3D-RISM Theory Research Articles

A method for protein structure sampling under three-dimensional reference interaction site model solvation based on hybrid Monte Carlo framework

An efficient sampling method for protein structure using molecular dynamics (MD) simulation and a three-dimensional reference interaction-site model (3D-RISM) theory has been developed based on the hybrid Monte Carlo framework. In this method, new structures are generated by MD simulation with the generalized Born implicit solvent model and the Metropolis-like criterion to accept or reject the structure candidate is applied based on the free energy corresponding to the 3D-RISM Hamiltonian at each specified time propagation interval. The resulting ensemble of structures satisfies the 3D-RISM Hamiltonian-based equilibrium distribution. The method was applied to alanine dipeptide and methionine-enkephalin polypeptides in aqueous solution as test cases. The results demonstrated the efficiency of the method.

EPISOL: A software package with expanded functions to perform 3D-RISM calculations for the solvation of chemical and biological molecules.

Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.

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.

The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules.

The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute-solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl-, [ClO]- (a two-site anion), and [NO2]- (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl-. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.

Gr Predictor: A Deep Learning Model for Predicting the Hydration Structures around Proteins.

Among the factors affecting biological processes such as protein folding and ligand binding, hydration, which is represented by a three-dimensional water site distribution function around the protein, is crucial. The typical methods for computing the distribution functions, including molecular dynamics simulations and the three-dimensional reference interaction site model (3D-RISM) theory, require a long computation time ranging from hours to tens of hours. Here, we propose a deep learning (DL) model that rapidly estimates the distribution functions around proteins obtained using the 3D-RISM theory from the protein 3D structure. The distribution functions predicted using our DL model are in good agreement with those obtained using the 3D-RISM theory. Particularly, the coefficient of determination between the distribution function obtained by the DL model and that obtained using the 3D-RISM theory is approximately 0.98. Furthermore, using a graphics processing unit, the prediction by the DL model is completed in less than 1 min, more than 2 orders of magnitude faster than the calculation time of the 3D-RISM theory. The position of water molecules around the protein was estimated based on the distribution function obtained by our DL model, and the position of waters estimated by our DL model was in good agreement with that of water molecules estimated using the 3D-RISM theory and of crystallographic waters. Therefore, our DL model provides a practical and efficient way to calculate the three-dimensional water site distribution functions and to estimate the position of water molecules around the protein. The program called "gr Predictor" is available under the GNU General Public License from https://github.com/YoshidomeGroup-Hydration/gr-predictor.

Free Energy and Solvation Structure Analysis for Adsorption of Aromatic Molecules at Pt(111)/Water Interface by 3D-RISM Theory

Abstract The free energy change of aromatic molecules adsorbed at a Pt(111)/water interface was analyzed using the three-dimensional reference interaction site model (3D-RISM) theory with density functional theory (DFT), compared with the reported experimental data. The changes in the solvation structure induced by molecular adsorption were discussed.

Computational Analysis of the SARS-CoV-2 RBD-ACE2-Binding Process Based on MD and the 3D-RISM Theory.

The binding process of angiotensin-converting enzyme 2 (ACE2) to the receptor-binding domain (RBD) of the severe acute respiratory syndrome-like coronavirus 2 spike protein was investigated using molecular dynamics simulation and the three-dimensional reference interaction-site model theory. The results suggested that the protein-binding process consists of a protein–protein approaching step, followed by a local structural rearrangement step. In the approaching step, the interprotein interaction energy decreased as the proteins approached each other, whereas the solvation free energy increased. As the proteins approached, the glycan of ACE2 first established a hydrogen bond with the RBD. Thereafter, the number of interprotein hydrogen bonds increased rapidly. The solvation free energy increased because of the desolvation of the protein as it approached its partner. The spatial distribution function of the solvent revealed the presence of hydrogen bonds bridged by water molecules on the RBD–ACE2 interface. Finally, principal component analysis revealed that ACE2 showed a pronounced conformational change, whereas there was no significant change in RBD.

Development of a deep-learning model for predicting the hydration structures around proteins

Hydration is an important factor in understanding a variety of biological processes, such as protein folding and ligand binding. With the use of all-atom molecular dynamics simulation, the three-dimensional distribution function of water molecules around a protein can be obtained as a hydration structure. However, its high computational cost hinders its application to a large number of proteins. In the present paper, we propose that a hybrid of the 3D-RISM theory and a deep-learning technique can resolve this issue.

Comprehensive 3D-RISM Analysis of the Hydration of Small Molecule Binding Sites in Ligand-Free Protein Structures

Ligand binding to proteins involves displacing water molecules at the binding site and rearranging water molecules close to the ligand. The hydration state of ligand binding sites is important for the stability of the ligand-protein complex. Using the three-dimensional reference interaction site model (3D-RISM) theory, here we calculated the three-dimensional distribution function of the water oxygen site, gO(r), for 3,706 ligand-free protein structures of small molecule-protein complexes [1]. The 3D-RISM theory allowed the first comprehensive analysis of the hydration state for a large number of protein structures, a difficult subject for existing methods based on molecular dynamics simulations. The probability distribution of gO(r) at the positions of approximately 620,000 crystallographic waters (CWs) was calculated and analyzed. The gO(r) for CWs close to the ligand revealed that several CWs were stabilized by interaction networks formed between the ligand, CW, and protein. Analysis of gO(r) at the position of ligand heavy atoms indicated that, in the crystallographic binding poses (correct poses) of the ligand, hydrogen bond interactions are dominant in the highly hydrated regions whereas weak interactions such as CH-O are dominant in the moderately hydrated regions. Further, polar heteroatoms of the ligand tend to occupy highly hydrated regions in the correct poses and less hydrated regions in the wrongly docked poses, suggesting a way to distinguish these two poses. [1] T. Yoshidome, M. Ikeguchi, and M. Ohta, J. Comp. Chem., 41, 2406 (2020).

Hydration Thermodynamics of the N-Terminal FAD Mutants of Amyloid-β.

The hydration thermodynamics of amyloid-β (Aβ) and its pathogenic familial Alzheimer's disease (FAD) mutants such as A2V, Taiwan (D7H), Tottori (D7N), and English (H6R) and the protective A2T mutant is investigated by a combination of all-atom, explicit water molecular dynamics (MD) simulations and the three-dimensional reference interaction site model (3D-RISM) theory. The change in the hydration free energy on mutation is decomposed into the energetic and entropic components, which comprise electrostatic and nonelectrostatic contributions. An increase in the hydration free energy is observed for A2V, D7H, D7N, and H6R mutations that increase the aggregation propensity of Aβ and lead to an early onset of Alzheimer's disease, while a reverse trend is noted for the protective A2T mutation. An antiphase correlation is found between the change in the hydration energy and the internal energy of Aβ upon mutation. A residue-wise decomposition analysis shows that the change in the hydration free energy of Aβ on mutation is primarily due to the hydration/dehydration of the side-chain atoms of the negatively charged residues. The decrease in the hydration of the negatively charged residues on mutation may decrease the solubility of the mutant, which increases the observed aggregation propensity of the FAD mutants. Results obtained from the theory show an excellent match with the experimentally reported data.

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.

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.

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, , 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, reveals that several CWs are stabilized by interaction networks formed between the ligand, CW, and protein. Based on the 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 of polar heteroatoms may be used to distinguish the correct binding poses.

Continuum Electrostatic Behavior of a 3D-RISM Theory.

The electrostatic response underlying the 3D-RISM theory and its general relationship to models in which the solvent is represented in terms of a dielectric continuum are examined. It is found that the theory provides a coherent picture of solvation, although its behavior is not entirely consistent with the trends that are expected in the limit of a large solute. The electrostatic discrepancy is due to the nature of the isotropic pair additive site-site correlation function associated with the susceptibility response of the uniform fluid. The influence of the discrepancy in the magnitude of the solvation free energy is negligible for a solvent with a large dielectric constant.

New Protocol for Predicting the Ligand-Binding Site and Mode Based on the 3D-RISM/KH Theory.

An efficient algorithm to find the binding position and mode of small ligands bound at an active site of protein is proposed based on the spatial distribution function (SDF) obtained from the three-dimensional reference interaction site model (3D-RISM) theory with the Kovalenko-Hirata (KH) closure relation. The ligand examined includes hydrophobic, acidic, and basic molecules and zwitterions. Eighteen different types of proteins, which serve as targets for those ligands, are selected to examine the robustness of the algorithm. An imaginary atom, referred to as an "anchor site", is defined at the center of geometry of a ligand molecule that serves as a center for searching the binding position and mode of the ligand molecule in the translational and rotational spaces. The probable binding sites (PBSs) are identified based on the SDFs of the ligand molecules around the protein, and the PBS is ranked according to the peak height of SDF. The deviations from the mean height of the peak values of SDFs for 50 PBSs are analyzed based on the z-score, which is a measure of prominence of the site. The PBS found at the closest distance from the anchor site of the crystal structure is referred to as the "nearest site". The orientation of the ligand molecule at each PBS is explored by changing the Euler angles, and the most probable binding mode is determined based on the superposition approximation. The binding position of ligand molecules is successfully predicted as one of the distinct peaks in SDF of the anchor site, with a few exceptions. The binding mode of the ligand molecule predicted based on the superposition approximation is consistent with the X-ray crystal structure in nine systems, a half of the systems investigated. The significance of the results is discussed in detail. An application of the new protocol to fragment-based drug discovery is suggested.

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

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

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.

Recent Developments in Integral Equation Theory for Solvation to Treat Density Inhomogeneity at Solute–Solvent Interface

AbstractThe integration equation theory (IET) provides highly efficient tools for the calculation of structural and thermodynamic properties of molecular liquids. In recent years, the 3D reference interaction site model (3DRISM), the most developed IET for solvation, has been widely applied to study protein solvation, aggregation, and drug‐receptor binding. However, hydrophobic solutes with sufficient size (>nm) can induce water density depletion at the solute–solvent interface. This density depletion is not considered in the original 3DRISM theory. The authors here review the recent developments of 3DRISM at hydrophobic surfaces and related theories to address this challenge. At hydrophobic surfaces, an additional hydrophobicity‐induced density inhomogeneity equation is introduced to 3DRISM theory to consider this density depletion. Accordingly, several new closures equations including D2 closure and D2MSA closures are developed to enable stable numerical solutions of 3DRISM equations. These newly developed theories hold great promise for an accurate and rapid calculation of the solvation effect for complex molecular systems such as proteins. At the end of the report, the authors also provide a perspective on other challenges of the IETs as an efficient solvation model.

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.

Including diverging electrostatic potential in 3D-RISM theory: The charged wall case.

Although three-dimensional site-site molecular integral equations of liquids are a powerful tool of the modern theoretical chemistry, their applications to the problem of characterizing the electrical double layer originating at the solid-liquid interface with a macroscopic substrate are severely limited by the fact that an infinitely extended charged plane generates a divergent electrostatic potential. Such potentials cannot be treated within the standard 3D-Reference Interaction Site Model equation solution framework since it leads to functions that are not Fourier transformable. In this paper, we apply a renormalization procedure to overcome this obstacle. We then check the validity and numerical accuracy of the proposed computational scheme on the prototypical gold (111) surface in contact with water/alkali chloride solution. We observe that despite the proposed method requires, to achieve converged charge densities, a higher spatial resolution than that suited to the estimation of biomolecular solvation with either 3D-RISM or continuum electrostatics approaches, it still is computationally efficient. Introducing the electrostatic potential of an infinite wall, which is periodic in 2 dimensions, we avoid edge effects, permit a robust integration of Poisson's equation, and obtain the 3D electrostatic potential profile for the first time in such calculations. We show that the potential within the electrical double layer presents oscillations which are not grasped by the Debye-Hückel and Gouy-Chapman theories. This electrostatic potential deviates from its average of up to 1-2 V at small distances from the substrate along the lateral directions. Applications of this theoretical development are relevant, for example, for liquid scanning tunneling microscopy imaging.