at 250 MPa were similar to those reported previously at ambient pressure, and the trends with temperature are similar as well, although the pressure-unfolded state appears to undergo more pronounced expansion at high temperature than the unfolded state at atmospheric pressure. At 250 MPa, the compaction of the unfolded chain was maximal between 25 and 30°C, and the chain expanded upon both cooling and heating. These results reveal that the pressure-unfolded state of this protein is very similar to that observed at ambient pressure, demonstrating that pressure perturbation represents a powerful approach for observing the unfolded states of proteins under otherwise near-native conditions.

A Data-Driven Hydrophobicity Scale for Predicting Liquid-Liquid Phase Separation of Proteins

An accurate model for macroscale disordered assemblies of biological macromolecules such as those formed in so-called membraneless organelles would greatly assist in studying their structure, function, and dynamics. Recent evidence has suggested that liquid-liquid phase separation (LLPS) underlies the formation of membraneless organelles. While the general mechanism of exchange of macromolecule/water for macromolecule/macromolecule interactions is known to be the driving force for LLPS, the specific interactions involved are not well understood. One way that protein-water and protein-protein interactions have been understood historically is via hydrophobicity scales. However, these scales are typically optimized for describing these relative interactions in certain cases, such as protein folding or insertion of proteins into membranes. To better describe the relative interactions of proteins that undergo LLPS, we have developed a new, data-driven hydrophobicity scale. To determine the new scale, we used coarse-grained molecular dynamics simulations using the hydrophobicity scale coarse-grained model, which relates the interactions between amino acids to their hydrophobicity. Hydrophobicity values were determined via the force-balance method on a library of proteins that includes unfolded, intrinsically disordered, and phase-separating proteins (PSP). The resulting hydrophobicity scale can better predict whether a given protein will undergo LLPS at physiological conditions by using coarse-grained molecular dynamics simulations than existing hydrophobicity scales. This new scale confirms the importance of π-π interactions between amino acids as important drivers of LLPS. This new hydrophobicity scale provides a convenient and compact description of protein-protein interactions for proteins that undergo LLPS and could be used to develop new models to describe interactions between PSP and other components, such as nucleic acids.

Insignificant Effect of Temperature on the Structure and Angular Jumps of Water near a Hydrophobic Cation

The ambiguity in the behavior of water molecules around hydrophobic solutes is a matter of interest for many studies. Motivated by the earlier results on the dynamics of water molecules around tetramethylammonium (TMA) cation, we present the effect of temperature on the structure and angular jumps of water due to hydrophobicity using first principles molecular dynamics simulations. The average intermolecular distance between the central oxygen and four nearest neighbors is found to be the highest for water molecules in the solvation shell of TMA at 400 K, followed by the same at 330 K. The hydrogen bond (HB) donor-acceptor count, HB per water molecule, and tetrahedral order parameter suggests the loss of tetrahedrality in the solvation shell. Elevated temperature affects the tetrahedral parameter in local regions. The HB jump mechanism is studied for methyl hydrogen and water molecules in the solvation shell. Observations hint at the presence of dangling water molecules in the vicinity of the hydrophobic cation, and no evidence is found for the enhanced structural ordering of nearby water molecules.

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.

A minireview on the perturbation effects of polar groups to direct nanoscale hydrophobic interaction and amphiphilic peptide assembly

Hydrophobic interaction provides the essential driving force for creating diverse native and artificial supramolecular architectures. Accumulating evidence leads to a hypothesis that the hydrophobicity of a nonpolar patch of a molecule is non-additive and susceptible to the chemical context of a judicious polar patch. However, the quantification of the hydrophobic interaction at the nanoscale remains a central challenge to validate the hypothesis. In this review, we aim to outline the recent efforts made to determine the hydrophobic interaction at a nanoscopic length scale. The advances achieved in the understanding of proximal polar groups perturbing the magnitude of hydrophobic interaction generated by the nonpolar patch are introduced. We will also discuss the influence of chemical heterogeneity on the modulation of amphiphilic peptide/protein assembly and molecular recognition.

Hydrophobic interaction provides the essential driving force for creating diverse native and artificial supramolecular architectures.