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.

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.

Site Density Functional Theory and Structural Bioinformatics Analysis of the SARS-CoV Spike Protein and hACE2 Complex.

The entry of the SARS-CoV-2, a causative agent of COVID-19, into human host cells is mediated by the SARS-CoV-2 spike (S) glycoprotein, which critically depends on the formation of complexes involving the spike protein receptor-binding domain (RBD) and the human cellular membrane receptor angiotensin-converting enzyme 2 (hACE2). Using classical site density functional theory (SDFT) and structural bioinformatics methods, we investigate binding and conformational properties of these complexes and study the overlooked role of water-mediated interactions. Analysis of the three-dimensional reference interaction site model (3DRISM) of SDFT indicates that water mediated interactions in the form of additional water bridges strongly increases the binding between SARS-CoV-2 spike protein and hACE2 compared to SARS-CoV-1-hACE2 complex. By analyzing structures of SARS-CoV-2 and SARS-CoV-1, we find that the homotrimer SARS-CoV-2 S receptor-binding domain (RBD) has expanded in size, indicating large conformational change relative to SARS-CoV-1 S protein. Protomer with the up-conformational form of RBD, which binds with hACE2, exhibits stronger intermolecular interactions at the RBD-ACE2 interface, with differential distributions and the inclusion of specific H-bonds in the CoV-2 complex. Further interface analysis has shown that interfacial water promotes and stabilizes the formation of CoV-2/hACE2 complex. This interaction causes a significant structural rigidification of the spike protein, favoring proteolytic processing of the S protein for the fusion of the viral and cellular membrane. Moreover, conformational dynamics simulations of RBD motions in SARS-CoV-2 and SARS-CoV-1 point to the role in modification of the RBD dynamics and their impact on infectivity.

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.

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.

Extraction of site-site bridge functions and effective pair potentials from simulations of polar molecular liquids.

We develop an efficient method to extract site-site bridge functions from molecular simulations. The method is based on the inverse solution of the reference site interaction model. Using the exact long-range asymptotics of site-site direct correlation functions defined by the site-site Ornstein-Zernike equations, we regularize the ill-posed inverse problem, and then calculate site-site bridge functions and effective pair potentials for ambient water, methanol, and ethanol. We have tested the proposed algorithm and checked its performance. Our study has revealed various peculiarities of the site-site bridge functions, such as long-range behavior, strong dependence on the electrostatic interactions. Using the obtained data, we have calculated thermodynamic properties of the solvents, namely, isothermal compressibility, internal energy, and Kirkwood-Buff integrals. The obtained values are in excellent agreement not only with molecular simulations but also with available experimental data. Further extensions of the method are discussed.

Integral Equation Theory of Molecular Solvation Coupled with Quantum Mechanical/Molecular Mechanics Method in NWChem Package.

We have developed a hybrid approach based on a combination of integral equation theory of molecular liquids and quantum mechanical/molecular mechanics (QM/MM) methodology in NorthWest computational Chemistry (NWChem) software package. We have split the evaluations into consequent QM/MM and statistical mechanics calculations based on the one-dimensional reference interaction site model, which allows us to reduce significantly the time of computation. The method complements QM/MM capabilities existing in the NWChem package. The accuracy of the presented method was tested through computation of the water structure around several organic solutes and their hydration free energies. We have also evaluated the solvent effect on the conformational equilibria. The applicability and limitations of the developed approach are discussed.

In silico screening of bioactive and biomimetic solutes using Integral Equation Theory.

The Integral Equation Theory (IET) of Molecular Liquids is a theoretical framework for modelling solution phase behaviour that has recently found new applications in computational drug design. IET allows calculation of solvation thermodynamic parameters at significantly lower computational expense than explicit solvent simulations, but also provides information about the microscopic solvent structure that is not accessible by implicit continuum models. In this review we focus on recent advances in two fields of research using these methods: (i) calculation of the hydration free energies of bioactive molecules; (ii) modelling the aggregation of biomimetic molecules. In addition, we discuss sources of experimental solvation data for druglike molecules.

An accurate prediction of hydration free energies by combination of molecular integral equations theory with structural descriptors.

In this work, we report a novel method for the estimation of the hydration free energy of organic molecules, the structural descriptors correction (SDC) model. The method is based on a combination of the reference interaction site model (RISM) with several empirical corrections. The model requires only a small number of chemical descriptors associated with the main features of the chemical structure of solutes: excluded volume, branch, double bond, benzene ring, hydroxyl group, halogen atom, aldehyde group, ketone group, ether group, and phenol fragment. The optimum model was selected after testing of different RISM free energy expressions on a training set of 65 molecules. We show that the correction parameters of the SDC model are transferable between different chemical classes, which allows one to cover a wide range of organic solutes. The new model substantially increases the accuracy of calculated HFEs by RISM giving the standard deviation of the error for a test set of 120 organic molecules around 1.2 kcal/mol.

Dispersion forces between solvated electrons.

Using the path integral centroid approach, we investigate dispersion interactions between electrons solvated in metal-ammonia solutions. We have argued that at finite metal concentrations, the behavior of the solvated electrons is controlled by these interactions. The latter result in a peculiar nonmetal-metal transition, which appears as a sharp dielectric enhancement and a mechanical instability of the system. Our results indicate also that the solvated electrons are to be considered as a two-component mixture consisting of localized and delocalized electrons beyond the critical density corresponding to this mechanical instability.

Reference interaction site model study of self-aggregating cyanine dyes.

Using the reference interaction site model and supramolecular approach, we modeled the aggregation of thea-monomethinecyanine dyes in water. Various modifications of the hypernetted-closure expression for the excess free energy have been studied. We found that the partial wave approximation with semiempirical corrections for excluded volume and hydrogen bonding effects provides estimations of the binding and dimerization energies of the aggregates, which are in agreement with available experimental data. The hydrated H-dimers are obtained to be more stable than the hydrated J-dimers. However, the complexes consisting from more than four monomers change their arrangement while self-assembling in water and form ladderlike structures. We propose a model explaining this structural transition.

Hydration of ionic species studied by the reference interaction site model with a repulsive bridge correction.

We have tested the reference interaction site model (RISM) for the case of the hypernetted chain (HNC) and the partially linearized hypernetted chain (PLHNC) closures improved by a repulsive bridge correction (RBC) for ionic hydrated species. We have analyzed the efficiency of the RISM/HNC+RBC and RISM/PLHNC+RBC techniques for decomposition of the electrostatic and the nonpolar hydration energies on the energetic and the enthalpic parts for polyatomic ions when the repulsive bridge correction is treated as a thermodynamic perturbation, and investigate the repulsive bridge effect on the electrostatic potential induced by solvent on solute atoms. For a number of univalent and bivalent atomic ions, molecular cations, and anions, the method provides hydration energies deviating only by several percents from the experimental data. In most cases, the enthalpic contributions to the free energies are also close to the experimental results. The above models are able to satisfactory predict the hydration energies as well as the electrostatic potential around the ionic species. For univalent atomic ions, they also provide qualitative estimates of the Samoilov activation energies.

Nature of metal-nonmetal transition in metal-ammonia solutions. II. From uniform metallic state to inhomogeneous electronic microstructure.

Applying semianalytical models of nonideal plasma, we evaluate the behavior of the metallic phase in metal-ammonia solutions (MAS). This behavior is mainly controlled by the degenerate electron gas, which remains stable down to 5 MPM due to high solvent polarizability and strong dielectric screening of solvated ions. Comparing the behavior of the metallic state with those of localized solvated electrons, we have estimated the miscibility gap Delta n for various alkali metals and found Delta n(Na)>Delta n(K). It is rather narrow in Rb-NH3 and does not occur in Cs-NH3 solutions, which is in full agreement with the experiments. The case of Li is discussed separately. The difference calculated in the excess free energies of the metallic and nonmetallic phases is in the order of kBT, yielding a thermally fluctuating mixed state at intermediate metal concentrations. It results in a continuous metal-nonmetal (MNM) transition above the consolute point Tc and a phase separation below Tc. We propose a criterion for the MNM transition which may be attributed to the line of the maximum of compressibility above Tc. This line crosses the spinodal one at the critical temperature. Finally, we assert that a new electronic phase similar to microemulsion should also arise between the spinodal and the binodal lines.

Comment on "Model of saturated lithium ammonia as a single-component liquid metal" [J. Chem. Phys. 124, 074702 (2006)].

We demonstrate in this Comment that the theory of simple metals applied to the saturated Li-NH3 solution in the titled paper [U. Pinsook and S. Hannongbua, J. Chem. Phys.124, 074702 (2006)] should account for the peculiarities of the solution, namely, the high solvent polarizability and different energy scales for ion-ion and electron-electron interactions. Calculations not taking into account these peculiarities contradict the experimental phase diagram of the Li-NH3 solution.

Nature of the metal-nonmetal transition in metal-ammonia solutions. I. Solvated electrons at low metal concentrations.

Using a theory of polarizable fluids, we extend a variational treatment of an excess electron to the many-electron case corresponding to finite metal concentrations in metal-ammonia solutions (MAS). We evaluate dielectric, optical, and thermodynamical properties of MAS at low metal concentrations. Our semianalytical calculations based on a mean-spherical approximation correlate well with the experimental data on the concentration and temperature dependencies of the dielectric constant and the optical absorption spectrum. The properties are found to be mainly determined by the induced dipolar interactions between localized solvated electrons, which result in the two main effects: the dispersion attractions between the electrons and a sharp increase in the static dielectric constant of the solution. The first effect creates a classical phase separation for the light alkali metal solutes (Li, Na, K) below a critical temperature. The second effect leads to a dielectric instability, i.e., polarization catastrophe, which is the onset of metallization. The locus of the calculated critical concentrations is in a good agreement with the experimental phase diagram of Na-NH(3) solutions. The proposed mechanism of the metal-nonmetal transition is quite general and may occur in systems involving self-trapped quantum quasiparticles.

Fundamental measure theory of hydrated hydrocarbons.

To calculate the solvation of hydrophobic solutes, we have developed a method based on the fundamental measure treatment of density functional theory. This method allows us to carry out calculations of density profiles and the solvation energy for various hydrophobic molecules with high accuracy. We have applied the method to the hydration of various hydrocarbons (linear, branched and cyclic). The calculations of the entropic and enthalpic parts are also carried out. We have examined the question of the temperature dependence of the entropy convergence. Finally, we have calculated the mean force potential between two large hydrophobic nanoparticles immersed in water.

Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model.

A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20% of that required for the conventional hybrid method.