Model for the fast estimation of basis set superposition error in biomolecular systems

Intermolecular Interactions of Nucleoside Antibiotic Tunicamycin with On-Target MraYCB-TUN and Off-Target DPAGT1-TUN in the Active Sites Delineated by Quantum Mechanics/Molecular Mechanics Calculations

Tunicamycin (TUN) is a nucleoside antibiotic with a complex structure comprising uracil, tunicamine sugar, N-acetylglucosamine (GlcNAc), and fatty acyl tail moieties. TUN, known as a canonical inhibitor, blocks vital functions of certain transmembrane protein families, for example, the insect enzyme dolichyl phosphate α-N-acetylglucosaminylphosphotransferase (DPAGT1) of Spodoptera frugiperda and the bacterial enzyme phospho-N-acetylmuramoylpentapeptide translocase (MraYCB) of Clostridium bolteae. Accurate description of protein-drug interactions has an immense impact on structure-based drug design, while the main challenge is to create proper topology and parameter entries for TUN in modeling protein-TUN interactions given the structural complexity. Starting from DPAGT1-TUN and MraYCB-TUN crystal structures, we first sketched these structural complexes on the basis of the CHARMM36 force field and optimized each of them using quantum mechanics/molecular mechanics (QM/MM) calculations. By continuing calculations on the active site (QM region) of each optimized structure, we specified the characteristics of intermolecular interactions contributing to the binding of TUN to each active site by quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analyses at the M06-2X/6-31G** level. The results outlined that TUN insertion into each active site requires multiple weak, moderate, and strong hydrogen bonds accompanying charge-dipole, dipole-dipole, and hydrophobic interactions among different TUN moieties and adjacent residues. The water-mediated interactions also play central roles in situating the uracil and tunicamine moieties of TUN within the DPAGT1 active site as well as in preserving the uracil-binding pocket in the MraYCB active site. The TUN binds more strongly to DPAGT1 than to MraYCB. The information garnered here is valuable particularly for better understanding mode of action at the molecular level, as it is conducive to developing next generations of nucleoside antibiotics.

Assessing the Applicability of the Geometric Counterpoise Correction in B2PLYP/Double-ζ Calculations for Thermochemistry, Kinetics, and Noncovalent Interactions

We present a proof-of-concept study of the suitability of Kruse and Grimme’s geometric counterpoise correction (gCP) for basis set superposition errors (BSSEs) in double-hybrid density functional calculations with a double-ζ basis set. The gCP approach only requires geometrical information as an input and no orbital/density information is needed. Therefore, this correction is practically free of any additional cost. gCP is trained against the Boys and Bernardi counterpoise correction across a set of 528 noncovalently bound dimers. We investigate the suitability of the approach for the B2PLYP/def2-SVP level of theory, and reveal error compensation effects—missing London dispersion and the BSSE—associated with B2PLYP/def2-SVP calculations, and present B2PLYP-gCP-D3(BJ)/def2-SVP with the reparametrised DFT-D3(BJ) and gCP corrections as a more balanced alternative. Benchmarking results on the S66x8 benchmark set for noncovalent interactions and the GMTKN55 database for main-group thermochemistry, kinetics, and noncovalent interactions show a statistical improvement of the B2PLYP-gCP-D3(BJ) scheme over plain B2PLYP and B2PLYP-D3(BJ). B2PLYP-D3(BJ) shows significant overestimation of interaction energies, barrier heights with larger deviations from the reference values, and wrong relative stabilities in conformers, all of which can be associated with BSSE. We find that the gCP-corrected method represents a significant improvement over B2PLYP-D3(BJ), particularly for intramolecular noncovalent interactions. These findings encourage future developments of efficient double-hybrid DFT strategies that can be applied when double-hybrid calculations with large basis sets are not feasible due to system size.

Characterization of Dimeric Interactions within Protrusion-Domain Interfaces of Parallel and X-Shaped Conformations of Macrobrachium rosenbergii Nodavirus: A Theoretical Study Using the DFT Method along with QTAIM and NBO Analyses

The protrusion domain (P-domain; MrNVPd) of Macrobrachium rosenbergii nodavirus (MrNV) exists in two conformations, parallel and X-shaped. We have performed a theoretical study to gain insight into the nature of the dimeric interactions involving the dimeric interfaces within parallel and X-shaped conformations of MrNVPd by applying the quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analyses in the framework of the density functional theory (DFT) approach. The results reveal that the dimer-dimer interfaces of MrNVPd have hydrogen bonds of common types. Leu255-Lys287, Tyr257-Lys287, Lys287-Ser253, Met294-Cys328, Asp295-Lys327, Ser298-Ser324, Ile326-Asp295, and Cys328-Met294 are the key residue pairs of the dimer-dimer interfaces to maintain the dimer-dimer structures of MrNVPd through charge-charge, charge-dipole, dipole-dipole, hydrophobic, and hydrogen bonding interactions. The strengths of these intermolecular dimer-dimer interactions in the parallel conformation are much greater than those in the X-shaped conformation. The parallel trimeric interface is held basically by electrostatic and hydrophobic interactions. The electrostatic interactions accompanying a strong hydrogen bond of Oγ1-Hγ1···Oγ1 in the Thr276 A-Thr276 D pair maintain the intermolecular interface of two X-shaped MrNVPd dimers.

SAMPL6 host-guest challenge: binding free energies via a multistep approach

In this effort in the SAMPL6 host-guest binding challenge, a combination of molecular dynamics and quantum mechanical methods were used to blindly predict the host-guest binding free energies of a series of cucurbit[8]uril (CB8), octa-acid (OA), and tetramethyl octa-acid (TEMOA) hosts bound to various guest molecules in aqueous solution. Poses for host-guest systems were generated via molecular dynamics (MD) simulations and clustering analyses. The binding free energies for the structures obtained via cluster analyses of MD trajectories were calculated using the MMPBSA method and density functional theory (DFT) with the inclusion of Grimme's dispersion correction, an implicit solvation model to model the aqueous solution, and the resolution-of-the-identity (RI) approximation (MMPBSA, RI-B3PW91-D3, and RI-B3PW91, respectively). Among these three methods tested, the results for OA and TEMOA systems showed MMPBSA and RI-B3PW91-D3 methods can be used to qualitatively rank binding energies of small molecules with an overbinding by 7 and 37 kcal/mol respectively, and RI-B3PW91 gave the poorest quality results, indicating the importance of dispersion correction for the binding free energy calculations. Due to the complexity of the CB8 systems, all of the methods tested show poor correlation with the experimental results. Other quantum mechanical approaches used for the calculation of binding free energies included DFT without the RI approximation, utilizing truncated basis sets to reduce the computational cost (memory, disk space, CPU time), and a corrected dielectric constant to account for ionic strength within the implicit solvation model.

Detailed potential of mean force studies on host-guest systems from the SAMPL6 challenge

Accurately predicting receptor-ligand binding free energies is one of the holy grails of computational chemistry with many applications in chemistry and biology. Many successes have been reported, but issues relating to sampling and force field accuracy remain significant issues affecting our ability to reliably calculate binding free energies. In order to explore these issues in more detail we have examined a series of small host-guest complexes from the SAMPL6 blind challenge, namely octa-acids (OAs)-guest complexes and Curcurbit[8]uril (CB8)-guest complexes. Specifically, potential of mean force studies using umbrella sampling combined with the weighted histogram method were carried out on both systems with both known and unknown binding affinities. We find that using standard force fields and straightforward simulation protocols we are able to obtain satisfactory results, but that simply scaling our results allows us to significantly improve our predictive ability for the unknown test sets: the overall RMSD of the binding free energy versus experiment is reduced from 5.59 to 2.36 kcal/mol; for the CB8 test system, the RMSD goes from 8.04 to 3.51 kcal/mol, while for the OAs test system, the RSMD goes from 2.89 to 0.95 kcal/mol. The scaling approach was inspired by studies on structurally related known benchmark sets: by simply scaling, the RMSD was reduced from 6.23 to 1.19 kcal/mol and from 2.96 to 0.62 kcal/mol for the CB8 benchmark system and the OA benchmark system, respectively. We find this scaling procedure to correct absolute binding affinities to be highly effective especially when working across a "congeneric" series with similar charge states. It is less successful when applied to mixed ligands with varied charges and chemical characteristics, but improvement is still realized in the present case. This approach suggests that there are large systematic errors in absolute binding free energy calculations that can be straightforwardly accounted for using a scaling procedure. Random errors are still an issue, but near chemical accuracy can be obtained using the present strategy in select cases.

DFT, QTAIM, and NBO studies on the trimeric interactions in the protrusion domain of a piscine betanodavirus

Crystal structure of the protrusion domain (P-domain) of the grouper nervous necrosis virus (GNNV) shows the presence of three-fold trimeric protrusions with two asymmetrical calcium cations along the non-crystallographic three-fold axis. The trimeric interaction natures of the interacting residues and the calcium cations with the neighboring residues within the trimeric interface have been studied by the quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analyses in the framework of the density-functional theory (DFT) approach. The results revealed that residues Leu259, Val274, Trp280, and Gln322 of subunit A, Arg261, Asp275, Ala277, and Gln322 of subunit B, Leu259, Asp260, Arg261, Ala277, Val278, and Leu324 of subunit C are the main residues involved in the trimeric interactions. Charge-dipole, dipole-dipole, and hydrogen bonding interactions make the significant contributions to these trimeric interactions. Among different interacting residues within trimeric interface, residue pair Arg261 B-Leu259C forms the strongest hydrogen bond inside the interface between subunits B and C. It was also found that calcium cations interact with residues Asp273, Val274, and Asp275 of subunits A, B, and C through charge-charge and charge transfer interactions.

Push it to the limit: Characterizing the convergence of common sequences of basis sets for intermolecular interactions as described by density functional theory

With the aim of systematically characterizing the convergence of common families of basis sets such that general recommendations for basis sets can be made, we have tested a wide variety of basis sets against complete-basis binding energies across the S22 set of intermolecular interactions-noncovalent interactions of small and medium-sized molecules consisting of first- and second-row atoms-with three distinct density functional approximations: SPW92, a form of local-density approximation; B3LYP, a global hybrid generalized gradient approximation; and B97M-V, a meta-generalized gradient approximation with nonlocal correlation. We have found that it is remarkably difficult to reach the basis set limit; for the methods and systems examined, the most complete basis is Jensen's pc-4. The Dunning correlation-consistent sequence of basis sets converges slowly relative to the Jensen sequence. The Karlsruhe basis sets are quite cost effective, particularly when a correction for basis set superposition error is applied: counterpoise-corrected def2-SVPD binding energies are better than corresponding energies computed in comparably sized Dunning and Jensen bases, and on par with uncorrected results in basis sets 3-4 times larger. These trends are exhibited regardless of the level of density functional approximation employed. A sense of the magnitude of the intrinsic incompleteness error of each basis set not only provides a foundation for guiding basis set choice in future studies but also facilitates quantitative comparison of existing studies on similar types of systems.

Testing the CP-correction procedure with different DFT methods on H-bonding complexes of κ-carrabiose with water molecules

Interaction of water molecules with κ-carrabiose disaccharide, within three H-bonding complexes, was investigated. Particular interest was focused on the way with which the BSSE correction has to be performed. Two strategies were used, either performing BSSE correction during or after optimization. For this aim, several DFT-functionals (hybrid GGA and hybrid meta-GGA) and 6-31 + G* basis set were considered. The results demonstrated the uselessness of including of BSSE-CP correction during optimization for all complexes. From a structural point of view, a proper H-bonding description was obtained using the PBE0 functional for all complexes. The basis set effect on the BSSE using B3LYP functional was also investigated. The reliability of B3LYP/6-31 + G** and B3LYP/6-31++G** models for the complexes involving one or two water molecules was reported while the use of B3LYP/6-311 + G** or B3LYP/6-311++G** levels was shown to be more appropriate for larger complexes equivalent to that involving three water molecules. CP-corrected interaction energies were demonstrated to be closer to CBS-4 M interaction energies than the uncorrected ones. Graphical abstract Functional and basis set effects on BSSE.

A Computational Tool for Accelerated Analysis of Oligomeric Proanthocyanidins in Plants

A computational tool was developed to facilitate proanthocyanidin analysis using data collected by ultra-high-performance liquid chromatography-diode array detection-high resolution accurate mass-mass spectrometry (UHPLC-DAD-HRAM-MS). Both identification and semi-quantitation of proanthocyanidins can be achieved by the developed computational tool. It can extract proanthocyanidin chromatographic peaks, deconvolute the isotopic patterns of A-type, B-type, and multi-charged proanthocyanidins ions, and predict proanthocyanidin structures. Proanthocyanidins were quantified by an external calibration curve of catechin and molar relative response factors (MRRFs) of proanthocyanidins. Quantitation results including concentrations of total proanthocyanidins, individual proanthocyanidins, and proanthocyanidins with different degrees of polymerization and different types of linkage were calculated by the program and exported into an Excel spreadsheet automatically. The program was applied to the analysis of seven plant materials including apple, cranberry, dark chocolate, grape seed extract, jujube, litchi, and mangosteen. The identification results were compared with the results obtained by manual processing. The program can greatly save the time needed for the data analysis of proanthocyanidins.

Exploring short intramolecular interactions in alkylaromatic substrates

From proteins and peptides to semiconducting polymers, aliphatic chains on aromatic groups are recurring motifs in macromolecules from very diverse application fields. Fields in which molecular folding and packing determine the macroscopic physical properties that make such advanced materials appealing in the first place. Within each macromolecule, the intrinsic structure of each unit defines how it interacts with its neighbours, ultimately opening up or denying certain backbone conformations. This eventually also determines how macromolecules interact with each other. This account deals specifically with the conformational problem of many common alkylaromatic units, examining the features of an intramolecular interaction involving a side chain with as few as three methylene groups. A set of 23 model compounds featuring an intramolecular interaction between an aliphatic X-H (X = C, N, O, and S) bond and an aromatic ring was considered. Quantitative computational analysis was made possible, thanks to complete basis set extrapolated CCSD(T) calculations and NCI topological analysis, the latter of which revealed an elaborate network of dispersive and steric interactions leading to somewhat unintuitive and unexpected results, such as the higher energetic stability of certain twisted conformational isomers over those with extended side chains. Vicinal covalent effects from polarizing groups and various heteroatoms, along with the occurrence of non-dispersive phenomena, were also investigated. The conclusions drawn from the investigation include a comprehensive set of guidelines intended to aid in the prediction of the most stable conformation for this class of building blocks. Our findings affect a variety of different research fields, including the tailoring of functional materials for organic electronics and photovoltaics, with insights into a rational treatment of conformational disorder, and the study of protein- and peptide-folding preferences, putting an emphasis on peculiar interactions between the backbone and aromatic residues.

A theoretical study on the characteristics of the intermolecular interactions in the active site of human androsterone sulphotransferase: DFT calculations of NQR and NMR parameters and QTAIM analysis

A theoretical study at the level of density functional theory (DFT) was performed to characterize noncovalent intermolecular interactions, especially hydrogen bond interactions, in the active site of enzyme human androsterone sulphotransferase (SULT2A1/ADT). Geometry optimization, interaction energy, (2)H, (14)N, and (17)O electric field gradient (EFG) tensors, (1)H, (13)C, (17)O, and (15)N chemical shielding (CS) tensors, Natural Bonding Orbital (NBO) analysis, and quantum theory of atoms in molecules (QTAIM) analysis of this active site were investigated. It was found that androsterone (ADT) is able to form hydrogen bonds with residues Ser80, Ile82, and His99 of the active site. The interaction energy calculations and NBO analysis revealed that the ADT molecule forms the strongest hydrogen bond with Ser80. Results revealed that ADT interacts with the other residues through electrostatic and Van der Waals interactions. Results showed that these hydrogen bonds influence on the calculated (2)H, (14)N, and (17)O quadrupole coupling constants (QCCs), as well as (1)H, (13)C, (17)O, and (15)N CS tensors. The magnitude of the QCC and CS changes at each nucleus depends directly on its amount of contribution to the hydrogen bond interaction.

The electronic donation and frequency shifts on the YCCH⋯BH₄⁻ boron-bonded complexes (Y=H, CH₃, CF₃ and CCl₃)

In this theoretical work, the tetrahydroborate ion (BH4(-)) was used as proton acceptor in the formation of the YCC-H⋯BH4(-) complexes (Y=H, CH3, CCl3 and CF3). Using B3LYP/6-311++G(d,p) level of theory, the results of structure corroborate with the analyses of infrared spectra showing that the changes in the bond lengths are in good agreement with the frequency shifts of the HCC-H, H3CCC-H, Cl3CCC-H and F3CCC-H proton donors. Based on the calculations carried out by the Quantum Theory of Atoms in Molecules (QTAIM), the reductions of electronic density corroborate with the red shifts in the frequencies of the C-H bonds. In addition to that, the C-H bonds are polarized because the contributions of s orbital diminish whereas of p increase. In line with this, the variations on the atomic radii computed via QTAIM calculations show that carbon outweigh hydrogen as follows (ΔrC>ΔrH). This scenario is indirectly supported by the Bent's rule of the chemical bonding. Although the interaction energies (corrected with BSSE and ZPE) vary between -19 and -67 kJ mol(-1), these complexes interact without covalent character.

A QSAR study on the inhibition mechanism of matrix metalloproteinase-12 by arylsulfone analogs based on molecular orbital calculations

The inhibition mechanism of matrix metalloproteinase-12 by arylsulfone analogs is revealed using a comprehensive computational approach including docking simulations, molecular orbital calculations, and QSAR.

Energy decomposition analysis approaches and their evaluation on prototypical protein–drug interaction patterns

The partitioning of the interaction energy into chemical components such as electrostatics, polarization, and charge transfer is possible with energy decomposition analysis approaches. We review and evaluate these for biomolecular applications.

Ab initio modelling of the anomeric and exo anomeric effects in 2-methoxytetrahydropyran and 2-methoxythiane corrected for intramolecular BSSE

Oxygen substitution in 2-methoxytetrahydropyran by sulphur in 2-methoxythiane approximately doubles the anomeric effect, which slows down enzymatic processing of 2-methoxythiane.

The Movable Type Method Applied to Protein-Ligand Binding

Accurately computing the free energy for biological processes like protein folding or protein-ligand association remains a challenging problem. Both describing the complex intermolecular forces involved and sampling the requisite configuration space make understanding these processes innately difficult. Herein, we address the sampling problem using a novel methodology we term "movable type". Conceptually it can be understood by analogy with the evolution of printing and, hence, the name movable type. For example, a common approach to the study of protein-ligand complexation involves taking a database of intact drug-like molecules and exhaustively docking them into a binding pocket. This is reminiscent of early woodblock printing where each page had to be laboriously created prior to printing a book. However, printing evolved to an approach where a database of symbols (letters, numerals, etc.) was created and then assembled using a movable type system, which allowed for the creation of all possible combinations of symbols on a given page, thereby, revolutionizing the dissemination of knowledge. Our movable type (MT) method involves the identification of all atom pairs seen in protein-ligand complexes and then creating two databases: one with their associated pairwise distant dependent energies and another associated with the probability of how these pairs can combine in terms of bonds, angles, dihedrals and non-bonded interactions. Combining these two databases coupled with the principles of statistical mechanics allows us to accurately estimate binding free energies as well as the pose of a ligand in a receptor. This method, by its mathematical construction, samples all of configuration space of a selected region (the protein active site here) in one shot without resorting to brute force sampling schemes involving Monte Carlo, genetic algorithms or molecular dynamics simulations making the methodology extremely efficient. Importantly, this method explores the free energy surface eliminating the need to estimate the enthalpy and entropy components individually. Finally, low free energy structures can be obtained via a free energy minimization procedure yielding all low free energy poses on a given free energy surface. Besides revolutionizing the protein-ligand docking and scoring problem this approach can be utilized in a wide range of applications in computational biology which involve the computation of free energies for systems with extensive phase spaces including protein folding, protein-protein docking and protein design.