Three-dimensional Reference Interaction Site Model Research Articles

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.

Calculation of salt-dependent free energy of binding of β-lactoglobulin homodimer formation and mechanism of dimer formation using molecular dynamics simulation and three-dimensional reference interaction site model (3D-RISM): diffuse salt ions and non-polar interactions between the monomers favor the dimer formation.

There are several important phenomena in chemistry, biology, and physics where molecules (or parts of a molecule) having charges of the same sign come closer together and become stable. DNA condensation, RNA folding, colloid-colloid interactions are some of the examples of this kind. In the current work, we have investigated how β-lactoglobulin, a protein found in milk, in spite of carrying +13 charge, favors the homodimer formation in the presence of salt. We have focussed on calculating the protein-protein binding free energy in the presence of salt and identifying the thermodynamic and microscopic mechanism of the process. Estimation of binding free energy of this salt-dependent process is done by combining molecular dynamics simulation with statistical mechanical theory of three-dimensional reference interaction site model (3D-RISM). Binding free energy is evaluated from the chemical potential of the solutes as opposed to potential of mean force calculation, which gives only a constrained free energy. Our calculated values semi-quantitatively match with the experimental results. By examining the different components of binding free energy, we have found that the role of salt ions (especially of Cl-) is to shift the equilibrium towards the dimer. Non-polar (Lennard-Jones) interactions between the monomers is also favorable to the binding free energy. However, water slightly disfavors the dimer formation. For the microscopic mechanism, heterogeneous of both Na+ and Cl- near the charged residues at the binding interface and change of this charge distribution on dimer formation contribute to the stability. A fine-tuning of enthalpic and entropic effects of salt ions is found to operate at different salt concentrations. Both thermodynamic and microscopic mechanism of dimer formation gives detailed insight into the complex electrostatics of charged protein-protein binding.

Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids.

We propose an enhanced approach to the extrapolation of mean potential forces acting on atoms of solute macromolecules due to their interactions with solvent atoms in complex biochemical liquids. It improves and extends our previous extrapolation schemes by additionally including new techniques such as an exponential scaling transformation of coordinate space with weights complemented by an automatically adjusted balancing between the least square minimization of force deviations and the norm of expansion coefficients in the approximation. The expensive mean potential forces are treated in terms of the three-dimensional reference interaction site model with Kovalenko-Hirata closure molecular theory of solvation. During the dynamics, they are calculated only after every long (outer) time interval, i.e., quite rarely to reduce the computational costs. At much shorter (inner) time steps, these forces are extrapolated on the basis of their outer values. The equations of motion are then solved using a multiple time step integration within an optimized isokinetic Nosé-Hoover chain thermostat. The new approach is applied to molecular dynamics simulations of various systems consisting of solvated organic and biomolecules of different complexity. For example, we consider hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y, and protein G in aqueous solution. It is shown that in all these cases, the enhanced extrapolation provides much better accuracy of the solvation force approximation than the existing approaches. As a result, it can be used with much larger outer time steps, leading to a significant speedup of the simulations.

Prediction of P-glycoprotein inhibitors with machine learning classification models and 3D-RISM-KH theory based solvation energy descriptors.

Development of novel in silico methods for questing novel PgP inhibitors is crucial for the reversal of multi-drug resistance in cancer therapy. Here, we report machine learning based binary classification schemes to identify the PgP inhibitors from non-inhibitors using molecular solvation theory with excellent accuracy and precision. The excess chemical potential and partial molar volume in various solvents are calculated for PgP± (PgP inhibitors and non-inhibitors) compounds with the statistical-mechanical based three-dimensional reference interaction site model with the Kovalenko-Hirata closure approximation (3D-RISM-KH molecular theory of solvation). The statistical importance analysis of descriptors identified the 3D-RISM-KH based descriptors as top molecular descriptors for classification. Among the constructed classification models, the support vector machine predicted the test set of Pgp± compounds with highest accuracy and precision of ~ 97% for test set. The validation of models confirms the robustness of state-of-the-art molecular solvation theory based descriptors in identification of the Pgp± compounds.

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.

Effects of Water Addition on a Catalytic Fluorination of Dienamine.

We investigate the effects of water addition on a highly stereocontrolled fluorination of dienamine generated by α-branched enals and 6′-hydroxy-9-amino-9-deoxy-epi-quinidine with N-fluorobenzenesulfonimide (NFSI) in the presence of Brønsted acid both experimentally and theoretically. It is experimentally found that water addition to organic solvent significantly shortens the reaction time whereas excessive water addition decreases the enantiomeric excess. The results calculated with three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) method are in good agreement with the experimental ones. It is revealed that the shortness of reaction time is caused by the reactant destabilization and that the decrease in enantiomeric excess is due to the difference of hydration free energy between two transition states.

Correction terms for the solvation free energy functional of three-dimensional reference interaction site model based on the reference-modified density functional theory

Recently, we derived the reference-modified density functional theory (RMDFT) to calculate the solvation free energy (SFE) with high accuracy, introducing a reference system to the DFT for polyatomic molecular liquids. The RMDFT functional consists of the DFT using second-order approximation (DFT(D)) functional and the correction terms. The DFT(D) functional are equivalent to the Singer-Chandler formula for the hypernetted chain closure equation. The contribution of the correction terms has a strong correlation with the partial molar volume (PMV) of solute. Thus, the RMDFT functional has almost the same accuracy as the PMV correction. Furthermore, we combined the Singer-Chandler formula for the Kovalenko-Hirata closure and the correction terms to avoid inconsistency between the closure equation and the SFE functional. It become clear that the inconsistency is unimportant, whereas the combined functional works well for the amino acid side chain analogues molecules.

Solvated lithium ions in defective Prussian blue

Prussian Blue (PB) or ferric hexacyanoferrate (II) is one of the most attractive materials in green battery industry. It has defective structure (d-PB), , that one of [Fe(CN)6]4− group is missing, and hydrated with water molecules at the 24e empty nitrogen site. In this study, we investigated the distributions of water and Li+ in d-PB by using three-dimensional reference interaction site-model (3D-RISM) theory, which is a statistical mechanics theory of molecular liquids. The theory can examine the selective ion adsorption in solvated molecular materials. The results from 3D-RISM show that there are 14 water molecules located in different positions inside the d-PB lattice, which are in good agreement with experiment. Moreover, we also found the Li+ distributed at inside d-PB lattice positioned closely to the 32f spherical cavity of d-PB.

Implementation of state-averaged MCSCF method to RISM- and 3D-RISM-SCF schemes

The state-averaged multiconfiguration self-consistent field (MCSCF) method was implemented to the reference interaction site model and three-dimensional reference interaction site model (RISM and 3D-RISM) SCF schemes, where the electronic structures of multiple states and solvation structure are determined simultaneously by the state-averaged MCSCF method and state-specific RISM-SCF/3D-RISM-SCF scheme, respectively, in a single calculation. The method was applied to the potential energy curves of the low-lying states of NaCl in aqueous solution and solvation shifts of the excitation energy of formaldehyde and p-nitroaniline. The results showed good agreement with those of the state-specific MCSCF and/or experiments.

Repurposing of FDA-Approved NSAIDs for DPP-4 Inhibition as an Alternative for Diabetes Mellitus Treatment: Computational and in Vitro Study.

A drug repurposing strategy could be a potential approach to overcoming the economic costs for diabetes mellitus (DM) treatment incurred by most countries. DM has emerged as a global epidemic, and an increase in the outbreak has led developing countries like Mexico, India, and China to recommend a prevention method as an alternative proposed by their respective healthcare sectors. Incretin-based therapy has been successful in treating diabetes mellitus, and inhibitors like sitagliptin, vildagliptin, saxagliptin, and alogliptin belong to this category. As of now, drug repurposing strategies have not been used to identify existing therapeutics that can become dipeptidyl peptidase-4 (DPP-4) inhibitors. Hence, this work presents the use of bioinformatics tools like the Activity Atlas model, flexible molecular docking simulations, and three-dimensional reference interaction site model (3D-RISM) calculations to assist in repurposing Food and Drug Administration (FDA)-approved drugs into specific nonsteroidal anti-inflammatory medications such as DPP-4 inhibitors. Initially, the Activity Atlas model was constructed based on the top scoring DPP-4 inhibitors, and then the model was used to understand features of nonsteroidal anti-inflammatory drugs (NSAIDs) as a function of electrostatic, hydrophobic, and active shape features of DPP-4 inhibition. The FlexX algorithm was used to infer protein–ligand interacting residues, and binding energy, to predict potential draggability towards the DPP-4 mechanism of action. 3D-RISM calculations on piroxicam-bound DPP-4 were used to understand the stability of water molecules at the active site. Finally, piroxicam was chosen as the repurposing drug to become a new DPP-4 inhibitor and validated experimentally using fluorescence spectroscopy assay. These findings are novel and provide new insights into the role of piroxicam as a new lead to inhibit DPP-4 and, taking into consideration the biological half-life of piroxicam, it can be proposed as a possible therapeutic strategy for treating diabetes mellitus.

Performance of 3D-RISM-KH in Predicting Hydration Free Energy: Effect of Solute Parameters.

The three-dimensional reference interaction site model molecular solvation theory with the Kovalenko-Hirata closure relation has been shown to produce excellent solvation characteristics for a large class of (bio)chemical systems in solution. Correct calculation of hydration free energy is central to successful application of any solvation model. In order to find out the best possible force-field parameters to be used for hydration free energy calculation with the aforementioned theory, we have developed an extended database containing a large number of experimental solvation free energies available in the current literature and used a plethora of theoretical models for assessment. The general Amber force field was found to perform satisfactorily, whereas special care should be taken in solute charge assignment with the universal force field.

Three-Dimensional Reference Interaction Site Model Self-Consistent Field Study on the Coordination Structure and Excitation Spectra of Cu(II)-Water Complexes in Aqueous Solution.

The molecular and solvation structures of the hydrated Cu2+ ions and their excitation spectra were investigated using the Kohn-Sham density functional theory (DFT) and the three-dimensional reference interaction site model (3D-RISM) self-consistent field method. Five stable geometrical structures were found to exist in aqueous solution: the distorted octahedral [Cu(H2O)6]2+ in C i and D2 h symmetries, the square pyramidal and trigonal bipyramidal [Cu(H2O)5]2+, and the square planar [Cu(H2O)4]2+. The distorted octahedral structure in the C i symmetry is preferred in [Cu(H2O)6]2+, and the square pyramidal and trigonal bipyramidal [Cu(H2O)5]2+ show almost the same stability. Among these geometries, the six-coordinate complex [Cu(H2O)6]2+ in the C i symmetry had the lowest Helmholtz energy. [Cu(H2O)6]2+ had a distorted octahedral structure, that is, two long axial bonds and four short equatorial bonds. The spatial and radial distribution function analyses for [Cu(H2O)5]2+ and [Cu(H2O)4]2+ showed that [Cu(H2O)5]2+ and [Cu(H2O)4]2+ had one and two solvent water molecules that constituted a distorted octahedron with ligand water distribution. The coordination numbers (CNs) derived from the distribution functions were 5.2-5.4 for [Cu(H2O)5]2+ and 5.3 for [Cu(H2O)4]2+. These results indicated that the Cu2+ ion in an aqueous solution had 5-6 coordination water molecules in the first hydration shell and some structures with different CNs may interchange in the solution. The excitation energies and electronic configurations of low-lying d-d excited states were calculated using the time-dependent DFT with the electric field generated by 3D-RISM. The orbital energies and electronic configurations were in a similar picture to those of the classical crystal field theory because of the highly symmetrical features of all structures. In [Cu(H2O)6]2+, the degeneracies of orbitals were resolved, whereas in [Cu(H2O)5]2+ and [Cu(H2O)4]2+, weak and strong quasi-degeneracies remained. As a result, only the four-coordinate complex generated third and fourth excited states, whereas in other complexes, there were no obvious characters of degeneracies. The resulting excitation energies were in good agreement with the absorption spectra.

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.

Dependence of Absorption and Emission Spectra on Polymorphs of Gold(I) Isocyanide Complexes: Theoretical Study with QM/MM Approach

We theoretically investigated phenyl(phenyl isocyanide) gold(I) (PhNC)Au(Ph) 1 and phenyl(dimethylphenyl isocyanide) gold(I) (dimPhNC)Au(Ph) 2 in crystal using our periodic quantum mechanics/molecular mechanics (QM/MM) method based on the self-consistent point charges to elucidate interesting mechano-chemical changes of absorption and emission spectra of 1 and 2 in crystal. To characterize 1 and 2 in crystal, their absorption and emission spectra in crystal were compared to those in gas phase and CHCl3 solvent, where a three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) was employed to incorporate solvation effect. To investigate the phosphorescence spectrum in crystal, we optimized the geometry of the molecule at the triplet state in crystal which had ground-state geometry because the population of the excited state is generally very small. The QM/MM calculations showed that 1 formed two polymorphs 1b and 1y, 2 formed two polymorphs 2b and 2g, and 1y was more stable tha...

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.

A tool written in Scala for preparation and analysis in MD simulation and 3D-RISM calculation of biomolecules.

Researchers studying biomolecules require easy-to-use, customizable tools allowing them to effectively use other molecular science packages written for molecular dynamics (MD), quantum chemistry, statistical mechanics, and molecular graphics. This paper presents a Scala tool for the computational science of biomolecules (STCSB) developed in Scala, which allows users to prepare and run MD simulations, as well as perform three-dimensional reference interaction site model (3D-RISM) calculations of biomolecules. Features of the STCSB include the following: (1) a cross-platform application running on a Java virtual machine; (2) handling hierarchical XML-based data formats such as the protein data bank markup language (PDBML); (3) prepared application programming interfaces (APIs) with both character user interface (CUI) and graphical user interface (GUI) options; (4) prepared APIs for molecular graphics; and (5) a scalable source code based on the Model-View-Controller (MVC) architectural pattern.

Molecular Mechanism of Depolarization-Dependent Inactivation in W366F Mutant of Kv1.2.

Voltage-gated potassium channels play crucial roles in regulating membrane potential. They are activated by membrane depolarization, allowing the selective permeation of K+ ions across the plasma membrane, and enter a nonconducting state after lasting depolarization, a process known as inactivation. Inactivation in voltage-activated potassium channels occurs through two distinct mechanisms, N-type and C-type inactivation. C-type inactivation is caused by conformational changes in the extracellular mouth of the channel, whereas N-type inactivation is elicited by changes in the cytoplasmic mouth of the protein. The W434F-mutated Shaker channel is known as a nonconducting mutant and is in a C-type inactivation state at a depolarizing membrane potential. To clarify the structural properties of C-type inactivated protein, we performed molecular dynamics simulations of the wild-type and W366F (corresponding to W434F in Shaker) mutant of the Kv1.2-2.1 chimera channel. The W366F mutant was in a nearly nonconducting state with a depolarizing voltage and recovered from inactivation with a reverse voltage. Our simulations and three-dimensional reference interaction site model analysis suggested that structural changes in the selectivity filter upon membrane depolarization trap K+ ions around the inner mouth of the selectivity filter and prevent ion permeation. This pore restriction is involved in the molecular mechanism of C-type inactivation.

Site density models of inhomogeneous classical molecular liquids

We present a general framework for developing site density descriptions of inhomogeneous molecular liquids. It avoids explicit construction of full site density functional in lieu of self-consistent field equations, and easily accommodates the case of flexible molecules. We illustrate our methodology with two particular examples. The first one, cluster site density functional theory (CSDFT), is based on molecular gas reference with a specific cluster representation. The resulting approach provides natural separation between intra- and inter-molecular effects, leading to a compact analytical form for the self-consistent density equation similar to simple liquid theory. The second example is related to an existing three-dimensional reference interaction site model (3D-RISM). We demonstrate that 3D-RISM arises from a specific non-Hamiltonian based reference decomposition. We establish a connection between CSDFT and 3D-RISM, and use it to analyze intra-molecular and inter-molecular errors associated with the 3D-RISM description of an inhomogeneous dimer molecular liquid system. We observe that the main source of errors can be traced to insufficient description of inter-molecular effects in 3D-RISM theory, and intra-molecular errors are fairly small.

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.

A new method for finding the minimum free energy pathway of ions and small molecule transportation through protein based on 3D-RISM theory and the string method

A new method for finding the minimum free energy pathway (MFEP) of ions and small molecule transportation through a protein based on the three-dimensional reference interaction site model (3D-RISM) theory combined with the string method has been proposed. The 3D-RISM theory produces the distribution function, or the potential of mean force (PMF), for transporting substances around the given protein structures. By applying the string method to the PMF surface, one can readily determine the MFEP on the PMF surface. The method has been applied to consider the Na+ conduction pathway of channelrhodopsin as an example.