Effect of Molecular Orientational Correlations on Solvation Free Energy Computed by Reference Interaction Site Model Theory

RISMiCal: A software package to perform fast RISM/3D-RISM calculations

Solvent plays an essential role in a variety of chemical, physical, and biological processes that occur in the solution phase. The reference interaction site model (RISM) and its three-dimensional extension (3D-RISM) serve as powerful computational tools for modeling solvation effects in chemical reactions, biological functions, and structure formations. We present the RISM integrated calculator (RISMiCal) program package, which is based on RISM and 3D-RISM theories with fast GPU code. RISMiCal has been developed as an integrated RISM/3D-RISM program that has interfaces with external programs such as Gaussian16, GAMESS, and Tinker. Fast 3D-RISM programs for single- and multi-GPU codes written in CUDA would enhance the availability of these hybrid methods because they require the performance of many computationally expensive 3D-RISM calculations. We expect that our package can be widely applied for chemical and biological processes in solvent. The RISMiCal package is available at https://rismical-dev.github.io.

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.

Coexistence of two coacervate phases of polyglycine in water suggested by polymer reference interaction site model theory

Mixing Gibbs energy and phase equilibria of aqueous solutions of polyglycine were studied theoretically by means of polymer reference interaction site model integral equation theory combined with the Gibbs-Duhem method. In addition to the ordinary liquid-liquid phase separation between dilute and concentrated solutions, the theoretical calculation predicted the coexistence of two coacervate phases, namely, the lower- and higher-density coacervates. The relative thermodynamic stabilities of these two phases change with the polymerization degree of polyglycine. The higher-density coacervate phase was rapidly stabilized by increasing the polymer length, and the lower-density phase became metastable at large polymers. The hydrogen bonds between the peptide chains were strengthened, and water was thermodynamically destabilized in the higher-density coacervate. A possible relation with the formation of amyloid fibril within a liquid droplet is also discussed.

Effects of intramolecular chain conformation on the hydration and miscibility of polyethylene glycol in water studied by means of polymer reference interaction site model theory

To examine the conventional idea that the gauche conformation of the OCCO dihedral angle promotes the dissolution of polyethylene glycol (PEG) in water through strong hydration, the thermodynamic properties of liquid mixtures of PEG and water were studied by means of polymer reference interaction site model (PRISM) theory. The intramolecular correlation functions required as input for PRISM theory were calculated by the generator matrix method, accompanied by changes in the distribution of dihedral angles. In the infinite dilution limit, the increased probability of gauche conformation of the OCCO dihedral angles stabilizes the hydration of PEG through enhanced hydrogen bonding between the ether oxygen of PEG and water. The mixing Gibbs energies of the liquid mixtures were also calculated in the whole concentration range based on the Gibbs-Duhem equation, as per our recent proposal. A liquid-liquid phase separation was observed when all the dihedral angles of PEG were in the trans conformation; for the liquid mixture to be miscible in the whole concentration range, the introduction of the OCCO gauche conformation was found to be indispensable. The above theoretical results support the conventional idea that the OCCO gauche conformation is important for the high miscibility of PEG and water.

Theoretical Analysis of the Role of Water in Ligand Binding to Cucurbit[n]uril of Different Sizes

The role of water in host-ligand binding was investigated using a combination of molecular dynamics simulation and three-dimensional reference interaction site model theory. Three different hosts were selected (CB6, CB7, and CB8). Six organic molecules were used as representative ligands: dimethyl sulfoxide (DMSO), N,N-dimethylformamide (DMF), acetone, 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO), cyclopentanone (CPN), and pyrrole. From the binding free energy and its components, we divided the ligands into two groups: those with relatively small molecular size (DMSO, DMF, acetone, and pyrrole) and those with relatively large molecular size (DBO and CPN). We established that the solvent water in the CB6 cavity can be completely displaced by small ligands, resulting in a greater binding affinity compared with larger CBs, except in the case of the small pyrrole ligand, due to outstanding intrinsic properties such as the relatively high hydrophobicity and low dipole moment. In the case of the large ligands, the solvent water can be displaced by DBO and CPN in both CB6 and CB7; there were similar tendencies in their binding affinities, with the greatest affinity in the CB7 complexes. However, the tendencies of the binding affinity components are completely different due to the difference between the complex structure and the solvation structure when a ligand binds with a CB structure. The binding affinities suggest that the size fit between the ligand and CB cannot guarantee the greatest binding affinity gain because the binding structure and intrinsic properties of CB and ligand equally play a crucial role.

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.

Phase equilibrium of three-component liquid systems composed of water, alcohol, and sodium chloride studied by the reference interaction-site model integral equation theory

A theoretical method for calculating the thermodynamic properties and phase equilibria of a binary liquid mixture using the reference interaction-site model (RISM) integral equation theory, which we had proposed recently, was extended to ternary liquid systems containing salt. A novel dielectric correction of the RISM theory for a mixture of solvents was also proposed. The theory was applied to mixtures composed of water, alcohol, and NaCl, where the alcohol was either methanol or ethanol. The decrease in NaCl solubility with increasing alcohol molar fractions in the solvent was calculated. In the ethanol system, the theory yielded salt-induced liquid-liquid phase separation, which was observed experimentally in a ternary mixture of water, 1-propanol, and NaCl. The phase diagram of the ternary system was determined theoretically.

Study of phase equilibria and thermodynamic properties of liquid mixtures using the integral equation theory: Application to water and alcohol mixtures

A theoretical method for calculating the thermodynamic properties and phase equilibria of liquid-liquid mixtures using the integral equation theory is proposed. The solvation chemical potentials of the two components are evaluated by the integral equation theory and the isothermal-isobaric variation of the total density with composition is determined to satisfy the Gibbs-Duhem relation. Given the density of a pure component, the method can calculate the densities of the mixture at any composition. Furthermore, it can treat the phase equilibrium without thermodynamic inconsistency with respect to the Gibbs-Duhem relation. This method was combined with the reference interaction-site model integral equation theory and applied to mixtures of water + 1-alcohol by changing the alcohol from methanol to 1-butanol. The destabilization of the mixing Gibbs energy by increasing the hydrophobicity of the alcohol and demixing of the water-butanol mixture were reproduced. However, quantitative agreement with experiments is not satisfactory, and further improvements of the integral equation theory and the molecular models are required.

Renormalized site density functional theory for models of ion hydration

The development of accurate statistical mechanics models of molecular liquid systems is a problem of great practical and fundamental importance. Site-density functional theory (SDFT) is one of the promising directions in this area, but its success hinges upon the ability to efficiently reconcile the co-existence of two distinct intra- and inter-molecular interaction regimes in a molecular liquid. The renormalized formulation of SDFT (RSDFT), which we have recently developed, resolves this problem by introducing an additional potential field variable that decouples two interaction scales and maps the molecular liquid problem onto the effective simple liquid mixture. This work provides a critical assessment of RSDFT for the hydrated ion system-a problem that historically has always been one of the most difficult cases for SDFT applications. Using a two-site model of water, we perform a comprehensive analysis of hydrated alkali metal and halogen ions, including both structural and free energy based characteristics. The results indicate that RSDFT provides a significant improvement over conventional three-dimensional reference interaction site model implementations and may prove useful in coarse grained simulations based on two-site solvent models.

Comprehensive 3D-RISM analysis of the hydration of small molecule binding sites in ligand-free protein structures

Hydration is a critical factor in the ligand binding process. Herein, to examine the hydration states of ligand binding sites, the three‐dimensional distribution function for the water oxygen site, g_O(r), is computed for 3,706 ligand‐free protein structures based on the corresponding small molecule–protein complexes using the 3D‐RISM theory. For crystallographic waters (CWs) close to the ligand, g_O(r) reveals that several CWs are stabilized by interaction networks formed between the ligand, CW, and protein. Based on the g_O(r) for the crystallographic binding pose of the ligand, hydrogen bond interactions are dominant in the highly hydrated regions while weak interactions such as CH‐O are dominant in the moderately hydrated regions. The polar heteroatoms of the ligand occupy the highly hydrated and moderately hydrated regions in the crystallographic (correct) and wrongly docked (incorrect) poses, respectively. Thus, the g_O(r) of polar heteroatoms may be used to distinguish the correct binding poses.

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.

Chemical bond effects in classical site density functional theory of inhomogeneous molecular liquids

Intra-molecular interactions or chemical bonds represent one of the main distinguishing characteristics of molecular fluids. Development of accurate and practical methods to treat these effects is one of the long standing problems in classical site density functional theory (SDFT). One particular instance when these issues become particularly severe is the case of classical interaction potentials with auxiliary sites or dummy atoms. In this situation, current SDFT implementations, such as the three-dimensional reference interaction site model, lead to nonphysical results. We re-examine this issue in this work using our recent reformulation of SDFT (Valiev and Chuev, J. Stat. Mech.: Theory Exp. 2018, 093201). We put forward a simple practical solution to this problem and illustrate its utility for the case of spherical solutes in diatomic liquids.

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.