Visualization analysis of inter-fragment interaction energies of CRP-cAMP-DNA complex based on the fragment molecular orbital method

FMOe: Preprocessing and Visualizing Package of the Fragment Molecular Orbital Method for Molecular Operating Environment and Its Applications in Covalent Ligand and Metalloprotein Analyses

The fragment molecular orbital (FMO) method is an efficient quantum chemical calculation technique for large biomolecules, dividing each into smaller fragments and providing interfragment interaction energies (IFIEs) that support our understanding of molecular recognition. The ab initio fragment MO method (ABINIT-MP), an FMO processing program, can automatically divide typical proteins and nucleic acids. In contrast, small molecules such as ligands and heterosystems must be manually divided. Thus, we developed a graphical user interface to easily handle such manual fragmentation as a library for the Molecular Operating Environment (MOE) that preprocesses and visualizes FMO calculations. We demonstrated fragmentation with IFIE analyses for the two following cases: (1) covalent cysteine-ligand bonding inside the SARS-CoV-2 main protease (Mpro) and nirmatrelvir (Paxlovid) complex and (2) the metal coordination inside a zinc-bound cyclic peptide. IFIE analysis successfully identified the key amino acid residues for the molecular recognition of nirmatrelvir with Mpro and the details of their interactions (e.g., hydrogen bonds and CH/π interactions) via ligand fragmentation of functional group units. In metalloproteins, we found an efficient and accurate scheme for the fragmentation of Zn2+ ions with four histidines coordinated to the ion. FMOe simplifies manual fragmentation, allowing users to experiment with various fragmentation patterns and perform in-depth IFIE analysis with high accuracy. In the future, our findings will provide valuable insight into complicated cases, such as ligand fragmentation in modality drug discovery, especially for medium-sized molecules and metalloprotein fragmentation around metals.

Combining the Fragment Molecular Orbital and GRID Approaches for the Prediction of Ligand-Metalloenzyme Binding Affinity: The Case Study of hCA II Inhibitors

Polarization and charge-transfer interactions play an important role in ligand-receptor complexes containing metals, and only quantum mechanics methods can adequately describe their contribution to the binding energy. In this work, we selected a set of benzenesulfonamide ligands of human Carbonic Anhydrase II (hCA II)-an important druggable target containing a Zn2+ ion in the active site-as a case study to predict the binding free energy in metalloprotein-ligand complexes and designed specialized computational methods that combine the ab initio fragment molecular orbital (FMO) method and GRID approach. To reproduce the experimental binding free energy in these systems, we adopted a machine-learning approach, here named formula generator (FG), considering different FMO energy terms, the hydrophobic interaction energy (computed by GRID) and logP. The main advantage of the FG approach is that it can find nonlinear relations between the energy terms used to predict the binding free energy, explicitly showing their mathematical relation. This work showed the effectiveness of the FG approach, and therefore, it might represent an important tool for the development of new scoring functions. Indeed, our scoring function showed a high correlation with the experimental binding free energy (R2 = 0.76-0.95, RMSE = 0.34-0.18), revealing a nonlinear relation between energy terms and highlighting the relevant role played by hydrophobic contacts. These results, along with the FMO characterization of ligand-receptor interactions, represent important information to support the design of new and potent hCA II inhibitors.

A computational insight on the aromatic amino acids conjugation with [Cp*Rh(H2O)3]2+ by using the meta-dynamics/FMO3 approach

CONTEXT

Rh(III) complexes demonstrated to exert promising pharmacological effects with potential applications as anti-cancer, anti-bacterial, and antimicrobial agents. One important Rh(III)-ligand is the pentamethylcyclopentadienyl (Cp*) group forming in water the [Cp*Rh(H2O)3]2+ complex. Among of its attractive chemical properties is the ability to react specifically with Tyr amino acid side chain of G-protein-coupled receptor (GPCR) peptides by means of highly chemoselective bioconjugation reaction, at room temperature and at pH 5-6. In this computational work, in order to deepen the mechanism of this chemoselective conjugation, we study the ligand exchange reaction between [Cp*Rh(H2O)3]2+ and three small molecules, namely p-cresol, 3-methylimidazole, and toluene, selected as mimetic of aromatic side chains of tyrosine (Tyr), tryptophan (Trp) and phenylalanine (Phe), respectively. Our outcomes suggest that the high selectivity for Tyr side chain might be related to OH group able to affect both thermodynamic and kinetic of ligand exchange reaction, due to its ability to act as both H bond acceptor and donor. These mechanistic aspects can be used to design new metal drugs containing the [Cp*Rh]2+ scaffold targeting specifically Tyr residues involved in biological/pathological processes such as phosphorylation by means of Tyr-kinase enzyme and protein-protein interactions.

METHODS

The geometry of three encounter complexes and product adducts were optimized at the B3LYP//CPCM/ωB97X-D level of theory, adopting the 6-311+G(d,p) basis set for all non-metal atoms and the LANL2DZ pseudopotential for the Rh atom. Meta-dynamics RMSD (MTD(RMSD)) calculations at GFN2-xTB level of theory were performed in NVT conditions at 298.15 K to investigate the bioconjugation reactions (simulation time: 100 ps; integration step 2.0; implicit solvent model: GBSA). The MTD(RMSD) simulation was performed in two replicates for each encounter complex. Final representative subsets of 100 structures for each run were gained with a sampling rate of 1 ps and analyzed by performing single point calculations using the FMO3 method at RI-MP2/6-311G//PCM[1] level of theory, adopting the MCP-TZP core potential for Rh atom.

Improving the accuracy of the FMO binding affinity prediction of ligand-receptor complexes containing metals

Polarization and charge transfer strongly characterize the ligand-receptor interaction when metal atoms are present, as for the Au(I)-biscarbene/DNA G-quadruplex complexes. In a previous work (J Comput Aided Mol Des2022, 36, 851-866) we used the ab initio FMO2 method at the RI-MP2/6-31G* level of theory with the PCM [1] solvation approach to calculate the binding energy (ΔEFMO) of two Au(I)-biscarbene derivatives, [Au(9-methylcaffein-8-ylidene)2]+ and [Au(1,3-dimethylbenzimidazole-2-ylidene)2]+, able to interact with DNA G-quadruplex motif. We found that ΔEFMO and ligand-receptor pair interaction energies (EINT) show very large negative values making the direct comparison with experimental data difficult and related this issue to the overestimation of the embedded charge transfer energy between fragments containing metal atoms. In this work, to improve the accuracy of the FMO method for predicting the binding affinity of metal-based ligands interacting with DNA G-quadruplex (Gq), we assess the effect of the following computational features: (i) the electron correlation, considering the Hartree-Fock (HF) and a post-HF method, namely RI-MP2; (ii) the two (FMO2) and three-body (FMO3) approaches; (iii) the basis set size (polarization functions and double-ζ vs. triple-ζ) and (iv) the embedding electrostatic potential (ESP). Moreover, the partial screening method was systematically adopted to simulate the solvent screening effect for each calculation. We found that the use of the ESP computed using the screened point charges for all atoms (ESP-SPTC) has a critical impact on the accuracy of both ΔEFMO and EINT, eliminating the overestimation of charge transfer energy and leading to energy values with magnitude comparable with typical experimental binding energies. With this computational approach, EINT values describe the binding efficiency of metal-based binders to DNA Gq more accurately than ΔEFMO. Therefore, to study the binding process of metal containing systems with the FMO method, the adoption of partial screening solvent method combined with ESP-SPCT should be considered. This computational protocol is suggested for FMO calculations on biological systems containing metals, especially when the adoption of the default ESP treatment leads to questionable results.

The FMO2 analysis of the ligand-receptor binding energy: the Biscarbene-Gold(I)/DNA G-Quadruplex case study

In this work, the ab initio fragment molecular orbital (FMO) method was applied to calculate and analyze the binding energy of two biscarbene-Au(I) derivatives, [Au(9-methylcaffein-8-ylidene)₂]⁺ and [Au(1,3-dimethylbenzimidazol-2-ylidene)₂]⁺, to the DNA G-Quadruplex structure. The FMO2 binding energy considers the ligand-receptor complex as well as the isolated forms of energy-minimum state of ligand and receptor, providing a better description of ligand-receptor affinity compared with simple pair interaction energies (PIE). Our results highlight important features of the binding process of biscarbene-Au(I) derivatives to DNA G-Quadruplex, indicating that the total deformation-polarization energy and desolvation penalty of the ligands are the main terms destabilizing the binding. The pair interaction energy decomposition analysis (PIEDA) between ligand and nucleobases suggest that the main interaction terms are electrostatic and charge-transfer energies supporting the hypothesis that Au(I) ion can be involved in π-cation interactions further stabilizing the ligand-receptor complex. Moreover, the presence of polar groups on the carbene ring, as C = O, can improve the charge-transfer interaction with K⁺ ion. These findings can be employed to design new powerful biscarbene-Au(I) DNA-G quadruplex binders as promising anticancer drugs. The procedure described in this work can be applied to investigate any ligand-receptor system and is particularly useful when the binding process is strongly characterized by polarization, charge-transfer and dispersion interactions, properly evaluated by ab initio methods.

Interspecies Comparison of Interaction Energies between Photosynthetic Protein RuBisCO and 2CABP Ligand

Ribulose 1,5-bisphosphate carboxylase/oxygenase (RuBisCO) functions as the initial enzyme in the dark reactions of photosynthesis, catalyzing reactions that extract CO2 from the atmosphere and fix CO2 into organic compounds. RuBisCO is classified into four types (isoforms I–IV) according to sequence-based phylogenetic trees. Given its size, the computational cost of accurate quantum-chemical calculations for functional analysis of RuBisCO is high; however, recent advances in hardware performance and the use of the fragment molecular orbital (FMO) method have enabled the ab initio analyses of RuBisCO. Here, we performed FMO calculations on multiple structural datasets for various complexes with the 2′-carboxylarabinitol 1,5-bisphosphate (2CABP) ligand as a substrate analog and investigated whether phylogenetic relationships based on sequence information are physicochemically relevant as well as whether novel information unobtainable from sequence information can be revealed. We extracted features similar to the phylogenetic relationships found in sequence analysis, and in terms of singular value decomposition, we identified residues that strongly interacted with the ligand and the characteristics of the isoforms for each principal component. These results identified a strong correlation between phylogenetic relationships obtained by sequence analysis and residue interaction energies with the ligand. Notably, some important residues were located far from the ligand, making comparisons among species using only residues proximal to the ligand insufficient.

Evaluation of protein descriptors in computer-aided rational protein engineering tasks and its application in property prediction in SARS-CoV-2 spike glycoprotein

The importance of protein engineering in the research and development of biopharmaceuticals and biomaterials has increased. Machine learning in computer-aided protein engineering can markedly reduce the experimental effort in identifying optimal sequences that satisfy the desired properties from a large number of possible protein sequences. To develop general protein descriptors for computer-aided protein engineering tasks, we devised new protein descriptors, one sequence-based descriptor (PCgrades), and three structure-based descriptors (PCspairs, 3D-SPIEs_5.4 Å, and 3D-SPIEs_8Å). While the PCgrades and PCspairs include general and statistical information in physicochemical properties in single and pairwise amino acids respectively, the 3D-SPIEs include specific and quantum–mechanical information with parameterized quantum mechanical calculations (FMO2-DFTB3/D/PCM). To evaluate the protein descriptors, we made prediction models with the new descriptors and previously developed descriptors for diverse protein datasets including protein expression and binding affinity change in SARS-CoV-2 spike glycoprotein. As a result, the newly devised descriptors showed a good performance in diverse datasets, in which the PCspairs showed the best performance (R2=0.783 for protein expression and R2=0.711 for binding affinity). As a result, the newly devised descriptors showed a good performance in diverse datasets, in which the PCspairs showed the best performance. Similar approaches with those descriptors would be promising and useful if the prediction models are trained with sufficient quantitative experimental data from high-throughput assays for industrial enzymes or protein drugs.

FMODB: The World's First Database of Quantum Mechanical Calculations for Biomacromolecules Based on the Fragment Molecular Orbital Method

We developed the world's first web-based public database for the storage, management, and sharing of fragment molecular orbital (FMO) calculation data sets describing the complex interactions between biomacromolecules, named FMO Database (https://drugdesign.riken.jp/FMODB/). Each entry in the database contains relevant background information on how the data was compiled as well as the total energy of each molecular system and interfragment interaction energy (IFIE) and pair interaction energy decomposition analysis (PIEDA) values. Currently, the database contains more than 13 600 FMO calculation data sets, and a comprehensive search function implemented at the front-end. The procedure for selecting target proteins, preprocessing the experimental structures, construction of the database, and details of the database front-end were described. Then, we demonstrated a use of the FMODB by comparing IFIE value distributions of hydrogen bond, ion-pair, and XH/π interactions obtained by FMO method to those by molecular mechanics approach. From the comparison, the statistical analysis of the data provided standard reference values for the three types of interactions that will be useful for determining whether each interaction in a given system is relatively strong or weak compared to the interactions contained within the data in the FMODB. In the final part, we demonstrate the use of the database to examine the contribution of halogen atoms to the binding affinity between human cathepsin L and its inhibitors. We found that the electrostatic term derived by PIEDA greatly correlated with the binding affinities of the halogen containing cathepsin L inhibitors, indicating the importance of QM calculation for quantitative analysis of halogen interactions. Thus, the FMO calculation data in FMODB will be useful for conducting statistical analyses to drug discovery, for conducting molecular recognition studies in structural biology, and for other studies involving quantum mechanics-based interactions.

Identification of correlated inter-residue interactions in protein complex based on the fragment molecular orbital method

A theoretical scheme to systematically describe correlated (network-like) interactions between molecular fragments is proposed within the framework of the fragment molecular orbital (FMO) method. The method is mathematically based on the singular value decomposition (SVD) of the inter-fragment interaction energy (IFIE) matrix obtained by the FMO calculation, and can be applied to a comprehensive description of protein-protein interactions in the context of molecular recognition. In the present study we apply the proposed method to a complex of measles virus hemagglutinin and human SLAM receptor, thus finding a usefulness for efficiently eliciting the correlated interactions among the amino-acid residues involved in the two proteins. Additionally, collective interaction networks by amino-acid residues important for mutation experiments can be clearly visualized.

Coulomb and CH-π interactions in (6-4) photolyase-DNA complex dominate DNA binding and repair abilities

(6–4) Photolyases ((6–4)PLs) are flavoenzymes that repair the carcinogenic UV-induced DNA damage, pyrimidine(6–4)pyrimidone photoproducts ((6–4)PPs), in a light-dependent manner. Although the reaction mechanism of DNA photorepair by (6–4)PLs has been intensively investigated, the molecular mechanism of the lesion recognition remains obscure. We show that a well-conserved arginine residue in Xenopus laevis (6–4)PL (Xl64) participates in DNA binding, through Coulomb and CH–π interactions. Fragment molecular orbital calculations estimated attractive interaction energies of –80–100 kcal mol^–1 for the Coulomb interaction and –6 kcal mol^–1 for the CH–π interaction, and the loss of either of them significantly reduced the affinity for (6–4)PP-containing oligonucleotides, as well as the quantum yield of DNA photorepair. From experimental and theoretical observations, we formulated a DNA binding model of (6–4)PLs. Based on the binding model, we mutated this Arg in Xl64 to His, which is well conserved among the animal cryptochromes (CRYs), and found that the CRY-type mutant exhibited reduced affinity for the (6–4)PP-containing oligonucleotides, implying the possible molecular origin of the functional diversity of the photolyase/cryptochrome superfamily.

Fragment Molecular Orbital Calculations with Implicit Solvent Based on the Poisson-Boltzmann Equation: II. Protein and Its Ligand-Binding System Studies

In this study, the electronic properties of bioactive proteins were analyzed using an ab initio fragment molecular orbital (FMO) methodology in solution: coupling with an implicit solvent model based on the Poisson-Boltzmann surface area called as FMO-PBSA. We investigated the solvent effects on practical and heterogeneous targets with uneven exposure to solvents unlike deoxyribonucleic acid analyzed in our recent study. Interfragment interaction energy (IFIE) and its decomposition analyses by FMO-PBSA revealed solvent-screening mechanisms that affect local stability inside ubiquitin protein: the screening suppresses excessiveness in bare charge-charge interactions and enables an intuitive IFIE analysis. The electrostatic character and associated solvation free energy also give consistent results as a whole to previous studies on the explicit solvent model. Moreover, by using the estrogen receptor alpha (ERα) protein bound to ligands, we elucidated the importance of specific interactions that depend on the electric charge and activatability as agonism/antagonism of the ligand while estimating the influences of the implicit solvent on the ligand and helix-12 bindings. The predicted ligand-binding affinities of bioactive compounds to ERα also show a good correlation with their in vitro activities. The FMO-PBSA approach would thus be a promising tool both for biological and pharmaceutical research targeting proteins.

Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems

Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein-ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.

The 1.6Å resolution structure of activated D138L mutant of catabolite gene activator protein with two cAMP bound in each monomer

The X-ray crystal structure of the cAMP-liganded D138L mutant of Escherichia coli catabolite gene activator protein (CAP) was determined at a resolution of 1.66Å. This high resolution crystal structure reveals four cAMP binding sites in the homodimer. Two anti conformations of cAMPs (anti-cAMP) locate between the β-barrel and the C-helix of each subunit; two syn conformations of cAMPs (syn-cAMP) bind on the surface of the C-terminal domain. With two syn-cAMP molecules bound, the D138L CAP is highly symmetrical with both subunits assuming a "closed" conformation. These differences make the hinge region of the mutant more flexible. Protease susceptibility measurements indicate that D138L is more susceptible to proteases than that of wild type (WT) CAP. The results of protein dynamic experiments (H/D exchange measurements) indicate that the structure of D138L mutant is more dynamic than that of WT CAP, which may impact the recognition of specific DNA sequences.

Prediction of cyclin-dependent kinase 2 inhibitor potency using the fragment molecular orbital method

BACKGROUND

The reliable and robust estimation of ligand binding affinity continues to be a challenge in drug design. Many current methods rely on molecular mechanics (MM) calculations which do not fully explain complex molecular interactions. Full quantum mechanical (QM) computation of the electronic state of protein-ligand complexes has recently become possible by the latest advances in the development of linear-scaling QM methods such as the ab initio fragment molecular orbital (FMO) method. This approximate molecular orbital method is sufficiently fast that it can be incorporated into the development cycle during structure-based drug design for the reliable estimation of ligand binding affinity. Additionally, the FMO method can be combined with approximations for entropy and solvation to make it applicable for binding affinity prediction for a broad range of target and chemotypes.

RESULTS

We applied this method to examine the binding affinity for a series of published cyclin-dependent kinase 2 (CDK2) inhibitors. We calculated the binding affinity for 28 CDK2 inhibitors using the ab initio FMO method based on a number of X-ray crystal structures. The sum of the pair interaction energies (PIE) was calculated and used to explain the gas-phase enthalpic contribution to binding. The correlation of the ligand potencies to the protein-ligand interaction energies gained from FMO was examined and was seen to give a good correlation which outperformed three MM force field based scoring functions used to appoximate the free energy of binding. Although the FMO calculation allows for the enthalpic component of binding interactions to be understood at the quantum level, as it is an in vacuo single point calculation, the entropic component and solvation terms are neglected. For this reason a more accurate and predictive estimate for binding free energy was desired. Therefore, additional terms used to describe the protein-ligand interactions were then calculated to improve the correlation of the FMO derived values to experimental free energies of binding. These terms were used to account for the polar and non-polar solvation of the molecule estimated by the Poisson-Boltzmann equation and the solvent accessible surface area (SASA), respectively, as well as a correction term for ligand entropy. A quantitative structure-activity relationship (QSAR) model obtained by Partial Least Squares projection to latent structures (PLS) analysis of the ligand potencies and the calculated terms showed a strong correlation (r2 = 0.939, q2 = 0.896) for the 14 molecule test set which had a Pearson rank order correlation of 0.97. A training set of a further 14 molecules was well predicted (r2 = 0.842), and could be used to obtain meaningful estimations of the binding free energy.

CONCLUSIONS

Our results show that binding energies calculated with the FMO method correlate well with published data. Analysis of the terms used to derive the FMO energies adds greater understanding to the binding interactions than can be gained by MM methods. Combining this information with additional terms and creating a scaled model to describe the data results in more accurate predictions of ligand potencies than the absolute values obtained by FMO alone.