Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme.

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH) 3 $$ {}_3 $$ and (FH) 2 $$ {}_2 $$ -H 2 $$ {}_2 $$ O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH) 2 $$ {}_2 $$ -H 2 $$ {}_2 $$ O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.

Towards tailoring hydrophobic interaction with uranyl(VI) oxygen for C-H activation.

Bovine serum albumin (BSA) has a uranyl(VI) binding hotspot where uranium is tightly bound by three carboxylates. Uranyl oxygen is "soaked" into the hydrophobic core of BSA. Isopropyl hydrogen of Val is trapped near UO22+ and upon photoexcitation, C-H bond cleavage is initiated. A unique hydrophobic contact with "yl"-oxygen, as observed here, can be used to induce C-H activation.

Prediction of Binding Pose and Affinity of Nelfinavir, a SARS-CoV-2 Main Protease Repositioned Drug, by Combining Docking, Molecular Dynamics, and Fragment Molecular Orbital Calculations.

A novel in silico drug design procedure is described targeting the Main protease (Mpro) of the SARS-CoV-2 virus. The procedure combines molecular docking, molecular dynamics (MD), and fragment molecular orbital (FMO) calculations. The binding structure and properties of Mpro were predicted for Nelfinavir (NFV), which had been identified as a candidate compound through drug repositioning, targeting Mpro. Several poses of the Mpro and NFV complexes were generated by docking, from which four docking poses were selected by scoring with FMO energy. Then, each pose was subjected to MD simulation, 100 snapshot structures were sampled from each of the generated MD trajectories, and the structures were evaluated by FMO calculations to rank the pose based on binding energy. Several residues were found to be important in ligand recognition, including Glu47, Asp48, Glu166, Asp187, and Gln189, all of which interacted strongly with NFV. Asn142 is presumably regarded to form hydrogen bonds or CH/π interaction with NFV; however, in the present calculation, their interactions were transient. Moreover, the tert-butyl group of NFV had no interaction with Mpro. Identifying such strong and weak interactions provides candidates for maintaining and substituting ligand functional groups and important suggestions for drug discovery using drug repositioning. Besides the interaction between NFV and the amino acid residues of Mpro, the desolvation effect of the binding pocket also affected the ranking order. A similar procedure of drug design was applied to Lopinavir, and the calculated interaction energy and experimental inhibitory activity value trends were consistent. Our approach provides a new guideline for structure-based drug design starting from a candidate compound whose complex crystal structure has not been obtained.

Enhancement of energy decomposition analysis in fragment molecular orbital calculations.

Energy decomposition analysis is one of the most attractive features of fragment molecular orbital (FMO) calculations from the point of view of practical applications. Here we report some enhancements for PIEDA in the ABINIT-MP program. One is a separation of the dispersion-type stabilization from the electron correlation energy, traditionally referred to as the "dispersion interaction" (DI). Another is an alternative evaluation of the electrostatic (ES) interaction using the restrained electrostatic potential (RESP) charges. The GA:CT stacked base pair and the Trp-Cage miniprotein were used as illustrative examples.

Correction to "Bifurcated Hydrogen Bonds in a Peptide Crystal Unveiled by X-ray Diffraction and Polarized Raman Spectroscopy".

[This corrects the article DOI: 10.1021/acs.cgd.3c00302.].

Variational quantum eigensolver simulations with the multireference unitary coupled cluster ansatz: a case study of the C2v quasi-reaction pathway of beryllium insertion into a H2 molecule.

Variational quantum eigensolver (VQE)-based quantum chemical calculations have been extensively studied as a computational model using noisy intermediate-scale quantum devices. The VQE uses a parametrized quantum circuit defined through an "ansatz" to generate approximated wave functions, and the appropriate choice of an ansatz is the most important step. Because most chemistry problems focus on the energy difference between two electronic states or structures, calculating the total energies in different molecular structures with the same accuracy is essential to correctly understand chemistry and chemical processes. In this context, the development of ansatzes that are capable of describing electronic structures of strongly correlated systems accurately is an important task. Here we applied a conventional unitary coupled cluster (UCC) and a newly developed multireference unitary coupled cluster with partially generalized singles and doubles (MR-UCCpGSD) ansatzes to the quasi-reaction pathway of Be insertion into H2, LiH molecule under covalent bond dissociation, and a rectangular tetra-hydrogen cluster known as a P4 cluster; these are representative systems in which the static electron correlation effect is prominent. Our numerical simulations revealed that the UCCSD ansatz exhibits extremely slow convergence behaviour around the point where an avoided crossing occurs in the Be + H2 → BeH2 reaction pathway, resulting in a large discrepancy of the simulated VQE energy from the full-configuration interaction (full-CI) value. By contrast, the MR-UCCpGSD ansatz can give more reliable results with respect to total energy and the overlap with the full-CI solution, insisting the importance of multiconfigurational treatments in the calculations of strongly correlated systems. The MR-UCCpGSD ansatz allows us to compute the energy with the same accuracy regardless of the strength of multiconfigurational character, which is an essential property to discuss energy differences of various molecular systems.

Interaction Analysis on the SARS-CoV-2 Spike Protein Receptor Binding Domain Using Visualization of the Interfacial Electrostatic Complementarity.

Visualization of the interfacial electrostatic complementarity (VIINEC) is a recently developed method for analyzing protein-protein interactions using electrostatic potential (ESP) calculated via the ab initio fragment molecular orbital method. In this Letter, the molecular interactions of the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein with human angiotensin-converting enzyme 2 (ACE2) and B38 neutralizing antibody were examined as an illustrative application of VIINEC. The results of VIINEC revealed that the E484 of RBD has a role in making a local electrostatic complementary with ACE2 at the protein-protein interface, while it causes a considerable repulsive electrostatic interaction. Furthermore, the calculated ESP map at the interface of the RBD/B38 complex was significantly different from that of the RBD/ACE2 complex, which is discussed herein in association with the mechanism of the specificity of the antibody binding to the target protein.

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.

Interaction analyses of SARS-CoV-2 spike protein based on fragment molecular orbital calculations.

At the stage of SARS-CoV-2 infection in human cells, the spike protein consisting of three chains, A, B, and C, with a total of 3300 residues plays a key role, and thus its structural properties and the binding nature of receptor proteins to host human cells or neutralizing antibodies has attracted considerable interest. Here, we report on interaction analyses of the spike protein in both closed (PDB-ID: 6VXX) and open (6VYB) structures, based on large-scale fragment molecular orbital (FMO) calculations at the level of up to the fourth-order Møller-Plesset perturbation with singles, doubles, and quadruples (MP4(SDQ)). Inter-chain interaction energies were evaluated for both structures, and a mutual comparison indicated considerable losses of stabilization energies in the open structure, especially in the receptor binding domain (RBD) of chain-B. The role of charged residues in inter-chain interactions was illuminated as well. By two separate calculations for the RBD complexes with angiotensin-converting enzyme 2 (ACE2) (6M0J) and B38 Fab antibody (7BZ5), it was found that the binding with ACE2 or antibody partially compensated for this stabilization loss of RBD.

Fragment Molecular Orbital Based Interaction Analyses on COVID-19 Main Protease - Inhibitor N3 Complex (PDB ID: 6LU7).

The worldwide spread of COVID-19 (new coronavirus found in 2019) is an emergent issue to be tackled. In fact, a great amount of works in various fields have been made in a rather short period. Here, we report a fragment molecular orbital (FMO) based interaction analysis on a complex between the SARS-CoV-2 main protease (Mpro) and its peptide-like inhibitor N3 (PDB ID: 6LU7). The target inhibitor molecule was segmented into five fragments in order to capture site specific interactions with amino acid residues of the protease. The interaction energies were decomposed into several contributions, and then the characteristics of hydrogen bonding and dispersion stabilization were made clear. Furthermore, the hydration effect was incorporated by the Poisson-Boltzmann (PB) scheme. From the present FMO study, His41, His163, His164, and Glu166 were found to be the most important amino acid residues of Mpro in interacting with the inhibitor, mainly due to hydrogen bonding. A guideline for optimizations of the inhibitor molecule was suggested as well based on the FMO analysis.

Fragmentation at sp2 carbon atoms in fragment molecular orbital method.

In the fragment molecular orbital (FMO) method, a given molecular system is usually fragmented at sp3 carbon atoms. However, fragmentation at different sites sometimes becomes necessary. Hence, we propose fragmentation at sp2 carbon atoms in the FMO method. Projection operators are constructed using sp2 local orbitals. To maintain practical accuracy, it is essential to consider the three-body effect. In order to suppress the corresponding increase of computational cost, we propose approximate models considering local trimers. Numerical verification shows that the present models are as accurate as or better than the standard FMO2 method in total energy with fragmentation at sp3 carbon atoms.

Stabilization Mechanism for a Nonfibrillar Amyloid ß Oligomer Based on Formation of a Hydrophobic Core Determined by Dissipative Particle Dynamics.

Neurotoxicity caused by nonfibrillar amyloid ß (Aß) oligomers in the brain is suggested to be associated with the onset of Alzheimer's disease (AD). Elucidating the structural features of Aß oligomers is critical for promoting drug discovery research for AD. One of the Aß oligomers, known as Aß*56, is a dodecamer that impairs memory when injected into healthy rats, suggesting that Aß*56 may contribute to cognitive deficits in AD patients. Another dodecamer structure, formed by 20-residue peptide segments derived from the Aß peptide (Aß17-36), has been revealed by X-ray crystallography. The structure of the Aß17-36 dodecamer is composed of trimer units and shows the oligomer antibody A11 reactivity, which are characteristic of Aß*56, indicating that Aß*56 and the Aß17-36 dodecamer share a similar structure. However, the structure of the C-terminal regions (Aß37-42) remains unclear. The C-terminal region, which is abundant in hydrophobic residues, is thought to play a key role in stabilizing the oligomer structure by forming a hydrophobic core. In this study, we employed dissipative particle dynamics, a coarse-grained simulation method with soft core potentials, utilizing the crystal structure information to unravel Aß dodecamer structures with C-terminal regions. The simulation results were validated by the reported experimental data. Hence, an analysis of the simulation results can provide structural insights into Aß oligomers. Our simulations revealed the stabilization mechanism of the dodecamer structure at the molecular level. We showed that C-terminal regions spontaneously form a hydrophobic core in the central cavity, contributing to stabilizing the dodecamer structure. Furthermore, four consecutive hydrophobic residues in the C-terminal region (i.e., Val39-Ala42) are important for core formation.

Cm3+/Eu3+ induced structural, mechanistic and functional implications for calmodulin.

Trivalent actinides and their lanthanide homologues are being scrutinized for their potential health risk when ingested as a result of a range of industrial activities such as mining. Importantly, these ions are known to exhibit high affinity towards calmodulin (CaM). In case of their inadvertent uptake, the holoproteins that are occupied by these cations may block signal transduction pathways or increase the concentration of these ions in intact cells, which could lead to accumulation in human organs. Accordingly, this investigation employed spectroscopy, computational chemistry, calorimetry, and biochemistry to study the results of metal ion substitution on the protein structure, enzymatic activity and chemo- and cytotoxicity of An3+/Ln3+ ions. As will be demonstrated herein, our data confirm the higher affinity of Cm3+ and Eu3+ compared to Ca2+ to all 4 binding sites of CaM, with one site differing from the remaining three. This higher-affinity site will complex Eu3+ in an exothermic fashion; in contrast, ion binding to the three lower-affinity EF-hands was found to be endothermic. The overall endothermic binding process is ascribed to the loss of the hydration shells of the trivalent ions upon protein binding. These findings are supported by extensive quantum chemical calculations of full holo-CaM, which were performed at the MP2 level using the fragment molecular orbital method. The exceptional binding site (EF-hand 3) features fewer negatively charged residues compared to the other EF-hands, thereby allowing Eu3+ and Cm3+ to carry one or two additional waters compared to Ca2+-CaM, while also causing the structure of Cm3+/Eu3+-CaM to become slightly disordered. Moreover, the enzymatic activity decreases somewhat in comparison to Ca2+-CaM. By utilizing a combination of techniques, we were able to generate a comprehensive picture of the CaM-actinide/lanthanide system from the molecular level to its functional impact. Such knowledge could also be applied to other metal-binding proteins.

Destabilization of DNA through interstrand crosslinking by UO22.

UO22+ was shown to form an interstrand crosslink between two different strands of a single DNA molecule. This crosslink hardly affected the hydrogen bonds between nucleobase pairs but destabilized the π-π stacking between the two nucleobases in the vicinity of UO22+-bound phosphate. Thereby, the fragility of the DNA backbone increased upon UO22+ binding.

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.

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.

RI-MP3 calculations of biomolecules based on the fragment molecular orbital method.

In this study, the third-order Møller-Plesset perturbation (MP3) theory using the resolution of the identity (RI) approximation was combined with the fragment molecular orbital (FMO) method to efficiently calculate a high-order electron correlation energy of biomolecular systems. We developed a new algorithm for the RI-MP3 calculation, which can be used with the FMO scheme. After test calculations using a small molecule, the FMO-RI-MP3 calculations were performed for two biomolecular systems comprising a protein and a ligand. The computational cost of these calculations was only around 5 and 4 times higher than those of the FMO-RHF calculations. The error associated with the RI approximation was around 2.0% of the third-order correlation contribution to the total energy. However, the RI approximation error in the interaction energy between the protein and ligand molecule was insignificantly small, which reflected the negligible error in the inter fragment interaction energy. © 2018 Wiley Periodicals, Inc.

Fragment Molecular Orbital Calculations with Implicit Solvent Based on the Poisson-Boltzmann Equation: Implementation and DNA Study.

In this study, an ab initio fragment molecular orbital (FMO) methodology was developed to evaluate the solvent effects on electrostatic interactions, which make a significant contribution to the physical and chemical processes occurring in biological systems. Here, a fully polarizable solute consisting of the FMO electron density was electrostatically coupled with an implicit solvent based on the Poisson-Boltzmann (PB) equation; in addition, the nonpolar contributions empirically obtained from the molecular surface area (SA) were added. Interaction analysis considering solvent-screening and dispersion effects is now available as a powerful tool to determine the local stabilities inside solvated biomolecules. This methodology is applied to a deoxyribonucleic acid (DNA) duplex known as the Dickerson dodecamer. We found that excessively large electrostatic interactions inside the duplex are effectively damped by the screening, and the frontier molecular orbital energies are also successfully lowered. These observations indicate the stability of highly charged DNA duplexes in solution. Moreover, the solvation free energies in the implicit model show fairly good agreement with those in the explicit model while avoiding the costly statistical sampling of the electrolyte distribution. Consequently, our FMO-PBSA approach could yield new insights into biological phenomena and pharmacological problems via this ab initio methodology.

Development of the Fragment Molecular Orbital Method for Calculating Nonlocal Excitations in Large Molecular Systems.

We developed the fragment-based method for calculating nonlocal excitations in large molecular systems. This method is based on the multilayer fragment molecular orbital method and the configuration interaction single (CIS) wave function using localized molecular orbitals. The excited-state wave function for the whole system is described as a superposition of configuration state functions (CSFs) for intrafragment excitations and for interfragment charge-transfer excitations. The formulation and calculations of singlet excited-state Hamiltonian matrix elements in the fragment CSFs are presented in detail. The efficient approximation schemes for calculating the matrix elements are also presented. The computational efficiency and the accuracy were evaluated using the molecular dimers and molecular aggregates. We confirmed that absolute errors of 50 meV (relative to the conventional calculations) are achievable for the molecular systems in their equilibrium geometries. The perturbative electron correlation correction to the CIS excitation energies is also demonstrated. The present theory can compute a large number of excited states in large molecular systems; in addition, it allows for the systematic derivation of a model exciton Hamiltonian. These features are useful for studying excited-state dynamics in condensed molecular systems based on the ab initio electronic structure theory.

Fragment Molecular Orbital Based Parametrization Procedure for Mesoscopic Structure Prediction of Polymeric Materials.

In the analyses of miscibility behaviors of macromolecules and polymers, dissipative particle dynamics (DPD) simulations are generally performed. In these simulations, the so-called χ parameters describing the effective interactions among particles are crucial. It has been known that such parameters can be obtained within the classical or empirical force field frameworks. However, there is a potential problem that charge transfer and polarization occasionally occur. Additionally, satisfactory reference parameters are not available for some cases. Therefore, we developed a new procedure to evaluate the set of parameters by using the ab initio fragment molecular orbital (FMO) method which can provide the set of interaction energies among segments as polymer units. Moreover, we evaluated the anisotropy of molecules by using the FMO-based effective interaction parameters for three standard binary mixture systems (hexane-nitrobenzene, polyisobutylene-diisobutyl ketone, and polyisoprene-polystyrene). The calculated values showed good agreement with the experimental values with about 10% errors.