Interfragment Interaction Energies Research Articles

Protein-Protein Interaction Modelling with the Fragment Molecular Orbital Method.

Fragment molecular orbital (FMO) method enables ab initio quantum-chemical calculations for biomolecular systems with high accuracy and moderate computational cost. Through this analysis we can evaluate the inter-fragment interaction energies (IFIEs) that provide useful measures for effective interactions between the fragments representing amino-acid residues and ligand molecules. Here I describe how to prepare the input structures and perform the FMO calculations for protein-protein complex system. In addition to the pre-processing, some useful tools for the post-processing analysis are also illustrated.

Evaluating the correlation of binding affinities between isothermal titration calorimetry and fragment molecular orbital method of estrogen receptor beta with diarylpropionitrile (DPN) or DPN derivatives

Estrogen receptors (ERs) are ligand-activated transcription factors, with two subtypes ERα and ERβ. The endogenous ligand of ERs is the common 17β-estradiol, and the ligand-binding pocket of ERα and ERβ is very similar. Nevertheless, some ERβ-selective agonist ligands have been reported. DPN (diarylpropionitrile) is a widely used ERβ-selective agonist; however, the structure of the ERβ-DPN complex has not been solved. Therefore, the bound-state conformation of DPN and its enantioselectivity remain unresolved. In this report, we present the structures of the complexes of ERβ with DPN or its derivatives that include a chlorine atom by the X-ray crystallography. Additionally, we measured the binding affinity between ERβ and DPN or derivatives by isothermal titration calorimetry (ITC) and estimated the binding affinity by fragment molecular orbital (FMO) calculations. We also examined the correlation between the ITC data and results from the FMO calculations. FMO calculations showed that S-DPN interacts strongly with three amino acids (Glu305, Phe356, and His475) of ERβ, and ITC measurements confirmed that the chlorine atom of the DPN derivatives enhances binding affinity. The enthalpy change by ITC correlated strongly with the interaction energy (total IFIEs; inter-fragment interaction energies) calculated by FMO (R = 0.870). We propose that FMO calculations are a valuable approach for enhancing enthalpy contributions in drug design, and its scope of applications includes halogen atoms such as chlorine. This study is the first quantitative comparison of thermodynamic parameters obtained from ITC measurements and FMO calculations, providing new insights for future precise drug design.

Collective residue interactions in trimer complexes of SARS-CoV-2 spike proteins analyzed by fragment molecular orbital method

In large biomolecular systems such as protein complexes, there are huge numbers of combinations of inter-residue interactions whose comprehensive analyses are often beyond the intuitive processing by researchers. Here we propose a computational method to allow for a systematic analysis of these interactions based on the fragment molecular orbital calculations, in which the inter-fragment interaction energies are comprehensively processed by the singular value decomposition. For a trimer complex of SARS-CoV-2 spike protein, three-body interactions among residues belonging to three chains are analyzed to elicit a small number of essential interaction modes or networks crucial for the structural stability of the complex.

In silico, theoretical biointerface analysis and in vitro kinetic analysis of amine compounds interaction with acetylcholinesterase and butyrylcholinesterase

Acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) are considered important target for drug design against Alzheimer's disease. In the present study in silico analysis; theoretical analysis of biointerface between ligand and interacting amino acid residues of proteins; and in vitro analysis of enzyme inhibition kinetics were carried out to delineate the inhibitory property of amine compounds against AChE/BChE. High throughput virtual screening of amine compounds identified three compounds (2-aminoquinoline, 2-aminobenzimidazole and 2-amino-1-methylbenzimidazole) that best interacted with AChE/BChE. Molecular docking analysis revealed the interaction of these compounds in the active site gorge of AChE/BChE, in particular with amino acid residues present in the peripheral anionic site. Molecular dynamics simulation confirmed the stable binding of these compounds with AChE/BChE. Binding energy calculated through MMGBSA method identified the non-covalent interactions (electrostatic and Van der Waals interactions) have contributed to the stable binding of the amine compounds with the AChE/BChE. Biointerface between amine compounds and AChE/BChE were visualized through Hirshfeld surface analysis. The inter-fragment interaction energies for the possible contacts between amine compounds and amino acid residues were carried out for the first time. All the amine compounds showed mixed-type of inhibition with moderate Ki value in in vitro analysis.

Dynamic Cooperativity of Ligand-Residue Interactions Evaluated with the Fragment Molecular Orbital Method.

By the splendid advance in computation power realized with the Fugaku supercomputer, it has become possible to perform ab initio fragment molecular orbital (FMO) calculations for thousands of dynamic structures of protein-ligand complexes in a parallel way. We thus carried out electron-correlated FMO calculations for a complex of the 3C-like (3CL) main protease (Mpro) of the new coronavirus (SARS-CoV-2) and its inhibitor N3 incorporating the structural fluctuations sampled by classical molecular dynamics (MD) simulation in hydrated conditions. Along with a statistical evaluation of the interfragment interaction energies (IFIEs) between the N3 ligand and the surrounding amino-acid residues for 1000 dynamic structure samples, in this study we applied a novel approach based on principal component analysis (PCA) and singular value decomposition (SVD) to the analysis of IFIE data in order to extract the dynamically cooperative interactions between the ligand and the residues. We found that the relative importance of each residue is modified via the structural fluctuations and that the ligand is bound in the pharmacophore in a dynamic manner through collective interactions formed by multiple residues, thus providing new insight into structure-based drug discovery.

Machine learning prediction of inter-fragment interaction energies between ligand and amino-acid residues on the fragment molecular orbital calculations for Janus kinase – inhibitor complex

Inter-Fragment Interaction Energies (IFIEs) obtained by Fragment Molecular Orbital (FMO) method can quantitatively measure the effective interactions between ligand and residues in protein, which are therefore useful for drug discovery. However, it has not been clarified whether the IFIEs can be reproduced using only geometrical (e.g., interatomic distances) information of biomolecular complex without resort to explicit FMO calculations. In this study, through machine learning technique, we propose a highly accurate reproduction or prediction scheme for ligand-protein IFIEs using only the distance information as descriptors, thereby drastically saving the computational cost in FMO analysis for a variety of conformations.

A self-consistent coulomb bath model using density fitting.

A self-consistent Coulomb bath model is presented to provide an accurate and efficient way of performing calculations for interfragment electrostatic and polarization interactions. In this method, a condensed-phase system is partitioned into molecular fragment blocks. Each fragment is embedded in the Coulomb bath due to other fragments. Importantly, the present Coulomb bath is represented using a density fitting method in which the electron densities of molecular fragments are fitted using an atom-centered auxiliary basis set of Gaussian type. The Coulomb bath is incorporated into an effective Hamiltonian for each fragment, with which the electron density is optimized through an iterative double self-consistent field (DSCF) procedure to realize the mutual many-body polarization effects. In this work, the accuracy of interfragment interaction energies enumerated using the Coulomb bath is tested, showing a good agreement with the exact results from an energy decomposition analysis. The qualitative features of many-body polarization effects are visualized by electron density difference plots. It is also shown that the present DSCF method can yield fast and robust convergence with near-linear scaling in performance with increase in system size.

Prediction of Free Energy by Docking Simulation using Inter-Fragment Interaction Energies

It is still difficult to predict binding free energy of novel inhibitors having potent activity in docking simulation. In recent years, the fragment molecular orbital (FMO) method has been used for the analysis of the interaction between protein and inhibitor and the sum of inter-fragment interaction energies (IFIE) between protein and inhibitor obtained by the calculation can evaluate the static interaction considering the inter-electron interaction. If there is a high correlation between IFIE and ΔH by FMO calculation, the regression between ΔH and IFIE can be constructed. Compensation law is established for ΔH and TΔS, so that finally ΔG can be predicted only IFIE. Therefore, it is possible to establish a method that can predict ΔG without considering entropy. This study examined the correlation between IFIE and ΔH of HIV protease with its inhibitors using supercomputer K and FX100. We calculated 14 complexes by the FMO calculation. The correlation between the IFIE obtained by the calculation and the experimental value was R2 = 0.3652, indicating a poor correlation. Then we analyzed the IFIE between the inhibitor and the amino acid residues. There was a difference in IFIE between inhibitor and GLY49 in each complex. From the structure, there were complexes with and without water molecules between the inhibitor and GLY49, so we classified the complex with water as group 1 and the complex without water as group 2. As a result, a better correlation of R2=0.9754 for group 1 and R2=0.7272 for group 2 was obtained. From these results, by classifying and calculated the complex according to the binding state of water, it was able to be obtained the correlation between IFIE and ΔH required for ΔG prediction.

Taking Water into Account with the Fragment Molecular Orbital Method.

This chapter describes the current status of development of the fragment molecular orbital (FMO) method for analyzing the electronic state and intermolecular interactions of biomolecular systems in solvent. The orbital energies and the inter-fragment interaction energies (IFIEs) for a specific molecular structure can be obtained directly by performing FMO calculations by exposing water molecules and counterions around biomolecular systems. Then, it is necessary to pay attention to the thickness of the water shell surrounding the biomolecules. The single-point calculation for snapshots from MD trajectory does not incorporate the effects of temperature and configurational fluctuation, but the SCIFIE (statistically corrected IFIE) method is proposed as a many-body correlated method that partially compensates for this deficiency. Furthermore, implicit continuous dielectric models have been developed as effective approaches to incorporating the screening effect of the solvent in thermal equilibrium, and we illustrate their usefulness for theoretical evaluation of IFIEs and ligand-binding free energy on the basis of the FMO-PBSA (Poisson-Boltzmann surface area) method and other computational methods.

Development of an Analysis Toolkit, AnalysisFMO, to Visualize Interaction Energies Generated by Fragment Molecular Orbital Calculations.

In modern praxis, a knowledge-driven design of pharmaceutical compounds relies heavily on protein structure data. Nonetheless, quantification of the interaction between protein and ligand is of great importance in the theoretical evaluation of the ability of a pharmaceutical compound to comply with certain expectations. The FMO (fragment molecular orbital) method is handy in this regard. However, the physical complexity and the number of the interactions within a protein-ligand complex renders analysis of the results somewhat complicated. This situation prompted us to develop the 3D-visualization of interaction energies in protein (3D-VIEP) method; the toolkit AnalysisFMO, which should enable a more efficient and convenient workflow with FMO data generated by quantum-chemical packages such as GAMESS, PAICS, and ABINIT-MP. AnalysisFMO consists of two separate units, RbAnalysisFMO, and the PyMOL plugins. The former can extract interfragment interaction energies (IFIEs) or pair interaction energies (PIEs) from the FMO output files generated by the aforementioned quantum-chemical packages. The PyMOL plugins enable visualization of IFIEs or PIEs in the protein structure in PyMOL. We demonstrate the use of this tool on a lectin protein from Burkholderia cenocepacia in which FMO analysis revealed the existence of a new interaction between Gly84 and fucose. Moreover, we found that second-shell interactions are crucial in forming the sugar binding site. In the case of bilirubin oxidase from Myrothecium verrucaria (MvBO), we predict that interactions between Asp105 and three His residues (His401, His403, and His136) are essential for optimally positioning the His residues to coordinate Cu atoms to form one Type 2 and two Type 3 Cu ions.

Computational Analysis of the Interaction Energies between Amino Acid Residues of the Measles Virus Hemagglutinin and Its Receptors.

Measles virus (MV) causes an acute and highly devastating contagious disease in humans. Employing the crystal structures of three human receptors, signaling lymphocyte-activation molecule (SLAM), CD46, and Nectin-4, in complex with the measles virus hemagglutinin (MVH), we elucidated computationally the details of binding energies between the amino acid residues of MVH and those of the receptors with an ab initio fragment molecular orbital (FMO) method. The calculated inter-fragment interaction energies (IFIEs) revealed a number of significantly interacting amino acid residues of MVH that played essential roles in binding to the receptors. As predicted from previously reported experiments, some important amino-acid residues of MVH were shown to be common but others were specific to interactions with the three receptors. Particularly, some of the (non-polar) hydrophobic residues of MVH were found to be attractively interacting with multiple receptors, thus indicating the importance of the hydrophobic pocket for intermolecular interactions (especially in the case of Nectin-4). In contrast, the electrostatic interactions tended to be used for specific molecular recognition. Furthermore, we carried out FMO calculations for in silico experiments of amino acid mutations, finding reasonable agreements with virological experiments concerning the substitution effect of residues. Thus, the present study demonstrates that the electron-correlated FMO method is a powerful tool to search exhaustively for amino acid residues that contribute to interactions with receptor molecules. It is also applicable for designing inhibitors of MVH and engineered MVs for cancer therapy.

Towards good correlation between fragment molecular orbital interaction energies and experimental IC50 for ligand binding: A case study of p38 MAP kinase

We describe several procedures for the preprocessing of fragment molecular orbital (FMO) calculations on p38 mitogen-activated protein (MAP) kinase and discuss the influence of the procedures on the protein–ligand interaction energies represented by inter-fragment interaction energies (IFIEs). The correlation between the summation of IFIEs for a ligand and amino acid residues of protein (IFIE-sum) and experimental affinity values (IC50) was poor when considered for the whole set of protein–ligand complexes. To improve the correlation for prediction of ligand binding affinity, we carefully classified data set by the ligand charge, the DFG-loop state (DFG-in/out loop), which is characteristic of kinase, and the scaffold of ligand. The correlation between IFIE-sums and the activity values was examined using the classified data set. As a result, it was confirmed that there was a selected data set that showed good correlation between IFIE-sum and activity value by appropriate classification. In addition, we found that the differences in protonation and hydrogen orientation caused by subtle differences in preprocessing led to a relatively large difference in IFIE values. Further, we also examined the effect of structure optimization with different force fields. It was confirmed that the difference in the force field had no significant effect on IFIE-sum. From the viewpoint of drug design using FMO calculations, various investigations on IFIE-sum in this research, such as those regarding several classifications of data set and the different procedures of structural preparation, would be expected to provide useful knowledge for improvement of prediction ability about the ligand binding affinity.

Deciphering the catalytic amino acid residues of l-2-haloacid dehalogenase (DehL) from Rhizobium sp. RC1: An in silico analysis

The l-2-haloacid dehalogenases (EC 3.8.1.2) specifically cleave carbon-halogen bonds in the L-isomers of halogenated organic acids. These enzymes have potential applications for the bioremediation and synthesis of various industrial products. One such enzyme is DehL, the l-2-haloacid dehalogenase from Rhizobium sp. RC1, which converts the L-isomers of 2-halocarboxylic acids into the corresponding D-hydroxycarboxylic acids. However, its catalytic mechanism has not been delineated, and to enhance its efficiency and utility for environmental and industrial applications, knowledge of its catalytic mechanism, which includes identification of its catalytic residues, is required. Using ab initio fragment molecular orbital calculations, molecular mechanics Poisson-Boltzmann surface area calculations, and classical molecular dynamic simulation of a three-dimensional model of DehL-l-2-chloropropionic acid complex, we predicted the catalytic residues of DehL and propose its catalytic mechanism. We found that when Asp13, Thr17, Met48, Arg51, and His184 were individually replaced with an alanine in silico, a significant decrease in the free energy of binding for the DehL-l-2-chloropropionic acid model complex was seen, indicating the involvement of these residues in catalysis and/or structural integrity of the active site. Furthermore, strong inter-fragment interaction energies calculated for Asp13 and L-2-chloropropionic acid, and for a water molecule and His184, and maintenance of the distances between atoms in the aforementioned pairs during the molecular dynamics run suggest that Asp13 acts as the nucleophile and His184 activates the water involved in DehL catalysis. The results of this study should be important for the rational design of a DehL mutant with improved catalytic efficiency.

Ion-Pairing Crystal Polymorphs of Interlocked [2 + 1]-Type Receptor-Anion Complexes.

The formation of a solid-state totally charge-segregated assembly (polymorph A) of negatively charged layers comprising [2 + 1]-type Cl(-) complexes of an arylethynyl-substituted dipyrrolyldiketone boron complex and positively charged layers of tetrabutylammonium (TBA) cations has already been reported. The formation of two new crystalline polymorphs (polymorphs B and C), in addition to polymorph A, is reported in this study. Both polymorphs B and C formed charge-by-charge assemblies, and the dihedral angles between two receptor units in the interlocked complexes depended on the geometries of TBA cations and the resulting packing structures. Two nonorthogonally arranged planes induced P- and M-form chiral geometries, providing diverse arrangements of chiral species according to crystal polymorphs. Furthermore, the stabilities of the three polymorphs were examined by interfragment interaction energies, which were calculated by ab initio electronic structure calculations using the fragment molecular orbital (FMO) method.

Interaction Analysis of FABP4 Inhibitors by X-ray Crystallography and Fragment Molecular Orbital Analysis.

X-ray crystal structural determination of FABP4 in complex with four inhibitors revealed the complex binding modes, and the resulting observations led to improvement of the inhibitory potency of FABP4 inhibitors. However, the detailed structure-activity relationship (SAR) could not be explained from these structural observations. For a more detailed understanding of the interactions between FABP4 and inhibitors, fragment molecular orbital analyses were performed. These analyses revealed that the total interfragment interaction energies of FABP4 and each inhibitor correlated with the ranking of the K i value for the four inhibitors. Furthermore, interactions between each inhibitor and amino acid residues in FABP4 were identified. The oxygen atom of Lys58 in FABP4 was found to be very important for strong interactions with FABP4. These results might provide useful information for the development of novel potent FABP4 inhibitors.

Charge clamps of lysines and hydrogen bonds play key roles in the mechanism to fix helix 12 in the agonist and antagonist positions of estrogen receptor α: intramolecular interactions studied by the ab initio fragment molecular orbital method.

The mechanism to fix helix 12 (H12) in the agonist/antagonist position, which is involved in controlling transcriptional activation, of the human estrogen receptor α ligand binding domain (hERαLBD) is studied by using fragment molecular orbital calculations at the Møller-Plesset second-order perturbation levels to analyze inter-fragment interaction energies (IFIEs), electrostatic potentials (ESPs), and atomic charges. The mutually attractive and complementary relationships between H12 and highly conserved Lys529/Lys362 are shown through the IFIEs and ESPs. The highly conserved Lys529 and Lys362 are found to have strong attractive interactions with the anionic residues of H12 in the agonist and antagonist positions, respectively, thus playing roles of charge clamps to fix H12. Additionally, intramolecular interactions between the neutral residues of H12 including the LXXML motif and the other part of hERα are strengthened by the hydrogen bonds and polarization. It is noted that the highly conserved Asp351 forms a hydrogen bond with Leu540 of H12 in the hERα-agonist complex, while it is also involved in stabilization of ligand binding in the hERα-antagonist complex. The charges of residues at the interface between H12 and the other part of hERα approach approximately neutral upon forming the agonist/antagonist binding conformation so as to relax the electrostatic repulsion caused by the negative charges of H12 and the other part of hERα. Our observations would thus provide useful information to control the H12 position for regulation of transcription in hERα and other nuclear receptors.

Modeling of peptide–silica interaction based on four-body corrected fragment molecular orbital (FMO4) calculations

We have applied the four-body corrected fragment molecular orbital (FMO4) method to the investigation of the interaction between an artificially designed peptide, with sequence of Arg1-Lys2-Leu3-Pro4-Asp5-Ala6 [Sano et al., Langmuir, 21 (2005) 3090], and the silica surface modeled by a large cluster model including 257 silicon atoms. The second-order Møller-Plesset perturbation calculation was accelerated by the Cholesky decomposition with adaptive metric technique (CDAM-MP2). Systematic analyses were made for inter-fragment interaction energies (IFIEs) with and without a statistical correction for screening. As the result, the importance of three charged residues (Arg1, Lys2 and Asp5) in the peptide-silica interaction was illuminated.

Statistical correction to effective interactions in the fragment molecular orbital method

A theoretical scheme to evaluate effective, screened interactions between fragments is proposed within the framework of the fragment molecular orbital (FMO) method. In this theory, the presence of implicit, dielectric continuum solvent is not assumed, but only the information on bare, inter-fragment interaction energies obtained through the FMO calculation for explicit, molecular system is employed. The effective interactions with inclusion of entropic effect are then described and optimized as a consequence of inter-fragment correlations on the basis of classical-mechanical many-body theories. Test calculations for a simple model system and a realistic protein system are performed, and their implications are discussed.

The fragment molecular orbital method and understanding monomer polarization

The magnitudes of select π–π interactions are studied with MP2, as well as the fragment molecular orbital (FMO) method, which evaluates the total energy as a sum of polarized monomer energies and interfragment interaction energies. The monomer polarization is of particular interest and is found to increase in magnitude with system size and the electrostatic contribution to the interaction. As a result, differences will exist in the interaction energy reported from FMO calculations, and those calculated using a traditional supermolecular approach.

Prediction of probable mutations in influenza virus hemagglutinin protein based on large-scale ab initio fragment molecular orbital calculations

Ab initio electronic-state calculations for influenza virus hemagglutinin (HA) trimer complexed with Fab antibody were performed on the basis of the fragment molecular orbital (FMO) method at the second and third-order Møller–Plesset (MP2 and MP3) perturbation levels. For the protein complex containing 2351 residues and 36,160 atoms, the inter-fragment interaction energies (IFIEs) were evaluated to illustrate the effective interactions between all the pairs of amino acid residues. By analyzing the calculated data on the IFIEs, we first discussed the interactions and their fluctuations between multiple domains contained in the trimer complex. Next, by combining the IFIE data between the Fab antibody and each residue in the HA antigen with experimental data on the hemadsorption activity of HA mutants, we proposed a protocol to predict probable mutations in HA. The proposed protocol based on the FMO-MP2.5 calculation can explain the historical facts concerning the actual mutations after the emergence of A/Hong Kong/1/68 influenza virus with subtype H3N2, and thus provides a useful methodology to enumerate those residue sites likely to mutate in the future.