The Three-Dimensional Reference Interaction Site Model Approach as a Promising Tool for Studying Hydrated Viruses and Their Complexes with Ligands.

Viruses are the most numerous biological form living in any ecosystem. Viral diseases affect not only people but also representatives of fauna and flora. The latest pandemic has shown how important it is for the scientific community to respond quickly to the challenge, including critically assessing the viral threat and developing appropriate measures to counter this threat. Scientists around the world are making enormous efforts to solve these problems. In silico methods, which allow quite rapid obtention of, in many cases, accurate information in this field, are effective tools for the description of various aspects of virus activity, including virus-host cell interactions, and, thus, can provide a molecular insight into the mechanism of virus functioning. The three-dimensional reference interaction site model (3D-RISM) seems to be one of the most effective and inexpensive methods to compute hydrated viruses, since the method allows us to provide efficient calculations of hydrated viruses, remaining all molecular details of the liquid environment and virus structure. The pandemic challenge has resulted in a fast increase in the number of 3D-RISM calculations devoted to hydrated viruses. To provide readers with a summary of this literature, we present a systematic overview of the 3D-RISM calculations, covering the period since 2010. We discuss various biophysical aspects of the 3D-RISM results and demonstrate capabilities, limitations, achievements, and prospects of the method using examples of viruses such as influenza, hepatitis, and SARS-CoV-2 viruses.

Structural Fluctuation, Relaxation, and Folding of Protein: An Approach Based on the Combined Generalized Langevin and RISM/3D-RISM Theories.

In 2012, Kim and Hirata derived two generalized Langevin equations (GLEs) for a biomolecule in water, one for the structural fluctuation of the biomolecule and the other for the density fluctuation of water, by projecting all the mechanical variables in phase space onto the two dynamic variables: the structural fluctuation defined by the displacement of atoms from their equilibrium positions, and the solvent density fluctuation. The equation has an expression similar to the classical Langevin equation (CLE) for a harmonic oscillator, possessing terms corresponding to the restoring force proportional to the structural fluctuation, as well as the frictional and random forces. However, there is a distinct difference between the two expressions that touches on the essential physics of the structural fluctuation, that is, the force constant, or Hessian, in the restoring force. In the CLE, this is given by the second derivative of the potential energy among atoms in a protein. So, the quadratic nature or the harmonicity is only valid at the minimum of the potential surface. On the contrary, the linearity of the restoring force in the GLE originates from the projection of the water's degrees of freedom onto the protein's degrees of freedom. Taking this into consideration, Kim and Hirata proposed an ansatz for the Hessian matrix. The ansatz is used to equate the Hessian matrix with the second derivative of the free-energy surface or the potential of the mean force of a protein in water, defined by the sum of the potential energy among atoms in a protein and the solvation free energy. Since the free energy can be calculated from the molecular mechanics and the RISM/3D-RISM theory, one can perform an analysis similar to the normal mode analysis (NMA) just by diagonalizing the Hessian matrix of the free energy. This method is referred to as the Generalized Langevin Mode Analysis (GLMA). This theory may be realized to explore a variety of biophysical processes, including protein folding, spectroscopy, and chemical reactions. The present article is devoted to reviewing the development of this theory, and to providing perspective in exploring life phenomena.

Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction.

Hydration free energies of small molecules are commonly used as benchmarks for solvation models. However, errors in predicting hydration free energies are partially due to the force fields used and not just the solvation model. To address this, we have used the 3D reference interaction site model (3D-RISM) of molecular solvation and existing benchmark explicit solvent calculations with a simple element count correction (ECC) to identify problems with the non-bond parameters in the general AMBER force field (GAFF). 3D-RISM was used to calculate hydration free energies of all 642 molecules in the FreeSolv database, and a partial molar volume correction (PMVC), ECC, and their combination (PMVECC) were applied to the results. The PMVECC produced a mean unsigned error of 1.01±0.04kcal/mol and root mean squared error of 1.44±0.07kcal/mol, better than the benchmark explicit solvent calculations from FreeSolv, and required less than 15 s of computing time per molecule on a single CPU core. Importantly, parameters for PMVECC showed systematic errors for molecules containing Cl, Br, I, and P. Applying ECC to the explicit solvent hydration free energies found the same systematic errors. The results strongly suggest that some small adjustments to the Lennard-Jones parameters for GAFF will lead to improved hydration free energy calculations for all solvent models.

Realization of the structural fluctuation of biomolecules in solution: Generalized Langevin mode analysis.

A new theoretical method, referred to as Generalized Langevin Mode Analysis (GLMA), is proposed to analyze the mode of structural fluctuations of a biomolecule in solution. The method combines the two theories in the statistical mechanics, or the Generalized Langevin theory and the RISM/3D-RISM theory, to calculate the second derivative, or the Hessian matrix, of the free energy surface of a biomolecule in aqueous solution, which consists of the intramolecular interaction among atoms in the biomolecule and the solvation free energy. The method is applied to calculate the wave-number spectrum of an alanine dipeptide in water for which the optical heterodyne-detected Raman-induced spectroscopy (RIKES) spectrum is available to compare with. The theoretical analysis reproduced the main features of the experimental spectrum with respect to the peak positions of the four bands around ~90 cm-1 , ~240 cm-1 , ~370 cm-1 , and 400 cm-1 , observed in the experimental spectrum, in spite that the physics involved in the two spectrum was not exactly the same: the experimental spectrum includes the contributions from the dipeptide and the water molecules interacting with the solute, while the theoretical one is just concerned with the solute molecule, influenced by solvation. Two major discrepancies between the theoretical and experimental spectra, one in the band intensity around ~100 cm-1 , and the other in the peak positions around ~370 cm-1 , are discussed in terms of the fluctuation mode of water molecules interacting with the dipeptide, which is not taken explicitly into account in the theoretical analysis.

Aggregation propensities of proteins with varying degrees of disorder.

The hydration thermodynamics of a globular protein (AcP), three intrinsically disordered protein regions (1CD3, 1MVF, 1F0R) and a fully disordered protein (α-synuclein) is studied by an approach that combines an all-atom explicit water molecular dynamics simulations and three-dimensional reference interaction site model (3D-RISM) theory. The variation in hydration free energy with percentage disorder of the selected proteins is investigated through its nonelectrostatic and electrostatic components. A decrease in hydration free energy is observed with an increase in percentage disorder, indicating favorable interactions of the disordered proteins with the solvent. This confirms the role of percentage disorder in determining the aggregation propensity of proteins which is measured in terms of the hydration free energy in addition to their respective mean net charge and mean hydrophobicity. The hydration free energy is decoupled into energetic and entropic terms. A residue-wise decomposition analysis of the hydration free energy for the selected proteins is evaluated. The decomposition shows that the disordered regions contribute more than the ordered ones for the intrinsically disordered protein regions. The dominant role of electrostatic interactions is confirmed from the residue-wise decomposition of the hydration free energy. The results depict that the negatively charged residues contribute more to the total hydration free energy for the proteins with negative mean net charge, while the positively charged residues contribute more for proteins with positive mean net charge.

Protein 3D Hydration: A Case of Bovine Pancreatic Trypsin Inhibitor.

Characterization of the hydrated state of a protein is crucial for understanding its structural stability and function. In the present study, we have investigated the 3D hydration structure of the protein BPTI (bovine pancreatic trypsin inhibitor) by molecular dynamics (MD) and the integral equation method in the three-dimensional reference interaction site model (3D-RISM) approach. Both methods have found a well-defined hydration layer around the protein and revealed the localization of BPTI buried water molecules corresponding to the X-ray crystallography data. Moreover, under 3D-RISM calculations, the obtained positions of waters bound firmly to the BPTI sites are in reasonable agreement with the experimental results mentioned above for the BPTI crystal form. The analysis of the 3D hydration structure (thickness of hydration shell and hydration numbers) was performed for the entire protein and its polar and non-polar parts using various cut-off distances taken from the literature as well as by a straightforward procedure proposed here for determining the thickness of the hydration layer. Using the thickness of the hydration shell from this procedure allows for calculating the total hydration number of biomolecules properly under both methods. Following this approach, we have obtained the thickness of the BPTI hydration layer of 3.6 Å with 369 water molecules in the case of MD simulation and 3.9 Å with 333 water molecules in the case of the 3D-RISM approach. The above procedure was also applied for a more detailed description of the BPTI hydration structure near the polar charged and uncharged radicals as well as non-polar radicals. The results presented for the BPTI as an example bring new knowledge to the understanding of protein hydration.

Understanding the Liquid States of Cyclic Hydrocarbons Containing N, O, and S Atoms via the 3D-RISM-KH Molecular Solvation Theory.

The 3D-reference interaction site model (3D-RISM) molecular solvation theory in combination with the Kovalenko-Hirata (KH) closure is extended to seven heterocyclic liquids to understand their liquid states and to test the performance of the theory in solvation free energy (SFE) calculations of solutes in select solvents. The computed solvent site distribution profiles were compared with the all-atom molecular dynamics (MD) simulations, showing comparable performances. The computational results were compared against the structural parameters for liquids, whenever available, as well as against the experimental SFEs. The liquids are found to have local ordered structures held together via weak interactions in both the RISM and MD simulations. The 3D-RISM-KH computed SFEs are in good agreement with the benchmark values for the tetrahydrothiophene-S,S-dioxide, and showed comparatively larger deviations in the case of the SFEs in the tetrahydrofuran continuum.

Allosteric Binding of MDMA to the Human Serotonin Transporter (hSERT) via Ensemble Binding Space Analysis with ΔG Calculations, Induced Fit Docking and Monte Carlo Simulations.

Despite the recent promising results of MDMA (3,4-methylenedioxy-methamphetamine) as a psychotherapeutic agent and its history of misuse, little is known about its molecular mode of action. MDMA enhances monoaminergic neurotransmission in the brain and its valuable psychoactive effects are associated to a dual action on the 5-HT transporter (SERT). This drug inhibits the reuptake of 5-HT (serotonin) and reverses its flow, acting as a substrate for the SERT, which possesses a central binding site (S1) for antidepressants as well as an allosteric (S2) one. Previously, we characterized the spatial binding requirements for MDMA at S1. Here, we propose a structure-based mechanistic model of MDMA occupation and translocation across both binding sites, applying ensemble binding space analyses, electrostatic complementarity, and Monte Carlo energy perturbation theory. Computed results were correlated with experimental data (r = 0.93 and 0.86 for S1 and S2, respectively). Simulations on all hSERT available structures with Gibbs free energy estimations (ΔG) revealed a favourable and pervasive dual binding mode for MDMA at S2, i.e., adopting either a 5-HT or an escitalopram-like orientation. Intermediate ligand conformations were identified within the allosteric site and between the two sites, outlining an internalization pathway for MDMA. Among the strongest and more frequent interactions were salt bridges with Glu494 and Asp328, a H-bond with Thr497, a π-π with Phe556, and a cation-π with Arg104. Similitudes and differences with the allosteric binding of 5-HT and antidepressants suggest that MDMA may have a distinctive chemotype. Thus, our models may provide a framework for future virtual screening studies and pharmaceutical design and to develop hSERT allosteric compounds with a unique psychoactive MDMA-like profile.

Accelerating the 3D reference interaction site model theory of molecular solvation with treecode summation and cut-offs.

The 3D reference interaction site model (3D-RISM) of molecular solvation is a powerful tool for computing the equilibrium thermodynamics and density distributions of solvents, such as water and co-ions, around solute molecules. However, 3D-RISM solutions can be expensive to calculate, especially for proteins and other large molecules where calculating the potential energy between solute and solvent requires more than half the computation time. To address this problem, we have developed and implemented treecode summation for long-range interactions and analytically corrected cut-offs for short-range interactions to accelerate the potential energy and long-range asymptotics calculations in non-periodic 3D-RISM in the AmberTools molecular modeling suite. For the largest single protein considered in this work, tubulin, the total computation time was reduced by a factor of 4. In addition, parallel calculations with these new methods scale almost linearly and the iterative solver remains the largest impediment to parallel scaling. To demonstrate the utility of our approach for large systems, we used 3D-RISM to calculate the solvation thermodynamics and density distribution of 7-ring microtubule, consisting of 910 tubulin dimers, over 1.2 million atoms.

Response to Comment on "Density Functional Theory and 3D-RISM-KH molecular theory of solvation studies of CO2 reduction on Cu-, Cu2O-, Fe-, and Fe3O4-based nanocatalysts".

In response to the Comment on "Density Functional Theory and 3D-RISM-KH molecular theory of solvation studies of CO2 reduction on Cu-, Cu2O-, Fe-, and Fe3O4-based nanocatalysts" (Gusarov J Mol Model 27:344-344, 1), the behavior of a CO* molecule on a Cu21 nanocatalyst slab without a solution considered in the Comment is considerably different from our case of this system in 1.0 Mol KH2PO4 ambient aqueous solution. Moreover, our calculations for CO* on Cu21 without a solution that we presented in our article are similar to those shown in the Comment. The Comment and its conclusions are controversial and should be treated with much caution.

Asymmetric Interplay Between K+ and Blocker and Atomistic Parameters From Physiological Experiments Quantify K+ Channel Blocker Release.

Modulating the activity of ion channels by blockers yields information on both the mode of drug action and on the biophysics of ion transport. Here we investigate the interplay between ions in the selectivity filter (SF) of K+ channels and the release kinetics of the blocker tetrapropylammonium in the model channel KcvNTS. A quantitative expression calculates blocker release rate constants directly from voltage-dependent ion occupation probabilities in the SF. The latter are obtained by a kinetic model of single-channel currents recorded in the absence of the blocker. The resulting model contains only two adjustable parameters of ion-blocker interaction and holds for both symmetric and asymmetric ionic conditions. This data-derived model is corroborated by 3D reference interaction site model (3D RISM) calculations on several model systems, which show that the K+ occupation probability is unaffected by the blocker, a direct consequence of the strength of the ion-carbonyl attraction in the SF, independent of the specific protein background. Hence, KcvNTS channel blocker release kinetics can be reduced to a small number of system-specific parameters. The pore-independent asymmetric interplay between K+ and blocker ions potentially allows for generalizing these results to similar potassium channels.

A computational method to simulate global conformational changes of proteins induced by cosolvent.

A computational method to investigate the global conformational change of a protein is proposed by combining the linear response path following (LRPF) method and three-dimensional reference interaction site model (3D-RISM) theory, which is referred to as the LRPF/3D-RISM method. The proposed method makes it possible to efficiently simulate protein conformational changes caused by either solutions of varying concentrations or the presence of cosolvent species by taking advantage of the LRPF and 3D-RISM. The proposed method is applied to the urea-induced denaturation of ubiquitin. The LRPF/3D-RISM trajectories successfully simulate the early stage of the denaturation process within the simulation time of 300 ns, whereas no significant structural change is observed even in the 1 µs standard MD simulation. The obtained LRPF/3D-RISM trajectories reproduce the mechanism of the urea denaturation of ubiquitin reported in previous studies, and demonstrate the high efficiency of the method.

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.

Predicting PAMPA permeability using the 3D-RISM-KH theory: are we there yet?

The parallel artificial membrane permeability assay (PAMPA), a non-cellular lab-based assay, is extensively used to measure the permeability of pharmaceutical compounds. PAMPA experiments provide a working mimic of a molecule passing through cells and PAMPA values are widely used to estimate drug absorption parameters. There is an increased interest in developing computational methods to predict PAMPA permeability values. We developed an in silico model to predict the permeability of compounds based on the PAMPA assay. We used the three-dimensional reference interaction site model (3D-RISM) theory with the Kovalenko-Hirata (KH) closure to calculate the excess chemical potentials of a large set of compounds and predicted their apparent permeability with good accuracy (mean absolute error or MAE = 0.69 units) when compared to a published experimental data set. Furthermore, our in silico PAMPA protocol performed very well in the binary prediction of 288 compounds as being permeable or impermeable (precision = 94%, accuracy = 93%). This suggests that our in silico protocol can mimic the PAMPA assay and could aid in the rapid discovery or screening of potentially therapeutic drug leads that can be delivered to a desired tissue.

Virtual screening and free energy estimation for identifying Mycobacterium tuberculosis flavoenzyme DprE1 inhibitors.

In Mycobacterium tuberculosis (MTB), the cell wall synthesis flavoenzyme decaprenylphosphoryl-ß-d-ribose 2'-epimerase (DprE1) plays a crucial role in host pathogenesis, virulence, lethality and survival under stress. The emergence of different variants of drug resistant MTB are a major threat worldwide which essentially requires more effective new drug molecules with no major side effects. Here, we used structure based virtual screening of bioactive molecules from the ChEMBL database targeting DprE1, having bioactive 78,713 molecules known for anti-tuberculosis activity. An extensive molecular docking, binding affinity and pharmacokinetics profile filtering results in the selection four compounds, C5 (ChEMBL2441313), C6 (ChEMBL2338605), C8 (ChEMBL441373) and C10 (ChEMBL1607606) which may explore as potential drug candidates. The obtained results were validated with thirteen known DprE1 inhibitors. We further estimated the free-binding energy, solvation and entropy terms underlying the binding properties of DprE1-ligand interactions with the implication of MD simulation, MM/GBSA, MM/PBSA and MM/3D-RISM. Interestingly, we find that C6 shows the highest ΔG scores (-41.28 ± 3.51, -22.36 ± 3.17, -10.33 ± 5.70 kcal mol-1) in MM/GBSA, MM/PBSA and MM/3D-RISM assay, respectively. Whereas, the lowest ΔG scores (-35.31 ± 3.44, -13.67 ± 2.65, -3.40 ± 4.06 kcal mol-1) observed for CT319, the inhibitor co-crystallized with DprE1. Collectively, the results demonstrated that hit-molecules: C5, C6, C8 and C10 having better binding free energy and molecular affinity as compared to CT319. Thus, we proposed that selected compounds may be explored as lead molecules in MTB therapy.

Density functional theory and 3D-RISM-KH molecular theory of solvation studies of CO2 reduction on Cu-, Cu2O-, Fe-, and Fe3O4-based nanocatalysts.

Using OpenMX quantum chemistry software for self-consistent field calculations of electronic structure with geometry optimization and 3D-RISM-KH molecular theory of solvation for 3D site distribution functions and solvation free energy, we modeled the reduction of CO2+H2 in ambient aqueous electrolyte solution of 1.0-M KH2PO4 into (i) formic acid HCOOH and (ii) CO H2O on the surfaces of Cu-, Fe-, Cu2O-, and Fe3O4-based nanocatalysts. It is applicable to its further reduction to hydrocarbons. The optimized geometries and free energies were obtained for the pathways of adsorption of the reactants from the solution, successive reduction on the surfaces of the nanocatalysts, and then release back to the solution bulk.

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.

The role of hydration effects in 5-fluorouridine binding to SOD1: insight from a new 3D-RISM-KH based protocol for including structural water in docking simulations.

Misfolded Cu/Zn superoxide dismutase enzyme (SOD1) shows prion-like propagation in neuronal cells leading to neurotoxic aggregates that are implicated in amyotrophic lateral sclerosis (ALS). Tryptophan-32 (W32) in SOD1 is part of a potential site for templated conversion of wild type SOD1. This W32 binding site is located on a convex, solvent exposed surface of the SOD1 suggesting that hydration effects can play an important role in ligand recognition and binding. A recent X-ray crystal structure has revealed that 5-Fluorouridine (5-FUrd) binds at the W32 binding site and can act as a pharmacophore scaffold for the development of anti-ALS drugs. In this study, a new protocol is developed to account for structural (non-displaceable) water molecules in docking simulations and successfully applied to predict the correct docked conformation binding modes of 5-FUrd at the W32 binding site. The docked configuration is within 0.58 Å (RMSD) of the observed configuration. The docking protocol involved calculating a hydration structure around SOD1 using molecular theory of solvation (3D-RISM-KH, 3D-Reference Interaction Site Model-Kovalenko-Hirata) whereby, non-displaceable water molecules are identified for docking simulations. This protocol was also used to analyze the hydrated structure of the W32 binding site and to explain the role of solvation in ligand recognition and binding to SOD1. Structural water molecules mediate hydrogen bonds between 5-FUrd and the receptor, and create an environment favoring optimal placement of 5-FUrd in the W32 binding site.

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.