Field-SEA: a model for computing the solvation free energies of nonpolar, polar, and charged solutes in water

Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains

The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.

Free-energy decomposition of salt effects on the solubilities of small molecules and the role of excluded-volume effects

The roles of cations and anions are different in the perturbation on solvation, and thus, the analyses of the separated contributions from cations and anions are useful to establish molecular pictures of ion-specific effects. In this work, we investigate the effects of cations, anions, and water separately in the solvation of n-alcohols and n-alkanes by free-energy decomposition. By utilising energy-representation theory of solvation, we address the contributions arising from the direct solute-solvent interactions and the excluded-volume effects. It is found that the change in solvation of n-alcohols and n-alkanes upon addition of salt depends primarily on the anion species. The direct interaction between the anion and solute is in agreement with the Setschenow coefficient in terms of the ranking of salting-in and salting-out for n-alkanes, which corresponds to the extent of accumulation of the anion on the solute surface. For each of the n-alcohols and n-alkanes examined, the excluded-volume component in the Setschenow coefficient is well correlated to the (total) Setschenow coefficient when the salt effects are concerned. The ranking of the excluded-volume component in the variation of the salt species is parallel to the water contribution, which is correlated further to the change in the water density upon the addition of the salt.

Cationic Side Chain Identity Directs the Hydrophobically Driven Self-Assembly of Amphiphilic β-Peptides in Aqueous Solution

Hydrophobic interactions mediated by nonpolar molecular fragments in water are influenced by local chemical and physical contexts in ways that are not yet fully understood. Here, we use globally amphiphilic (GA) β-peptides (GA-Lys and GA-Arg) with stable conformations to explore if replacement of β³-homolysine (βLys) with β³-homoarginine (βArg) influences the hydrophobically driven assembly of these peptides in bulk aqueous solution. The studies were conducted in 10 mM triethanolamine buffer at pH 7, where both βLys (ammonium) and βArg (guanidinium) side chains are substantially protonated. Comparisons of light scattering measurements and cryo-electron micrographs before and after the addition of 60 vol% MeOH indicate very different outcomes of the hydrophobically driven assembly of AcY-GA-Lys versus AcY-GA-Arg (AcY denotes an N-acetylated-β³-homotyrosine (βTyr) at each N-terminus). Nuclear magnetic resonance and analytical ultracentrifugation confirm that AcY-GA-Lys assembles into large aggregates in aqueous buffer, whereas AcY-GA-Arg at comparable concentrations forms only small oligomers. Titration of AcY-GA-Arg into aqueous solutions of AcY-GA-Lys reveals that the driving force for AcY-GA-Lys association is far stronger than that for AcY-GA-Arg association. We discuss these results in the light of past experimental observations involving single molecule force measurements with GA β-peptides and hydrophobically driven dimerization of conventional peptides that form a GA α-helix upon dimerization (but do not display the Lys versus Arg trend predicted by extrapolating from the earlier AFM studies with β-peptides). Overall, our results establish that the identity of proximal cationic groups, ammonium versus guanidinium, profoundly modulates the hydrophobically driven self-assembly of conformationally stable β-peptides in bulk aqueous solution.

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.

Atomic Force Microscopy and Molecular Dynamics Simulations for Study of Lignin Solution Self-Assembly Mechanisms in Organic-Aqueous Solvent Mixtures

Lignin-based nanomaterials fabricated by solution self-assembly in organic-aqueous solvent mixtures are among the most attractive biomass-derived products. To accurately control the structure, size, and properties of lignin-based nanomaterials, it is important to achieve fundamental understanding of its dissolution and aggregation mechanisms. In this work, atomic force microscopy (AFM) and molecular dynamics (MD) simulations are employed to explore the dissolution and aggregation behavior of enzymatic hydrolysis lignin (EHL) in different organic-aqueous solvent mixtures at molecular scale. EHL was found to dissolve well in appropriate organic-aqueous solvent mixtures, such as acetone-water mixture with a volume ratio of 7:3, whereas it aggregated in pure water, ethanol, acetone, and tetrahydrofuran. The interactions between the EHL-coated AFM probe and the substrate were 1.21±0.18 and 0.75±0.35 mN m^-1 in water and acetone, respectively. In comparison, the interaction decreased to 0.15±0.08 mN m^-1 in acetone-water mixture (7:3 v/v). MD simulations further indicate that the hydrophobic skeleton and hydrophilic groups of lignin could be solvated by acetone and water molecules, respectively, which significantly promoted its dissolution. Conversely, only the hydrophobic skeleton or the hydrophilic groups were solvated in organic solvent or water, respectively, inducing serious aggregation of lignin.

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.

Hexahydrated Mg2+ Binding and Outer-Shell Dehydration on RNA Surface

The interaction between metal ions, especially Mg²⁺ ions, and RNA plays a critical role in RNA folding. Upon binding to RNA, a metal ion that is fully hydrated in bulk solvent can become dehydrated. Here we use molecular dynamics simulation to investigate the dehydration of bound hexahydrated Mg²⁺ ions. We find that a hydrated Mg²⁺ ion in the RNA groove region can involve significant dehydration in the outer hydration shell. The first or innermost hydration shell of the Mg²⁺ ion, however, is retained during the simulation because of the strong ion-water electrostatic attraction. As a result, water-mediated hydrogen bonding remains an important form for Mg²⁺-RNA interaction. Analysis for ions at different binding sites shows that the most pronounced water deficiency relative to the fully hydrated state occurs at a radial distance of around 11 Å from the center of the ion. Based on the independent 200 ns molecular dynamics simulations for three different RNA structures (Protein Data Bank: 1TRA, 2TPK, and 437D), we find that Mg²⁺ ions overwhelmingly dominate over monovalent ions such as Na⁺ and K⁺ in ion-RNA binding. Furthermore, application of the free energy perturbation method leads to a quantitative relationship between the Mg²⁺ dehydration free energy and the local structural environment. We find that ΔΔG_hyd, the change of the Mg²⁺ hydration free energy upon binding to RNA, varies linearly with the inverse distance between the Mg²⁺ ion and the nearby nonbridging oxygen atoms of the phosphate groups, and ΔΔG_hyd can reach -2.0 kcal/mol and -3.0 kcal/mol for an Mg²⁺ ion bound to the surface and to the groove interior, respectively. In addition, the computation results in an analytical formula for the hydration ratio as a function of the average inverse Mg²⁺-O distance. The results here might be useful for further quantitative investigations of ion-RNA interactions in RNA folding.

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects

Metal ions play essential roles in nucleic acids folding and stability. The interaction between metal ions and nucleic acids can be highly complicated because of the interplay between various effects such as ion correlation, fluctuation, and dehydration. These effects may be particularly important for multivalent ions such as Mg²⁺ ions. Previous efforts to model ion correlation and fluctuation effects led to the development of the Monte Carlo tightly bound ion model. Here, by incorporating ion hydration/dehydration effects into the Monte Carlo tightly bound ion model, we develop a, to our knowledge, new approach to predict ion binding. The new model enables predictions for not only the number of bound ions but also the three-dimensional spatial distribution of the bound ions. Furthermore, the new model reveals several intriguing features for the bound ions such as the mutual enhancement/inhibition in ion binding between the fully hydrated (diffuse) ions, the outer-shell dehydrated ions, and the inner-shell dehydrated ions and novel features for the monovalent-divalent ion interplay due to the hydration effect.

MXene molecular sieving membranes for highly efficient gas separation

Molecular sieving membranes with sufficient and uniform nanochannels that break the permeability-selectivity trade-off are desirable for energy-efficient gas separation, and the arising two-dimensional (2D) materials provide new routes for membrane development. However, for 2D lamellar membranes, disordered interlayer nanochannels for mass transport are usually formed between randomly stacked neighboring nanosheets, which is obstructive for highly efficient separation. Therefore, manufacturing lamellar membranes with highly ordered nanochannel structures for fast and precise molecular sieving is still challenging. Here, we report on lamellar stacked MXene membranes with aligned and regular subnanometer channels, taking advantage of the abundant surface-terminating groups on the MXene nanosheets, which exhibit excellent gas separation performance with H2 permeability >2200 Barrer and H2/CO2 selectivity >160, superior to the state-of-the-art membranes. The results of molecular dynamics simulations quantitatively support the experiments, confirming the subnanometer interlayer spacing between the neighboring MXene nanosheets as molecular sieving channels for gas separation.

How Water's Properties Are Encoded in Its Molecular Structure and Energies

How are water's material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth's living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies-water's solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions-hydroxide and protons-diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water's molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water's orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties.

"Solvent hydrogen-bond occlusion": A new model of polar desolvation for biomolecular energetics

Water engages in two important types of interactions near biomolecules: it forms ordered "cages" around exposed hydrophobic regions, and it participates in hydrogen bonds with surface polar groups. Both types of interaction are critical to biomolecular structure and function, but explicitly including an appropriate number of solvent molecules makes many applications computationally intractable. A number of implicit solvent models have been developed to address this problem, many of which treat these two solvation effects separately. Here, we describe a new model to capture polar solvation effects, called SHO ("solvent hydrogen-bond occlusion"); our model aims to directly evaluate the energetic penalty associated with displacing discrete first-shell water molecules near each solute polar group. We have incorporated SHO into the Rosetta energy function, and find that scoring protein structures with SHO provides superior performance in loop modeling, virtual screening, and protein structure prediction benchmarks. These improvements stem from the fact that SHO accurately identifies and penalizes polar groups that do not participate in hydrogen bonds, either with solvent or with other solute atoms ("unsatisfied" polar groups). We expect that in future, SHO will enable higher-resolution predictions for a variety of molecular modeling applications. © 2017 Wiley Periodicals, Inc.

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.

Adapting the semi-explicit assembly solvation model for estimating water-cyclohexane partitioning with the SAMPL5 molecules

We describe here some tests we made in the SAMPL5 communal event of 'Semi-Explicit Assembly' (SEA), a recent method for computing solvation free energies. We combined the prospective tests of SAMPL5 with followup retrospective calculations, to improve two technical aspects of the field variant of SEA. First, SEA uses an approximate analytical surface around the solute on which a water potential is computed. We have improved and simplified the mathematical model of that surface. Second, some of the solutes in SAMPL5 were large enough to need a way to treat solvating waters interacting with 'buried atoms', i.e. interior atoms of the solute. We improved SEA with a buried-atom correction. We also compare SEA to Thermodynamic Integration molecular dynamics simulations, so that we can sort out force field errors.

Origin of Asymmetric Solvation Effects for Ions in Water and Organic Solvents Investigated Using Molecular Dynamics Simulations: The Swain Acity-Basity Scale Revisited

The asymmetric solvation of ions can be defined as the tendency of a solvent to preferentially solvate anions over cations or cations over anions, at identical ionic charge magnitudes and effective sizes. Taking water as a reference, these effects are quantified experimentally for many solvents by the relative acity (A) and basity (B) parameters of the Swain scale. The goal of the present study is to investigate the asymmetric solvation of ions using molecular dynamics simulations, and to connect the results to this empirical scale. To this purpose, the charging free energies of alkali and halide ions, and of their hypothetical oppositely charged counterparts, are calculated in a variety of solvents. In a first set of calculations, artificial solvent models are considered that present either a charge or a shape asymmetry at the molecular level. The solvation asymmetry, probed by the difference in charging free energy between the two oppositely charged ions, is found to encompass a term quadratic in the ion charge, related to the different solvation structures around the anion and cation, and a term linear in the ion charge, related to the solvation structure around the uncharged ion-sized cavity. For these simple solvent models, the two terms are systematically counteracting each other, and it is argued that only the quadratic term should be retained when comparing the results of simulations involving physical solvents to experimental data. In a second set of calculations, 16 physical solvents are considered. The theoretical estimates for the acity A are found to correlate very well with the Swain parameters, whereas the correlation for B is very poor. Based on this observation, the Swain scale is reformulated into a new scale involving an asymmetry parameter Σ, positive for acitic solvents and negative for basitic ones, and a polarity parameter Π. This revised scale has the same predictive power as the original scale, but it characterizes asymmetry in an absolute sense, the atomistic simulations playing the role of an extra-thermodynamic assumption, and is optimally compatible with the simulation results. Considering the 55 solvents in the Swain set, it is observed that a moderate basity (Σ between -0.9 and -0.3, related to electronic polarization) represents the baseline for most solvents, while a highly variable acity (Σ between 0.0 and 3.0, related to hydrogen-bond donor capacity modulated by inductive effects) represents a landmark of protic solvents.

Small molecule solvation changes due to the presence of salt are governed by the cost of solvent cavity formation and dispersion

We are interested in the free energies of transferring nonpolar solutes into aqueous NaCl solutions with salt concentrations upwards of 2 M, the Hofmeister regime. We use the semi-explicit assembly (SEA) computational model to represent these electrolyte solutions. We find good agreement with experiments (Setschenow coefficients) on 43 nonpolar and polar solutes and with TIP3P explicit-solvent simulations. Besides being much faster than explicit solvent calculations, SEA is more accurate than the PB models we tested, successfully capturing even subtle salt effects in both the polar and nonpolar components of solvation. We find that the salt effects are mainly due to changes in the cost of forming nonpolar cavities in aqueous NaCl solutions, and not mainly due to solute-ion electrostatic interactions.

Hydration in discrete water (II): from neutral to charged solutes

In our previous work, we introduced a solvation model based on discrete solvent representation and demonstrated its ability to estimate hydration free energies for neutral solutes. Here, we present modifications extending the applicability of the model to charged solutes. They include improvements in the representation of the first hydration shell and systematic treatment of long-range interactions. While sharing computational efficiency of implicit solvent models, our approach avoids some of their important limitations, both in the context of electrostatic and nonpolar hydration effects: it naturally captures hydration asymmetry of opposite charges, it relies on solute description by standard all atom force fields instead of utilizing specialized sets of atomic parameters, it predicts solvent distribution in space without the need to geometrically define solvent accessible surface. By combining discrete solvent representation in vicinity of a solute with continuum description of long-range interactions, the model addresses two distinct aspects of biomolecular hydration: complex, short-range effects arising due to molecular nature of aqueous solvent, and bulk contributions. We demonstrate that the model provides good agreement with experimental results for an extensive set of roughly 700 diverse compounds, including neutral and charged solutes with hydration free energies ranging from +3.4 to -536 kcal/mol.

Accurate evaluation of charge asymmetry in aqueous solvation

Charge hydration asymmetry (CHA)-a characteristic dependence of hydration free energy on the sign of the solute charge-quantifies the asymmetric response of water to electric field at microscopic level. Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in chemistry and biology. However, measuring hydration energies of charged species is fraught with significant difficulties, which lead to unacceptably large (up to 300%) variation in the available estimates of the CHA effect. We circumvent these difficulties by developing a framework which allows us to extract and accurately estimate the intrinsic propensity of water to exhibit CHA from accurate experimental hydration free energies of neutral polar molecules. Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K(+) /F(-) pair-a classical probe for the effect. We use these "CHA-conjugate" molecule pairs to quantify the intrinsic charge-asymmetric response of water to the microscopic charge perturbations: the asymmetry of the response is strong, ∼50% of the average hydration free energy of these molecules. The ability of widely used classical water models to predict hydration energies of small molecules correlates with their ability to predict CHA.

FreeSolv: a database of experimental and calculated hydration free energies, with input files

This work provides a curated database of experimental and calculated hydration free energies for small neutral molecules in water, along with molecular structures, input files, references, and annotations. We call this the Free Solvation Database, or FreeSolv. Experimental values were taken from prior literature and will continue to be curated, with updated experimental references and data added as they become available. Calculated values are based on alchemical free energy calculations using molecular dynamics simulations. These used the GAFF small molecule force field in TIP3P water with AM1-BCC charges. Values were calculated with the GROMACS simulation package, with full details given in references cited within the database itself. This database builds in part on a previous, 504-molecule database containing similar information. However, additional curation of both experimental data and calculated values has been done here, and the total number of molecules is now up to 643. Additional information is now included in the database, such as SMILES strings, PubChem compound IDs, accurate reference DOIs, and others. One version of the database is provided in the Supporting Information of this article, but as ongoing updates are envisioned, the database is now versioned and hosted online. In addition to providing the database, this work describes its construction process. The database is available free-of-charge via http://www.escholarship.org/uc/item/6sd403pz .

FreeSolv: a database of experimental and calculated hydration free energies, with input files

This work provides a curated database of experimental and calculated hydration free energies for small neutral molecules in water, along with molecular structures, input files, references, and annotations. We call this the Free Solvation Database, or FreeSolv. Experimental values were taken from prior literature and will continue to be curated, with updated experimental references and data added as they become available. Calculated values are based on alchemical free energy calculations using molecular dynamics simulations. These used the GAFF small molecule force field in TIP3P water with AM1-BCC charges. Values were calculated with the GROMACS simulation package, with full details given in references cited within the database itself. This database builds in part on a previous, 504-molecule database containing similar information. However, additional curation of both experimental data and calculated values has been done here, and the total number of molecules is now up to 643. Additional information is now included in the database, such as SMILES strings, PubChem compound IDs, accurate reference DOIs, and others. One version of the database is provided in the Supporting Information of this article, but as ongoing updates are envisioned, the database is now versioned and hosted online. In addition to providing the database, this work describes its construction process. The database is available free-of-charge via http://www.escholarship.org/uc/item/6sd403pz .

Using interpolation for fast and accurate calculation of ion-ion interactions

We perform extensive molecular dynamics (MD) simulations between pairs of ions of various diameters (2-5.5 Å in increments of 0.5 Å) and charge (+1 or -1) interacting in explicit water (TIP3P) under ambient conditions. We extract their potentials of mean force (PMFs). We develop an interpolation scheme, called i-PMF, that is capable of capturing the full set of PMFs for arbitrary combinations of ion sizes ranging from 2 to 5.5 Å. The advantage of the interpolation process is computational cost. Whereas it can take 100 h to simulate each PMF by MD, we can compute an equivalently accurate i-PMF in seconds. This process may be useful for rapid and accurate calculation of the strengths of salt bridges and the effects of bridging waters in biomolecular simulations. We also find that our data is consistent with Collins' "law of matching affinities" of ion solubilities: small-small or large-large ion pairs are poorly soluble in water, whereas small-large are highly soluble.

Testing the semi-explicit assembly model of aqueous solvation in the SAMPL4 challenge

Here, we test a method, called semi-explicit assembly (SEA), that computes the solvation free energies of molecules in water in the SAMPL4 blind test challenge. SEA was developed with the intention of being as accurate as explicit-solvent models, but much faster to compute. It is accurate because it uses pre-simulations of simple spheres in explicit solvent to obtain structural and thermodynamic quantities, and it is fast because it parses solute free energies into regionally additive quantities. SAMPL4 provided us the opportunity to make new tests of SEA. Our tests here lead us to the following conclusions: (1) The newest version, called Field-SEA, which gives improved predictions for highly charged ions, is shown here to perform as well as the earlier versions (dipolar and quadrupolar SEA) on this broad blind SAMPL4 test set. (2) We find that both the past and present SEA models give solvation free energies that are as accurate as TIP3P. (3) Using a new approach for force field parameter optimization, we developed improved hydroxyl parameters that ensure consistency with neat-solvent dielectric constants, and found that they led to improved solvation free energies for hydroxyl-containing compounds in SAMPL4. We also learned that these hydroxyl parameters are not just fixing solvent exposed oxygens in a general sense, and therefore do not improve predictions for carbonyl or carboxylic-acid groups. Other such functional groups will need their own independent optimizations for potential improvements. Overall, these tests in SAMPL4 indicate that SEA is an accurate, general and fast new approach to computing solvation free energies.