Hydration Free Energies of Molecular Ions from Theory and Simulation

Solvation entropy, enthalpy and free energy prediction using a multi-task deep learning functional in 1D-RISM

Simultaneous calculation of entropies, enthalpies and free energies has been a long-standing challenge in computational chemistry, partly because of the difficulty in obtaining estimates of all three properties from a single consistent simulation methodology. This has been particularly true for methods from the Integral Equation Theory of Molecular Liquids such as the Reference Interaction Site Model which have traditionally given large errors in solvation thermodynamics. Recently, we presented pyRISM-CNN, a combination of the 1 Dimensional Reference Interaction Site Model (1D-RISM) solver, pyRISM, with a deep learning based free energy functional, as a method of predicting solvation free energy (SFE). With this approach, a 40-fold improvement in prediction accuracy was delivered for a multi-solvent, multi-temperature dataset when compared to the standard 1D-RISM theory [Fowles et al., Digital Discovery, 2023, 2, 177-188]. Here, we report three further developments to the pyRISM-CNN methodology. Firstly, solvation free energies have been introduced for organic molecular ions in methanol or water solvent systems at 298 K, with errors below 4 kcal mol^-1 obtained without the need for corrections or additional descriptors. Secondly, the number of solvents in the training data has been expanded from carbon tetrachloride, water and chloroform to now also include methanol. For neutral solutes, prediction errors nearing or below 1 kcal mol^-1 are obtained for each organic solvent system at 298 K and water solvent systems at 273-373 K. Lastly, pyRISM-CNN was successfully applied to the simultaneous prediction of solvation enthalpy, entropy and free energy through a multi-task learning approach, with errors of 1.04, 0.98 and 0.47 kcal mol^-1, respectively, for water solvent systems at 298 K.

Impacts of targeting different hydration free energy references on the development of ion potentials

Hydration free energy (HFE) as the most important solvation parameter is often targeted in ion model development, even though the reported values differ by dozens of kcal mol^-1 mainly due to the experimentally undetermined HFE of the proton ΔG°(H⁺). The choice of ΔG°(H⁺) obviously affects the hydration of single ions and the relative HFE between the ions with different (magnitude or sign) charges, and the impacts of targeted HFEs on the ion solvation and ion-ion interactions are largely unrevealed. Here we designed point charge models of K⁺, Mg²⁺, Al³⁺, and Cl^- ions targeting a variety of HFE references and then investigated the HFE influences on the simulations of dilute and concentrated ion solutions and of the salt ion pairs in gas, liquid, and solid phases. Targeting one more property of ion-water oxygen distances (IOD) leaves the ion-water binding distance invariant, while the binding strength increases with the decreasing (more negative) HFE of ions as a result of a decrease in ΔG°(H⁺) for the cation and an increase in ΔG°(H⁺) for the anion. The increase in ΔG°(H⁺) leads to strengthened cation-anion interactions and thus to close ion-ion contacts, low osmotic pressures, and small activity derivatives in concentrated ion solutions as well as too stable ion pairs of the salts in different phases. The ion diffusivity and water exchange rates around the ions are simply not HFE dependent but rather more complex. Targeting both the aqueous IOD and salt crystal properties of KCl was also attempted and the comparison between different models indicates the complexity and challenge in obtaining a balanced performance between different phases using classical force fields. Our results also support that a real ΔG°(H⁺) value of -259.8 kcal mol^-1 recommended by Hünenberger and Reif guides ion models to reproduce ion-water and ion-ion interactions reasonably at relatively low salt concentrations. Simulations of a metalloprotein show that a relatively more positive ΔG°(H⁺) for Mg²⁺ model is better for a reasonable description of the metal binding network.

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.

Implementation and Optimization of the Embedded Cluster Reference Interaction Site Model with Atomic Charges

In this work, we implemented the embedded cluster reference interaction site model (EC-RISM) originally developed by Kloss, Heil, and Kast (J. Phys. Chem. B2008, 112, 4337–4343). This method combines quantum mechanical calculations with the 3D reference interaction site model (3D-RISM). Numerous options, such as buffer, grid space, basis set, charge model, water model, closure relation, and so forth, were investigated to find the best settings. Additionally, the small point charges, which are derived from the solvent distribution from the 3D-RISM solution to represent the solvent in the QM calculation, were neglected to reduce the overhead without the loss of accuracy. On the MNSOL[a], MNSOL, and FreeSolv databases, our implemented and optimized method provides solvation free energies in water with 5.70, 6.32, and 6.44 kJ/mol root-mean-square deviations, respectively, but with different settings, 5.22, 6.08, and 6.63 kJ/mol can also be achieved. Only solvent models containing fitting parameters, like COSMO-RS and EC-RISM with universal correction and directly used electrostatic potential, perform better than our EC-RISM implementation with atomic charges.

Rational Design of Nonbonded Point Charge Models for Monovalent Ions with Lennard-Jones 12-6 Potential

Ions are of central importance in nature, and a variety of potential models was proposed to model ions in different phases for an in-depth exploration of ion-related systems. Here, we developed point charge models of 14 monovalent ions with the traditional 12-6 Lennard-Jones (LJ) potential for use in conjunction with 11 water models of TIP3P, OPC3, SPC/E, SPC/E_b, TIP3P-FB, a99SB-disp, TIP4P-Ew, OPC, TIP4P/2005, TIP4P-D, and TIP4P-FB. The designed models reproduced the real hydration free energy (HFE) of ions and the ion-oxygen distance (IOD) in the first hydration shell accurately and simultaneously, a performance similar to the previously reported 12-6-4 LJ-type ion models (12-6 LJ plus an attractive C₄ term for cations or a repulsive one for anions). This work, along with our previous work on di-, tri-, and tetravalent metal cations (J. Chem. Inf. Model. 2021, 61, 4031-4044; J. Chem. Inf. Model. 2021, 61, 4613-4629), demonstrates the feasibility of the simple 12-6 LJ potential in ion modeling. In order for the 12-6 LJ potential to reproduce both the HFE and IOD, the LJ R parameters need to be close to Shannon's ionic radii for the highly charged cations and to the Stokes's van der Waals (vdW) radii for the monovalent ions. With an additional C₄ term, the R parameters of 12-6-4 LJ ion models agree well with the Stokes's vdW radii and have a more physical meaning. It appears that the C₄ term can be merged into the 12-6 LJ potential by a rational tuning of R and the LJ well depth. Simulations of the osmotic coefficients of alkali chloride solutions and the properties of gaseous and solid alkali halides indicate the necessity of further optimizing ion-ion interactions via, for instance, targeting more properties or using a more physical (polarizable) model.

A Martini Coarse Grained Model of Citrate-Capped Gold Nanoparticles Interacting with Lipid Bilayers

Citrate capping is one of the most common strategies to achieve the colloidal stability of Au nanoparticles (NPs) with diameters ranging from a few to hundreds of nanometers. Citrate-capped Au nanoparticles (CNPs) represent a step of the synthesis of Au NPs with specific functionalities, as CNPs can be further functionalized via ligand-exchange reactions, leading to the replacement of citrate with other organic ligands. In vitro, CNPs are also used to address the fundamental aspects of NP-membrane interactions, as they can directly interact with cells or model cell membranes. Their affinity for the bilayer is again mediated by the exchange of citrate with lipid molecules. Here, we propose a new computational model of CNPs compatible with the coarse grained Martini force field. The model, which we develop and validate through an extensive comparison with new all-atom molecular dynamics (MD) simulations and UV-vis and Fourier transform infrared spectroscopy data, is aimed at the MD simulation of the interaction between citrate-capped NPs and model phosphatidylcholine lipid membranes. As a test application we show that, during the interaction between a single CNP and a flat planar 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer, the citrate coating is spontaneously replaced by lipids on the surface of Au NPs, while the NP size and shape determine the final structural configuration of the NP-bilayer complex.

Rational Design of Nonbonded Point Charge Models for Highly Charged Metal Cations with Lennard-Jones 12-6 Potential

Here, we developed nonbonded point charge models using a simple Lennard-Jones (LJ) 12-6 potential for highly charged metal cations (18 trivalent and 6 tetravalent ions) for use with 11 water models of TIP3P, OPC3, SPC/E, SPC/E_b, TIP3P-FB, a99SB-disp, TIP4P-Ew, OPC, TIP4P/2005, TIP4P-D, and TIP4P-FB. The designed models simultaneously reproduce the hydration free energy (HFE) and ion-oxygen distance (IOD) in the first hydration shell with an error within 1 kcal/mol and 0.01 Å on average, respectively, and yield reasonable coordination numbers for most cations. Such performance is equivalent to the previously reported point charge models using a more complex 12-6-4 LJ-type potential, while the LJ R parameters of our models are much close to Shannon's revised effective ion radii than that of the 12-6-4 models. Our designed models overestimate the diffusion constants of several trivalent ions by 5-68%. The performance in predicting osmotic coefficients of trivalent chlorides in aqueous solution depends on the salt type. A calibration of cation-anion interacting LJ parameters reproduces the experimental osmotic coefficients of an AlCl₃ solution at 0.2-3.0 mol/L. The effectiveness of our new models is further demonstrated by simulating a metalloprotein system with four force field/water combinations. This work facilitates accurate modeling of metal-containing systems by a variety of force fields and water models in aqueous solution.

Rational Design of Nonbonded Point Charge Models for Divalent Metal Cations with Lennard-Jones 12-6 Potential

Exploring a metal-involved biochemical process at a molecular level often requires a reliable description of metal properties in aqueous solution by classical nonbonded models. An additional C₄ term for considering ion-induced dipole interactions was previously proposed to supplement the widely used Lennard-Jones 12-6 potential (known as the 12-6-4 LJ-type model) with good accuracy. Here, we demonstrate an alternative to modeling divalent metal cations (M²⁺) with the traditional 12-6 LJ potential by developing nonbonded point charge models for use with 11 water models: TIP3P, SPC/E, SPC/E_b, TIP4P-Ew, TIP4P-D, and TIP4P/2005 and the more recent OPC3, TIP3P-FB, OPC, TIP4P-FB, and a99SB-disp. Our designed models simultaneously reproduce the experimental hydration free energy, ion-oxygen distance, and coordination number in the first hydration shell accurately for most of the metal cations, an accuracy equivalent to that of the complex 12-6-4 LJ-type and double exponential potential models. A systematic comparison with the existing M²⁺ models is presented as well in terms of effective ion radii, diffusion constants, water exchange rates, and ion-water interactions. Molecular dynamics simulations of metal substitution in Escherichia coli glyoxalase I variants show the great potential of our new models for metalloproteins.

Toward Physics-Based Solubility Computation for Pharmaceuticals to Rival Informatics

We demonstrate that physics-based calculations of intrinsic aqueous solubility can rival cheminformatics-based machine learning predictions. A proof-of-concept was developed for a physics-based approach via a sublimation thermodynamic cycle, building upon previous work that relied upon several thermodynamic approximations, notably the 2RT approximation, and limited conformational sampling. Here, we apply improvements to our sublimation free-energy model with the use of crystal phonon mode calculations to capture the contributions of the vibrational modes of the crystal. Including these improvements with lattice energies computed using the model-potential-based Ψ_mol method leads to accurate estimates of sublimation free energy. Combining these with hydration free energies obtained from either molecular dynamics free-energy perturbation simulations or density functional theory calculations, solubilities comparable to both experiment and informatics predictions are obtained. The application to coronene, succinic acid, and the pharmaceutical desloratadine shows how the methods must be adapted for the adoption of different conformations in different phases. The approach has the flexibility to extend to applications that cannot be covered by informatics methods.

Developing and Assessing Nonbonded Dummy Models of Magnesium Ion with Different Hydration Free Energy References

A large diversity in the targeted hydration free energies (HFEs) during model parameterization of metal ions was reported in the literature with a difference by dozens of kcal/mol. Here, we developed a series of nonbonded dummy models of the Mg²⁺ ion targeting different HFE references in TIP3P water, followed by assessments of the designed models in the simulations of MgCl₂ solution and biological systems. Together with the comparison of existing models, we conclude that the difference in the targeted HFEs has a limited influence on the model performance, while the usability of these models differs from case to case. The feasibility of reproducing more properties of Mg²⁺ such as diffusion constants and water exchange rates using a nonbonded dummy model is demonstrated. Underestimated activity derivative and osmotic coefficient of MgCl₂ solutions in high concentration reveal a necessity for further optimization of ion-pair interactions. The developed dummy models are applicable to metal coordination with Asp, Glu, and His residues in metalloenzymes, and the performance in predicting monodentate or bidentate binding modes of Asp/Glu residues depends on the complexity of metal centers and the choice of protein force fields. When both the binding modes coexist, the nonbonded dummy models outperform point charge models, probably in need of considering polarization of metal-binding residues by, for instance, charge calibration in classical force fields. This work is valuable for the use and further development of magnesium ion models for simulations of metal-containing systems with good accuracy.

Uncovering Differences in Hydration Free Energies and Structures for Model Compound Mimics of Charged Side Chains of Amino Acids

Free energies of hydration are of fundamental interest for modeling and understanding conformational and phase equilibria of macromolecular solutes in aqueous phases. Of particular relevance to systems such as intrinsically disordered proteins are the free energies of hydration and hydration structures of model compounds that mimic charged side chains of Arg, Lys, Asp, and Glu. Here, we deploy a Thermodynamic Cycle-based Proton Dissociation (TCPD) approach in conjunction with data from direct measurements to obtain estimates for the free energies of hydration for model compounds that mimic the side chains of Arg+, Lys+, Asp-, and Glu-. Irrespective of the choice made for the hydration free energy of the proton, the TCPD approach reveals clear trends regarding the free energies of hydration for Arg+, Lys+, Asp-, and Glu-. These trends include asymmetries between the hydration free energies of acidic (Asp- and Glu-) and basic (Arg+ and Lys+) residues. Further, the TCPD analysis, which relies on a combination of experimental data, shows that the free energy of hydration of Arg+ is less favorable than that of Lys+. We sought a physical explanation for the TCPD-derived trends in free energies of hydration. To this end, we performed temperature-dependent calculations of free energies of hydration and analyzed hydration structures from simulations that use the polarizable Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field and water model. At 298 K, the AMOEBA model generates estimates of free energies of hydration that are consistent with TCPD values with a free energy of hydration for the proton of ca. -259 kcal/mol. Analysis of temperature-dependent simulations leads to a structural explanation for the observed differences in free energies of hydration of ionizable residues and reveals that the heat capacity of hydration is positive for Arg+ and Lys+ and negative for Asp- and Glu-.

Quantum-mechanical property prediction of solvated drug molecules: what have we learned from a decade of SAMPL blind prediction challenges?

Joint academic-industrial projects supporting drug discovery are frequently pursued to deploy and benchmark cutting-edge methodical developments from academia in a real-world industrial environment at different scales. The dimensionality of tasks ranges from small molecule physicochemical property assessment over protein-ligand interaction up to statistical analyses of biological data. This way, method development and usability both benefit from insights gained at both ends, when predictiveness and readiness of novel approaches are confirmed, but the pharmaceutical drug makers get early access to novel tools for the quality of drug products and benefit of patients. Quantum-mechanical and simulation methods particularly fall into this group of methods, as they require skills and expense in their development but also significant resources in their application, thus are comparatively slowly dripping into the realm of industrial use. Nevertheless, these physics-based methods are becoming more and more useful. Starting with a general overview of these and in particular quantum-mechanical methods for drug discovery we review a decade-long and ongoing collaboration between Sanofi and the Kast group focused on the application of the embedded cluster reference interaction site model (EC-RISM), a solvation model for quantum chemistry, to study small molecule chemistry in the context of joint participation in several SAMPL (Statistical Assessment of Modeling of Proteins and Ligands) blind prediction challenges. Starting with early application to tautomer equilibria in water (SAMPL2) the methodology was further developed to allow for challenge contributions related to predictions of distribution coefficients (SAMPL5) and acidity constants (SAMPL6) over the years. Particular emphasis is put on a frequently overlooked aspect of measuring the quality of models, namely the retrospective analysis of earlier datasets and predictions in light of more recent and advanced developments. We therefore demonstrate the performance of the current methodical state of the art as developed and optimized for the SAMPL6 pKa and octanol-water log P challenges when re-applied to the earlier SAMPL5 cyclohexane-water log D and SAMPL2 tautomer equilibria datasets. Systematic improvement is not consistently found throughout despite the similarity of the problem class, i.e. protonation reactions and phase distribution. Hence, it is possible to learn about hidden bias in model assessment, as results derived from more elaborate methods do not necessarily improve quantitative agreement. This indicates the role of chance or coincidence for model development on the one hand which allows for the identification of systematic error and opportunities toward improvement and reveals possible sources of experimental uncertainty on the other. These insights are particularly useful for further academia-industry collaborations, as both partners are then enabled to optimize both the computational and experimental settings for data generation.

Analytical 2-Dimensional Model of Nonpolar and Ionic Solvation in Water

A goal in computational chemistry is computing hydration free energies of nonpolar and charged solutes accurately, but with much greater computational speeds than in today's explicit-water simulations. Here, we take one step in that direction: a simple model of solvating waters that is analytical and thus essentially instantaneous to compute. Each water molecule is a 2-dimensional dipolar hydrogen-bonding disk that interacts around small circular solutes with different nonpolar and charge interactions. The model gives good qualitative agreement with experiments. As a function of the solute radius, it gives the solvation free energy, enthalpy and entropy as a function of temperature for the inert gas series Ne, Ar, Kr, and Xe. For anions and cations, it captures relatively well the trends versus ion radius. This approach should be readily generalizable to three dimensions.

Strong bases behave as weak bases in nanoscale chemical environments: implication in humidity-swing CO2 air capture

Hydration of ions/molecules in nanometer-sized clusters or nanoscopic pores is ubiquitous and plays a key role in many chemical and physical systems. In this work, guanidine-H2O reactions with n = 1-8 water molecules were systematically studied by ab initio methods. The result suggests that the reduced availability of water molecules greatly inhibits the strong base guanidine from producing OH-. That is, guanidine exhibits the behavior of a weak bases in low-humidity nanoscale environments. Intriguingly, this effect is not limited to guanidine but could be applied to other strong bases. Furthermore, we demonstrate that the direction of guanidine-CO2 reactions can be controlled by changing the number of water molecules present, which in turn responds to the humidity change in air. These findings not only shed some light on unconventional chemical reactions of strong bases in atmospheric clusters and on solid porous surfaces, but also provide insights into the development of guanidine-based CO2 air-capture sorbents.

Multisolvent Models for Solvation Free Energy Predictions Using 3D-RISM Hydration Thermodynamic Descriptors

The potential to predict solvation free energies (SFEs) in any solvent using a machine learning (ML) model based on thermodynamic output, extracted exclusively from 3D-RISM simulations in water is investigated. The models on multiple solvents take into account both the solute and solvent description and offer the possibility to predict SFEs of any solute in any solvent with root mean squared errors less than 1 kcal/mol. Validations that involve exclusion of fractions or clusters of the solutes or solvents exemplify the model's capability to predict SFEs of novel solutes and solvents with diverse chemical profiles. In addition to being predictive, our models can identify the solute and solvent features that influence SFE predictions. Furthermore, using 3D-RISM hydration thermodynamic output to predict SFEs in any organic solvent reduces the need to run 3D-RISM simulations in all these solvents. Altogether, our multisolvent models for SFE predictions that take advantage of the solvation effects are expected to have an impact in the property prediction space.

The SAMPL6 challenge on predicting octanol-water partition coefficients from EC-RISM theory

Results are reported for octanol–water partition coefficients (log P) of the neutral states of drug-like molecules provided during the SAMPL6 (Statistical Assessment of Modeling of Proteins and Ligands) blind prediction challenge from applying the “embedded cluster reference interaction site model” (EC-RISM) as a solvation model for quantum-chemical calculations. Following the strategy outlined during earlier SAMPL challenges we first train 1- and 2-parameter water-free (“dry”) and water-saturated (“wet”) models for n-octanol solvation Gibbs energies with respect to experimental values from the “Minnesota Solvation Database” (MNSOL), yielding a root mean square error (RMSE) of 1.5 kcal mol⁻¹ for the best-performing 2-parameter wet model, while the optimal water model developed for the pK_a part of the SAMPL6 challenge is kept unchanged (RMSE 1.6 kcal mol⁻¹ for neutral compounds from a model trained on both neutral and ionic species). Applying these models to the blind prediction set yields a log P RMSE of less than 0.5 for our best model (2-parameters, wet). Further analysis of our results reveals that a single compound is responsible for most of the error, SM15, without which the RMSE drops to 0.2. Since this is the only compound in the challenge dataset with a hydroxyl group we investigate other alcohols for which Gibbs energy of solvation data for both water and n-octanol are available in the MNSOL database to demonstrate a systematic cause of error and to discuss strategies for improvement.

Analysis of molecular dynamics simulations of 10-residue peptide, chignolin, using statistical mechanics: Relaxation mode analysis and three-dimensional reference interaction site model theory

Molecular dynamics simulation is a fruitful tool for investigating the structural stability, dynamics, and functions of biopolymers at an atomic level. In recent years, simulations can be performed on time scales of the order of milliseconds using special purpose systems. Since the most stable structure, as well as meta-stable structures and intermediate structures, is included in trajectories in long simulations, it is necessary to develop analysis methods for extracting them from trajectories of simulations. For these structures, methods for evaluating the stabilities, including the solvent effect, are also needed. We have developed relaxation mode analysis to investigate dynamics and kinetics of simulations based on statistical mechanics. We have also applied the three-dimensional reference interaction site model theory to investigate stabilities with solvent effects. In this paper, we review the results for designing amino-acid substitution of the 10-residue peptide, chignolin, to stabilize the misfolded structure using these developed analysis methods.

Delfos: deep learning model for prediction of solvation free energies in generic organic solvents

Prediction of aqueous solubilities or hydration free energies is an extensively studied area in machine learning applications in chemistry since water is the sole solvent in the living system. However, for non-aqueous solutions, few machine learning studies have been undertaken so far despite the fact that the solvation mechanism plays an important role in various chemical reactions. Here, we introduce Delfos (deep learning model for solvation free energies in generic organic solvents), which is a novel, machine-learning-based QSPR method which predicts solvation free energies for various organic solute and solvent systems. A novelty of Delfos involves two separate solvent and solute encoder networks that can quantify structural features of given compounds via word embedding and recurrent layers, augmented with the attention mechanism which extracts important substructures from outputs of recurrent neural networks. As a result, the predictor network calculates the solvation free energy of a given solvent-solute pair using features from encoders. With the results obtained from extensive calculations using 2495 solute-solvent pairs, we demonstrate that Delfos not only has great potential in showing accuracy comparable to that of the state-of-the-art computational chemistry methods, but also offers information about which substructures play a dominant role in the solvation process.

A molecular reconstruction approach to site-based 3D-RISM and comparison to GIST hydration thermodynamic maps in an enzyme active site

Computed, high-resolution, spatial distributions of solvation energy and entropy can provide detailed information about the role of water in molecular recognition. While grid inhomogeneous solvation theory (GIST) provides rigorous, detailed thermodynamic information from explicit solvent molecular dynamics simulations, recent developments in the 3D reference interaction site model (3D-RISM) theory allow many of the same quantities to be calculated in a fraction of the time. However, 3D-RISM produces atomic-site, rather than molecular, density distributions, which are difficult to extract physical meaning from. To overcome this difficulty, we introduce a method to reconstruct molecular density distributions from atomic-site density distributions. Furthermore, we assess the quality of the resulting solvation thermodynamics density distributions by analyzing the binding site of coagulation Factor Xa with both GIST and 3D-RISM. We find good qualitative agreement between the methods for oxygen and hydrogen densities as well as direct solute-solvent energetic interactions. However, 3D-RISM predicts lower energetic and entropic penalties for moving water from the bulk to the binding site.

Ab initio calculations and reduced density gradient analyses of the structure and energetics of hydrated calcium fluoride and calcium carbonate

We studied microhydrated calcium fluoride, calcium carbonate and their ions at the MP2/6-311++G** level of theory and found that water–water non-covalent interactions destabilize the solvation shell, and are compensated by cooperative hydrogen bonds.

3D matters! 3D-RISM and 3D convolutional neural network for accurate bioaccumulation prediction

In this work, we present a new method for predicting complex physical-chemical properties of organic molecules. The approach utilizes 3D convolutional neural network (ActivNet4) that uses solvent spatial distributions around solutes as input. These spatial distributions are obtained by a molecular theory called three-dimensional reference interaction site model. We have shown that the method allows one to achieve a good accuracy of prediction of bioconcentration factor which is difficult to predict by direct application of methods of molecular theory or simulations. Our research demonstrates that combination of molecular theories with modern machine learning approaches can be effectively used for predicting properties that are otherwise inaccessible to purely theory-based models.

Role of Ionic Charge Density in Donnan Exclusion of Monovalent Anions by Nanofiltration

The main objective of this study is to examine how the charge densities of four monovalent anions-fluoride (F^-), chloride (Cl^-), bromide (Br^-), and nitrate (NO₃^-)-influence their Donnan (charge) exclusion by a charged nanofiltration (NF) membrane. We systematically studied the rejection behavior of ternary ion solutions containing sodium cation (Na⁺) and two of the monovalent anions as a function of the pH with a polyamide NF membrane. In the solutions containing F^- and Cl^- or F^- and Br^-, F^- rejection was higher than Cl^- or Br^- rejection only when the solution pH was higher than 5.5, suggesting that F^- (which has a higher charge density) was repelled more strongly by the negatively charged membrane. The order of change in the activation energy for the transport of the four anions through the polyamide membrane as a response to the increase of the membrane negative charge was the following: F^- > Cl^- > NO₃^- > Br^-. This order corroborates our main hypothesis that an anion with a smaller ionic radius, and hence a higher charge density, is more affected by the Donnan (charge)-exclusion mechanism in NF. We conclude with a proposed mechanism for the role of ionic charge density in the rejection of monovalent anions in NF.

Free-Energy Calculations of Ionic Hydration Consistent with the Experimental Hydration Free Energy of the Proton

Computational free-energy correction strategies and the choice of experimental proton hydration free energy, ΔG_s^*(H⁺), are analyzed to investigate the apparent controversy in experimental thermodynamics of ionic hydration. Without corrections, the hydration free-energy (ΔG_hyd) calculations match experiments with ΔG_s^*(H⁺) = -1064 kJ/mol as reference. Using the Galvani surface potential the resulting (real) ΔG_hyd are consistent with ΔG_s^*(H⁺) = -1098 kJ/mol. When applying, in an ad hoc manner, the discrete solvent correction, ΔG_hyd matching the "consensus" ΔG_s^*(H⁺) of -1112 kJ/mol are obtained. This analysis rationalizes reports on ΔG_hyd calculations for ions using different experimental references. For neutral amino acid side chains ΔG_hyd are independent of the water model, whereas there are large differences in ΔG_hyd due to the water model for charged species, suggesting that long-range ordering of water around ions yields an important contribution to the ΔG_hyd. These differences are reduced significantly when applying consistent corrections, but to obtain the most accurate results it is recommended to use the water model belonging to the force field.

A closure relation to molecular theory of solvation for macromolecules

We propose a closure to the integral equations of molecular theory of solvation, particularly suitable for polar and charged macromolecules in electrolyte solution. This includes such systems as oligomeric polyelectrolytes at a finite concentration in aqueous and various non-aqueous solutions, as well as drug-like compounds in solution. The new closure by Kobryn, Gusarov, and Kovalenko (KGK closure) imposes the mean spherical approximation (MSA) almost everywhere in the solvation shell but levels out the density distribution function to zero (with the continuity at joint boundaries) inside the repulsive core and in the spatial regions of strong density depletion emerging due to molecular associative interactions. Similarly to MSA, the KGK closure reduces the problem to a linear equation for the direct correlation function which is predefined analytically on most of the solvation shells and has to be determined numerically on a relatively small (three-dimensional) domain of strong depletion, typically within the repulsive core. The KGK closure leads to the solvation free energy in the form of the Gaussian fluctuation (GF) functional. We first test the performance of the KGK closure coupled to the reference interaction site model (RISM) integral equations on the examples of Lennard-Jones liquids, polar and nonpolar molecular solvents, including water, and aqueous solutions of simple ions. The solvation structure, solvation chemical potential, and compressibility obtained from RISM with the KGK closure favorably compare to the results of the hypernetted chain (HNC) and Kovalenko-Hirata (KH) closures, including their combination with the GF solvation free energy. We then use the KGK closure coupled to RISM to obtain the solvation structure and thermodynamics of oligomeric polyelectrolytes and drug-like compounds at a finite concentration in electrolyte solution, for which no convergence is obtained with other closures. For comparison, we calculate their solvation structure from molecular dynamics (MD) simulations. We further couple the 3D-RISM integral equation with the 3D-version of the KGK closure, and solve it for molecular mixtures as well as oligomeric polyelectrolytes and drug-like molecules in electrolyte solutions.

Small molecule hydration energy and entropy from 3D-RISM

Implicit solvent models offer an attractive way to estimate the effects of a solvent environment on the properties of small or large solutes without the complications of explicit simulations. One common test of accuracy is to compute the free energy of transfer from gas to liquid for a variety of small molecules, since many of these values have been measured. Studies of the temperature dependence of these values (i.e. solvation enthalpies and entropies) can provide additional insights into the performance of implicit solvent models. Here, we show how to compute temperature derivatives of hydration free energies for the 3D-RISM integral equation approach. We have computed hydration free energies of 1123 small drug-like molecules (both neutral and charged). Temperature derivatives were also used to calculate hydration energies and entropies of 74 of these molecules (both neutral and charged) for which experimental data is available. While direct results have rather poor agreement with experiment, we have found that several previously proposed linear hydration free energy correction schemes give good agreement with experiment. These corrections also provide good agreement for hydration energies and entropies though simple extensions are required in some cases.

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.

The SAMPL5 challenge for embedded-cluster integral equation theory: solvation free energies, aqueous pK a, and cyclohexane-water log D

We predict cyclohexane-water distribution coefficients (log D _7.4) for drug-like molecules taken from the SAMPL5 blind prediction challenge by the "embedded cluster reference interaction site model" (EC-RISM) integral equation theory. This task involves the coupled problem of predicting both partition coefficients (log P) of neutral species between the solvents and aqueous acidity constants (pK _a) in order to account for a change of protonation states. The first issue is addressed by calibrating an EC-RISM-based model for solvation free energies derived from the "Minnesota Solvation Database" (MNSOL) for both water and cyclohexane utilizing a correction based on the partial molar volume, yielding a root mean square error (RMSE) of 2.4 kcal mol^-1 for water and 0.8-0.9 kcal mol^-1 for cyclohexane depending on the parametrization. The second one is treated by employing on one hand an empirical pK _a model (MoKa) and, on the other hand, an EC-RISM-derived regression of published acidity constants (RMSE of 1.5 for a single model covering acids and bases). In total, at most 8 adjustable parameters are necessary (2-3 for each solvent and two for the pK _a) for training solvation and acidity models. Applying the final models to the log D _7.4 dataset corresponds to evaluating an independent test set comprising other, composite observables, yielding, for different cyclohexane parametrizations, 2.0-2.1 for the RMSE with the first and 2.2-2.8 with the combined first and second SAMPL5 data set batches. Notably, a pure log P model (assuming neutral species only) performs statistically similarly for these particular compounds. The nature of the approximations and possible perspectives for future developments are discussed.