Application of an extended RISM equation to dipolar and quadrupolar fluids

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.

Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids

The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.

Electrocatalytic Mechanisms for an Oxygen Evolution Reaction at a Rhombohedral Boron Monosulfide Electrode/Alkaline Medium Interface

Rhombohedral boron monosulfide (r-BS) with a layer stacking structure is a promising electrocatalyst for an oxygen evolution reaction (OER) within an alkaline solution. We investigated the catalytic mechanisms at the r-BS electrode/alkaline medium interface for an OER using hybrid solvation theory based on the first-principles method combined with classical solution theory. In this study, we elucidate the activities of the OER at the outermost r-BS sheet with and without various surface defects. The Gibbs free energies along the OER path indicate that the boron vacancies at the first and second layers of the r-BS surface (VB1 and VB2) can promote the OER. However, we found that the VB1 is easily occupied by the oxygen atom during the OER, degrading its electrocatalytic performance. In contrast, VB2 is suitable for the active site of the OER due to its structure stability. Next, we applied a bias voltage with the OER potential to the r-BS electrode. The bias voltage incorporates the positive excess surface charge into pristine r-BS and VB2, which can be understood by the relationship between the OER potential and potentials of zero charge at the r-BS electrode. Because the OH- ions are the starting point of the OER, the positively charged surface is kinetically favorable for the electrocatalyst owing to the attractive interaction with the OH- ions. Finally, we qualitatively discuss the flat-band potential at a semiconductor/alkaline solution interface. It suggests that p-type carrier doping could promote the catalytic performance of r-BS. These results explain the previous measurement of the OER performance with the r-BS-based electrode and provide valuable insights into developing a semiconductor electrode/water interface.

Orientational Ordering in Nano-confined Polar Liquids

Water and other polar liquids exhibit nanoscale structuring near charged interfaces. When a polar liquid is confined between two charged surfaces, the interfacial solvent layers begin to overlap, resulting in solvation forces. Here, we perform molecular dynamics simulations of polar liquids with different dielectric constants and molecular shapes and sizes confined between charged surfaces, demonstrating strong orientational ordering in the nanoconfined liquids. To rationalize the observed structures, we apply a coarse-grained continuum theory that captures the orientational ordering and solvation forces of those liquids. Our findings reveal the subtle behavior of different nanoconfined polar liquids and establish a simple law for the decay length of the interfacial orientations of the solvents, which depends on their molecular size and polarity. These insights shed light on the nature of solvation forces, which are important in colloid and membrane science, scanning probe microscopy, and nano-electrochemistry.

Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions

Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges─local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. The simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent-solvent and solute-solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.

The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules

The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute-solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl^-, [ClO]^- (a two-site anion), and [NO₂]^- (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl^-. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.

Theoretical Analysis on the Stability of 1-Pyrenebutanoic Acid Succinimidyl Ester Adsorbed on Graphene

The adsorbed structure of 1-pyrenebutanoic acid succinimidyl ester (PASE) on graphene was investigated based on density functional theory. We found two locally stable structures: a straight structure with the chainlike part of butanoic acid succinimidyl ester (BSE) lying down and a bent structure with the BSE part directed away from graphene, keeping the pyrene (Py) part adsorbed on graphene. Then, to elucidate the adsorption mechanism, we separately estimated the contributions of the Py and BSE parts to the entire PASE adsorption, and the adsorption effect of the BSE part was found to be secondary in comparison to the contribution of the Py. Next, the mobility of the BSE part at room temperature was confirmed by the activation energy barrier between straight and bent structures. To take account of the external environment, we considered the presence of amino acids and the hydration effect by a three-dimensional reference interaction site model. The contributions of glycine molecules and the solvent environment to stabilizing the bent PASE structure relative to the straight PASE structure were found. Therefore, the effect of the external environment around PASE is of importance when the standing-up process of the BSE part from graphene is considered.

3D-RISM-AI: A Machine Learning Approach to Predict Protein-Ligand Binding Affinity Using 3D-RISM

Hydration free energy (HFE) is a key factor in improving protein–ligand binding free energy (BFE) prediction accuracy. The HFE itself can be calculated using the three-dimensional reference interaction model (3D-RISM); however, the BFE predictions solely evaluated using 3D-RISM are not correlated to the experimental BFE for abundant protein–ligand pairs. In this study, to predict the BFE for multiple sets of protein–ligand pairs, we propose a machine learning approach incorporating the HFEs obtained using 3D-RISM, termed 3D-RISM-AI. In the learning process, structural metrics, intra-/intermolecular energies, and HFEs obtained via 3D-RISM of ∼4000 complexes in the PDBbind database (ver. 2018) were used. The BFEs predicted using 3D-RISM-AI were well correlated to the experimental data (Pearson’s correlation coefficient of 0.80 and root-mean-square error of 1.91 kcal/mol). As important factors for the prediction, the difference in the solvent accessible surface area between the bound and unbound structures and the hydration properties of the ligands were detected during the learning process.

Polar liquids at charged interfaces: A dipolar shell theory

The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.

Integral equation models for solvent in macromolecular crystals

The solvent can occupy up to ∼70% of macromolecular crystals, and hence, having models that predict solvent distributions in periodic systems could improve the interpretation of crystallographic data. Yet, there are few implicit solvent models applicable to periodic solutes, and crystallographic structures are commonly solved assuming a flat solvent model. Here, we present a newly developed periodic version of the 3D-reference interaction site model (RISM) integral equation method that is able to solve efficiently and describe accurately water and ion distributions in periodic systems; the code can compute accurate gradients that can be used in minimizations or molecular dynamics simulations. The new method includes an extension of the Ornstein–Zernike equation needed to yield charge neutrality for charged solutes, which requires an additional contribution to the excess chemical potential that has not been previously identified; this is an important consideration for nucleic acids or any other charged system where most or all the counter- and co-ions are part of the “disordered” solvent. We present several calculations of proteins, RNAs, and small molecule crystals to show that x-ray scattering intensities and the solvent structure predicted by the periodic 3D-RISM solvent model are in closer agreement with the experiment than are intensities computed using the default flat solvent model in the refmac5 or phenix refinement programs, with the greatest improvement in the 2 to 4 Å range. Prospects for incorporating integral equation models into crystallographic refinement are discussed.

Hydration and counterion binding of aqueous acetylcholine chloride and carbamoylcholine chloride

The hydration and Cl^- ion binding of the neurot^†ransmitter acetylcholine (ACh⁺) and its synthetic analogue, carbamoylcholine (CCh⁺), were studied by combining dilute-solution conductivity measurements with dielectric relaxation spectroscopy and statistical mechanics calculations at 1D-RISM and 3D-RISM level. Chloride ion binding was found to be weak but not negligible. From the ∼30 water molecules coordinating ACh and CCh⁺ only ∼1/3 is affected in its rotational dynamics by the cation, with the majority - situated close to the hydrophobic moieties - only retarded by a factor of ∼2.5. At vanishing solute concentration cations and the ∼3-4 H₂O molecules hydrogen bonding to the CO group of the solute exhibit similar rotational dynamics but increasing concentration and temperature markedly dehydrates ACh⁺ and CCh⁺.

Ion Pairing of the Neurotransmitters Acetylcholine and Glutamate in Aqueous Solutions

Neurotransmitters (NTs) play an important role in neural communication, regulating a variety of functions such as motivation, learning, memory, and muscle contraction. Their intermolecular interactions in biological media are an important factor affecting their biological activity. However, the available information on the features of these interactions is scarce and contradictory, especially, in an estimation of possible ion binding. In this paper, we present the results of a study for two well-known NTs, acetylcholine (ACh) and glutamate (Glu), with relation to the NT-inorganic ion and the NT-NT binding in a water environment. The features of NT pairing are investigated in aqueous AChCl and NaGlu solutions over a wide concentration range using the integral equation method in 1D- and 3D- reference interaction site model (RISM) approaches. The data for ACh are given for its two bioactive TG (trans, gauche) and TT (trans, trans) conformers. As was found, for both NTs, the results indicate the NT-inorganic counterion contact pair to be the predominant associate type in the concentrated solutions. In this case, the counterions occupy the vacated "water" space in the hydration shell of the onium moiety (ACh) or carboxylate groups (Glu). For ACh, the "unfolded" TT conformer demonstrates a slightly greater possibility for counterion pairing in comparison with the "folded" TG conformer. For Glu, the probability of its binding with a counterion is slightly stronger for the "side-chain" carboxylate group than for the "backbone" group. The obtained results also revealed an insignificant probability of Glu^--Glu^- pairing. Namely, the RISM data indicate Glu^--Glu^- binding by NH₃⁺-COO^- interactions. A link between the ion binding of NTs and their biological activity is discussed. This contribution adds new knowledge to our understanding of the interactions between the NTs and their molecular environment, providing further insights into the behavior of these compounds in biological media.

Hydration and dynamics of L-glutamate ion in aqueous solution

Aqueous solutions of sodium l-glutamate (NaGlu) in the concentration range 0 < c/M ≤ 1.90 at 25 °C were investigated by dielectric relaxation spectroscopy (DRS) and statistical mechanics (1D-RISM and 3D-RISM calculations) to study the hydration and dynamics of the l-glutamate (Glu-) anion. Although at c → 0 water molecules beyond the first hydration shell are dynamically affected, Glu- hydration is rather fragile and for c ⪆ 0.3 M apparently restricted to H2O molecules hydrogen bonding to the carboxylate groups. These hydrating dipoles are roughly parallel to the anion moment, leading to a significantly enhanced effective dipole moment of Glu-. However, l-glutamate dynamics is determined by the rotational diffusion of individual anions under hydrodynamic slip boundary conditions. Thus, the lifetime of the hydrate complexes, as well as of possibly formed [Na+Glu-]0 ionpairs and l-glutamate aggregates, cannot exceed the characteristic timescale for Glu- rotation.

Molecular Recognition and Self-Organization in Life Phenomena Studied by a Statistical Mechanics of Molecular Liquids, the RISM/3D-RISM Theory

There are two molecular processes that are essential for living bodies to maintain their life: the molecular recognition, and the self-organization or self-assembly. Binding of a substrate by an enzyme is an example of the molecular recognition, while the protein folding is a good example of the self-organization process. The two processes are further governed by the other two physicochemical processes: solvation and the structural fluctuation. In the present article, the studies concerning the two molecular processes carried out by Hirata and his coworkers, based on the statistical mechanics of molecular liquids or the RISM/3D-RISM theory, are reviewed.

Solvation Thermodynamics from the Perspective of Endpoints DFT

Solvation thermodynamics is concerned with the evaluation and physical interpretation of solvation free energies. Endpoints DFT provides a framework for computing solvation free energies by combining molecular simulations with a version of the classical density-functional theory of solutions which focuses on ω, the indirect (solvent-mediated) part of the solute-solvent potential of mean force (indirect PMF). The simulations are performed at the endpoints of a hypothetical charging process which transforms the solvent density from the pure liquid state to that of the solution state. The endpoints DFT expression for solvation free energy can be shown to be equivalent to the standard expression for which the key quantity is the direct correlation function, but it has the advantage that the indirect term ω is more focused on the change in solvent-solvent correlations with respect to the pure liquid as the solute is inserted into the solution. In this Perspective, we review recent developments of endpoints DFT, highlighting a series of papers we have written together beginning in 2017. We emphasize the importance of dimensionality reduction as the key to the evaluation of endpoints DFT expressions and present a recently developed, spatially resolved version of the theory. The role of interfacial water at certain positions which stabilize or destabilize a solute in solution can be analyzed with the spatially resolved version, and it is of considerable interest to investigate how changes in solvation affect protein-ligand binding and conformational landscapes from an endpoints DFT perspective. Endpoints DFT can also be employed in materials science; an example involving the rational design strategy for polymer membrane separation is described. The endpoints DFT method is a scheme to evaluate the solvation free energy by introducing approximations to integrate the classical density functional over a charging parameter. We have further proposed a new functional which captures the correct dependence of the indirect PMF ω at both endpoints of the charging process, and we review how it might be employed in future work.

Molecular Modeling of Aquaporins from Leishmania major

Aquaporins are membrane proteins responsible for permeating water, ions, dissolved gases, and other small molecular weight compounds through the protective cell membranes of living organisms. These proteins have been gaining increased importance as targets for treating a variety of parasitic diseases, since they control key physiological processes in the life cycle of parasitic protozoans, such as the uptake of nutrients, release of metabolites, and alleviation of osmotic stress. In this work, we use homology modeling to build three-dimensional structures for the four main aquaporins encoded and expressed by Leishmania major, a protozoan that causes leishmaniasis and affects millions of people worldwide. Physico-chemical properties of the proposed models for LmAQP1, LmAQPα, LmAQPβ, and LmAQPγ are then investigated using molecular dynamics simulations and the reference interaction site model (RISM) molecular theory of solvation. Pore characteristics, water permeation, and potential of mean force across the AQP channels for water, methanol, urea, ammonia, and carbon dioxide are examined and compared with results obtained for a protozoan (Plasmodium falciparum) aquaporin for which a crystal structure is available.

Application of the Approximate 3D-Reference Interaction Site Model (RISM) Molecular Solvation Theory to Acetonitrile as Solvent

The integral equation formalism based reference interaction site model (RISM) molecular solvation theory is applied to pure liquid acetonitrile and water-acetonitrile binary mixtures of different compositions. Solvate formation of d- and f-block ions by ACN is also calculated to check applicability of the RISM theory. The generalized Amber force field (GAFF) and the universal force field (UFF) parameters were found to be suitable for applications with the RISM theory for acetonitrile solvent. The presence of local microsolvated clusters for water-acetonitrile mixtures is validated in the RISM calculations.

New Protocol for Predicting the Ligand-Binding Site and Mode Based on the 3D-RISM/KH Theory

An efficient algorithm to find the binding position and mode of small ligands bound at an active site of protein is proposed based on the spatial distribution function (SDF) obtained from the three-dimensional reference interaction site model (3D-RISM) theory with the Kovalenko-Hirata (KH) closure relation. The ligand examined includes hydrophobic, acidic, and basic molecules and zwitterions. Eighteen different types of proteins, which serve as targets for those ligands, are selected to examine the robustness of the algorithm. An imaginary atom, referred to as an "anchor site", is defined at the center of geometry of a ligand molecule that serves as a center for searching the binding position and mode of the ligand molecule in the translational and rotational spaces. The probable binding sites (PBSs) are identified based on the SDFs of the ligand molecules around the protein, and the PBS is ranked according to the peak height of SDF. The deviations from the mean height of the peak values of SDFs for 50 PBSs are analyzed based on the z-score, which is a measure of prominence of the site. The PBS found at the closest distance from the anchor site of the crystal structure is referred to as the "nearest site". The orientation of the ligand molecule at each PBS is explored by changing the Euler angles, and the most probable binding mode is determined based on the superposition approximation. The binding position of ligand molecules is successfully predicted as one of the distinct peaks in SDF of the anchor site, with a few exceptions. The binding mode of the ligand molecule predicted based on the superposition approximation is consistent with the X-ray crystal structure in nine systems, a half of the systems investigated. The significance of the results is discussed in detail. An application of the new protocol to fragment-based drug discovery is suggested.

Advances in the Treatment of Explicit Water Molecules in Docking and Binding Free Energy Calculations

Background:

The inclusion of direct effects mediated by water during the ligandreceptor recognition is a hot-topic of modern computational chemistry applied to drug discovery and development. Docking or virtual screening with explicit hydration is still debatable, despite the successful cases that have been presented in the last years. Indeed, how to select the water molecules that will be included in the docking process or how the included waters should be treated remain open questions.

Objective:

In this review, we will discuss some of the most recent methods that can be used in computational drug discovery and drug development when the effect of a single water, or of a small network of interacting waters, needs to be explicitly considered.

Results:

Here, we analyse the software to aid the selection, or to predict the position, of water molecules that are going to be explicitly considered in later docking studies. We also present software and protocols able to efficiently treat flexible water molecules during docking, including examples of applications. Finally, we discuss methods based on molecular dynamics simulations that can be used to integrate docking studies or to reliably and efficiently compute binding energies of ligands in presence of interfacial or bridging water molecules.

Conclusions:

Software applications aiding the design of new drugs that exploit water molecules, either as displaceable residues or as bridges to the receptor, are constantly being developed. Although further validation is needed, workflows that explicitly consider water will probably become a standard for computational drug discovery soon.

Application of the 3D-RISM-KH molecular solvation theory for DMSO as solvent

The molecular solvation theory in the form of the Three-Dimensional Reference Interaction Site Model (3D-RISM) with Kovalenko-Hirata (KH) closure relation is benchmarked for use with dimethyl sulfoxide (DMSO) as solvent for (bio)-chemical simulation within the framework of integral equation formalism. Several force field parameters have been tested to correctly reproduce solvation free energy in DMSO, ion solvation in DMSO, and DMSO coordination prediction. Our findings establish a united atom (UA) type parameterization as the best model of DMSO for use in 3D-RISM-KH theory based calculations.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

Solvent Composition Effects on the Structural Properties of the Aβ42 Monomer from the 3D-RISM-KH Molecular Theory of Solvation

Structural characterization of amyloid (A)β peptides implicated in Alzheimer's disease is a challenging problem due to their intrinsically disordered nature and their high propensity for aggregation. Only limited information is currently available from experiments on conformational properties and aggregation pathways of the peptides in cellular environments. In silico modeling complements experimental information, providing atomistic insight into structure and dynamics of different Aβ species. All-atom explicit solvent molecular dynamics (MD) simulations with a properly selected force field can deliver reliable structural and dynamic information. In the case of intrinsically disordered Aβ peptides, enhanced sampling simulations beyond the nanosecond time scale are required to obtain statistically meaningful results even for simple solvent conditions. To overcome the challenges of conformational sampling in crowded cellular environments, alternative approaches have to be used, including postprocessing of MD data. In this study, we employ the statistical-mechanical, three-dimensional reference interaction site model with the Kovalenko-Hirata closure integral equation molecular theory of solvation to describe solvent composition effects on the conformational equilibrium in a structural ensemble of the Aβ42 (covering residues 1-42) monomer based on a statistical reweighting technique. The methodology enables a computationally efficient prediction on how different factors in the cellular environment, such as solvent composition, nonpolar solvation, and macromolecular crowding, affect the structural properties of the monomer. Similarities have been identified between changes in the structural ensemble caused by nonpolar solvation and crowded environments modeled by ionic solution with large negative ions. In particular, both solvent conditions reduce the random coil content and enhance the helical structure content of the monomer. In contrast to the previous studies, which reported increased α-helical content of peptides in crowded environments, this work attributes these structural features to the difference in solvent exposure of hydrophilic residues of the monomer for different secondary structure elements, rather than to (entropic) excluded volume effects.

Hydration and ion association of aqueous choline chloride and chlorocholine chloride

Choline hydration occurs predominantly via its hydroxyl group, and weak contact ion pair formation with Cl⁻ is via the onium moiety.

Perspective: Structural fluctuation of protein and Anfinsen's thermodynamic hypothesis

The thermodynamics hypothesis, casually referred to as "Anfinsen's dogma," is described theoretically in terms of a concept of the structural fluctuation of protein or the first moment (average structure) and the second moment (variance and covariance) of the structural distribution. The new theoretical concept views the unfolding and refolding processes of protein as a shift of the structural distribution induced by a thermodynamic perturbation, with the variance-covariance matrix varying. Based on the theoretical concept, a method to characterize the mechanism of folding (or unfolding) is proposed. The transition state, if any, between two stable states is interpreted as a gap in the distribution, which is created due to an extensive reorganization of hydrogen bonds among back-bone atoms of protein and with water molecules in the course of conformational change. Further perspective to applying the theory to the computer-aided drug design, and to the material science, is briefly discussed.

Predicting Accurate Solvation Free Energy in n-Octanol Using 3D-RISM-KH Molecular Theory of Solvation: Making Right Choices

Molecular theory of solvation, a.k.a., three-dimensional reference interaction site model theory of solvation with Kovalenko-Hirata closure relation (3D-RISM-KH), is an accurate and fast theory predicting solvation free energy and structure. Here we report a benchmark study of n-octanol solvation free energy calculations using this theory. The choice of correct force field parameters is quintessential for the success of 3D-RISM theory, and we present a guideline to obtain them for n-octanol solvent. Our best prediction of the solvation free energy on a set of 205 small organic molecules supplemented with the so-called "universal correction" scheme yields relative mean unsigned error of 0.94 kcal/mol against the reported database. The best agreement is obtained with the united atom (UA) type force field parametrization of n-octanol with the van der Waals parameters of hydroxyl hydrogen reported by Kobryn et al. [ Kobryn , A. E. ; Kovalenko , A. J. Chem. Phys. 2008 , 129 , 134701 ].

Relationship between Solvation Thermodynamics from IST and DFT Perspectives

Inhomogeneous solvation theory (IST) and classical density functional theory (DFT) each provide a framework for relating distribution functions of solutions to their thermodynamic properties. As reviewed in this work, both IST and DFT can be formulated in a way that use two "end point" simulations, one of the pure solvent and the other of the solution, to determine the solute chemical potential and other thermodynamic properties of the solution and of subvolumes in regions local to the solute containing hydrating waters. In contrast to IST, where expressions for the excess energy and entropy of solution are the object of analysis, in the DFT end point formulation of the problem, the solute-solvent potential of mean force (PMF) plays a central role. The indirect part of the PMF corresponds to the lowest order (1-body) truncation of the IST expression. Because the PMF is a free energy function, powerful numerical methods can be used to estimate it. We show that the DFT expressions for the solute excess chemical potential can be written in a form which is local, involving integrals only over regions proximate to the solute. The DFT end point route to estimating solvation free energies provides an alternative path to that of IST for analyzing solvation effects on molecular recognition and conformational changes in solution, which can lead to new insights. In order to illustrate the kind of information that is contained in the solute-solvent PMF, we have carried out simulations of β-cyclodextrin in water. This solute is a well studied "host" molecule to which "guest" molecules bind; host-guest systems serve as models for molecular recognition. We illustrate the range of values the direct and indirect parts of the solute-solvent PMF can have as a water molecule is brought to the interface of β-cyclodextrin from the bulk; we discuss the "competition" between these two terms, and the role it plays in molecular recognition.

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing ([Formula: see text] for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining [Formula: see text] compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to [Formula: see text]. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple [Formula: see text] correction improved agreement with experiment from [Formula: see text] to [Formula: see text], despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.

Molecular density functional theory of water including density-polarization coupling

We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

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.

Competitive interaction of monovalent cations with DNA from 3D-RISM

The composition of the ion atmosphere surrounding nucleic acids affects their folding, condensation and binding to other molecules. It is thus of fundamental importance to gain predictive insight into the formation of the ion atmosphere and thermodynamic consequences when varying ionic conditions. An early step toward this goal is to benchmark computational models against quantitative experimental measurements. Herein, we test the ability of the three dimensional reference interaction site model (3D-RISM) to reproduce preferential interaction parameters determined from ion counting (IC) experiments for mixed alkali chlorides and dsDNA. Calculations agree well with experiment with slight deviations for salt concentrations >200 mM and capture the observed trend where the extent of cation accumulation around the DNA varies inversely with its ionic size. Ion distributions indicate that the smaller, more competitive cations accumulate to a greater extent near the phosphoryl groups, penetrating deeper into the grooves. In accord with experiment, calculated IC profiles do not vary with sequence, although the predicted ion distributions in the grooves are sequence and ion size dependent. Calculations on other nucleic acid conformations predict that the variation in linear charge density has a minor effect on the extent of cation competition.

Uranyl Solvation by a Three-Dimensional Reference Interaction Site Model

We report an implementation of the three-dimensional reference interaction site model (3D RISM) that in particular addresses the treatment of the long-range Coulomb field of charged species, represented by point charges and/or a distributed charge density. A comparison of 1D and 3D results for atomic ions demonstrates a reasonable accuracy, even for a moderate size of the unit cell and a moderate grid resolution. In an application to uranyl complexes with 4-6 explicit aqua ligands and an implicit bulk solvent modeled by RISM, we show that the 3D technique is not susceptible to the deficiencies of the 1D technique exposed in our previous work [Li, Matveev, Krüger, Rösch, Comp. Theor. Chem. 2015, 1051, 151]. The 3D method eliminates the artificial superposition of explicit aqua ligands and the RISM medium and predicts essentially the same values for uranyl and uranyl-water bond lengths as a state-of-the-art polarizable continuum model. With the first solvation shell treated explicitly, the observables are nearly independent of the order of the closure relationship used when solving the set of integral equations for the various distribution functions. Furthermore, we calculated the activation barrier of water exchange with a hybrid approach that combines the 3D RISM model for the bulk aqueous solvent and a quantum mechanical description (at the level of electronic density functional theory) of uranyl interacting with explicitly represented water molecules. The calculated result agrees very well with experiment and the best theoretical estimates.