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Identification of important residues in biochemical complexes is often a crucial step for many problems in molecular biology and biochemistry. A method is proposed to identify hotspots in biomolecular complexes based on a new metric, derived from networks representing molecular subunits (residues, bridging solvent molecules, ligands etc.) connected by interactions. A singular value decomposition of the weighted adjacency matrix is used to construct a scalar rank for each subunit that reflects its importance in the residue interaction network. This metric is called the singular value centrality. In addition, a new formalism is proposed to account for water-mediated interactions in the ranking of residues. Interactions for a residue network can be provided by various computational methods. In this work interactions are obtained from full quantum-mechanical calculations of protein-protein complexes using the fragment molecular orbital method. The ranking results are shown to be in good agreement with earlier computational and experimental studies. The developed method can be used to gain a deeper insight into the role of subunits in complex biomolecular systems.

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A partition analysis based on segments is developed for density functional theory defining solute dipole moments of functional groups, and the corresponding induced solvent dipoles representing solvent screening. The accuracy of dipoles from the fragment molecular orbital method is evaluated in comparison to unfragmented values. The analysis is applied to evaluate dipole moments of side chains, amino and carbonyl groups in common polypeptide motifs, α-helixes, ß-turns, and random coils in solution. The membrane domain of the ATP synthase (1B9U) is analyzed, revealing the effect of the bend splitting of the α-helix into two pieces.

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The enhancement of the peptide bond order by a resonance in the lone pair of N and the π-bond of CO is analyzed. A decomposition of the bond order in terms of localized molecular orbitals is developed and applied to the peptide bond. A combination of two rotations of hybrid orbitals is proposed to improve the boundary treatment in the fragment molecular orbital method. The developed approach is applied to peptide bonds, and it is found crucial to retain the π orbital in the variational space of both fragments across the boundary. The interaction energies between conventional amino acid residues in Trp-cage (1L2Y) are discussed.

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An auxiliary polarization formulation of the fragment molecular orbital (FMO) method is developed, combining a basis set correction computed for capped isolated fragments with a polarization obtained from uncapped fragments. For a set of organic and inorganic test systems, it is shown that the total energy and atomic charges are accurately reproduced with respect to full unfragmented calculations. It is demonstrated that the method is accurate for computing electronic excited states. The developed approach is applied to rank the isomers of chignolin from experimental NMR data (PDB: 1UAO) according to their relative energy. Contributions of polarization and basis set effects to pair interactions between fragments are elucidated.

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An excitonic coupling model is developed based on an equation-of-motion coupled cluster combined with the fragment molecular orbital method. The effects of polarization and excitonic coupling on the splitting of quasi-degenerate levels in systems containing multiple chromophores are elucidated on dimers of formaldehyde, water, formic acid, hydrogen fluoride, and carbon monoxide. It is shown that the level structure is mainly determined by the mutual polarization of chromophores and to a lesser extent by the excitonic coupling. The role of symmetry in excitonic coupling in dimers is discussed. The excitonic coupling between all residues in the photoactive yellow protein (PDB: 2PHY) is analyzed.

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A many-body expansion of ionization potentials and electron affinities is developed based on a combination of the fragment molecular orbital method and equation-of-motion coupled-cluster (EOM-CC). In addition to site-specific values, obtained as one-body properties, pair and triple corrections are added to account for nonlocal EOM-CC contributions of the molecular environment of a chromophore. The developed method is applied to carboxylic acids, alkyl cations, a protein ubiquitin (Protein Data Bank ID 1UBQ), and a nano ribbon of white graphene elucidating the effect of environment on ionization potential and electron affinity.

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Strategies for multiple-level parallelizations of quantum-mechanical calculations are discussed, with an emphasis on using groups of workers for performing parallel tasks. These parallel programming models can be used for a variety ab initio quantum chemistry approaches, including the fragment molecular orbital method and replica-exchange molecular dynamics. Strategies for efficient load balancing on problems of increasing granularity are introduced and discussed. A four-level parallelization is developed based on a multi-level hierarchical grouping, and a high parallel efficiency is achieved on the Theta supercomputer using 131 072 OpenMP threads.

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The analytic energy gradient of energy with respect to nuclear coordinates is derived for the fragment molecular orbital (FMO) method combined with time-dependent density functional theory (TDDFT). The response terms arising from the use of a polarizable embedding are derived. The obtained analytic FMO-TDDFT gradient is shown to be accurate in comparison to both numerical FMO-TDDFT and unfragmented TDDFT gradients, at the level of two- and three-body expansions. The gradients are used for geometry optimizations, molecular dynamics, vibrational calculations, and simulations of IR and Raman spectra of excited states. The developed method is used to optimize the geometry of the ground and excited electronic states of the photoactive yellow protein (PDB: 2PHY).

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Fast parameterized methods such as density-functional tight-binding (DFTB) facilitate realistic calculations of large molecular systems, which can be accelerated by the fragment molecular orbital (FMO) method. Fragmentation facilitates interaction analyses between functional parts of molecular systems. In addition to DFTB, other parameterized methods combined with FMO are also described. Applications of FMO methods to biochemical and inorganic systems are reviewed.

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Quantum mechanical (QM) calculations at the level of density-functional tight-binding are applied to a protein-DNA complex (PDB: 2o8b) consisting of 3763 atoms, averaging 100 snapshots from molecular dynamics simulations. A detailed comparison of QM and force field (Amber) results is presented. It is shown that, when solvent screening is taken into account, the contributions of the backbones are small, and the binding of nucleotides in the double helix is governed by the base-base interactions. On the other hand, the backbones can make a substantial contribution to the binding of amino acid residues to nucleotides and other residues. The effect of charge transfer on the interactions is also analyzed, revealing that the actual charge of nucleotides and amino acid residues can differ by as much as 6 and 8% from the formal integer charge, respectively. The effect of interactions on topological models (protein -residue networks) is elucidated.

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Protein-protein interactions (PPIs) are essential for the function of many proteins. Aberrant PPIs have the potential to lead to disease, making PPIs promising targets for drug discovery. There are over 64,000 PPIs in the human interactome reference database; however, to date, very few PPI modulators have been approved for clinical use. Further development of PPI-specific therapeutics is highly dependent on the availability of structural data and the existence of reliable computational tools to explore the interface between two interacting proteins. The fragment molecular orbital (FMO) quantum mechanics method offers comprehensive and computationally inexpensive means of identifying the strength (in kcal/mol) and the chemical nature (electrostatic or hydrophobic) of the molecular interactions taking place at the protein-protein interface. We have integrated FMO and PPI exploration (FMO-PPI) to identify the residues that are critical for protein-protein binding (hotspots). To validate this approach, we have applied FMO-PPI to a dataset of protein-protein complexes representing several different protein subfamilies and obtained FMO-PPI results that are in agreement with published mutagenesis data. We observed that critical PPIs can be divided into three major categories: interactions between residues of two proteins (intermolecular), interactions between residues within the same protein (intramolecular), and interactions between residues of two proteins that are mediated by water molecules (water bridges). We extended our findings by demonstrating how this information obtained by FMO-PPI can be utilized to support the structure-based drug design of PPI modulators (SBDD-PPI).

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Using isolated and polarized states of fragments, a method for computing the polarization energies in density functional theory (DFT) and density-functional tight-binding (DFTB) is developed in the framework of the fragment molecular orbital method. For DFTB, the method is extended into the use of periodic boundary conditions (PBC), for which a new component, a periodic self-polarization energy, is derived. The couplings of the polarization to other components in the pair interaction energy analysis (PIEDA) are derived for DFT and DFTB, and compared to Hartree-Fock and second-order Møller-Plesset perturbation theory (MP2). The effect of the self-consistent (DFT) and perturbative (MP2) treatment of the electron correlation on the polarization is discussed. The difference in the polarization in the bulk (PBC) and micro (cluster) solvation is elucidated.

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Adsorption and chemical reactions occurring on industrially important ZSM-5 and faujasite zeolite catalysts are investigated with the quantum-mechanical fragment molecular orbital method combined with periodic boundary conditions. Suitable fragmentation patterns are devised and tested providing important case studies of computing real materials with fragmentation methods. A good accuracy is demonstrated in comparison to full calculations, and a good agreement with the available experimental data is obtained. The full production cycle of p-xylene on faujasite zeolite is mapped. The catalytic role of the zeolite in the dehydration reaction, analyzed with the partition analysis, is attributed to the delocalization of the negative charge over the zeolite. On the other hand, an increase of the barrier in the Diels-Alder reaction by the zeolite is attributed to the preferential stabilization of the reactants over the transition state as demonstrated by the guest-zeolite interaction energy.

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A decomposition of the free energy is developed in the many-body expansion framework of the fragment molecular orbital (FMO) method combined with umbrella sampling molecular dynamics (MD). In FMO/MD simulations, performed with density-functional tight-binding and periodic boundary conditions, all atoms are treated quantum mechanically. The free energy is computed and decomposed for a series of SN2 Menshutkin reactions in water. The barrier lowering by the solvent is attributed to the competition between the solvent polarization and the solute-solvent interactions including charge transfer.

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A structure-based quantitative calculation of excitonic couplings between photosynthetic pigments has to describe the dynamical polarization of the protein/solvent environment of the pigments, giving rise to reaction field and screening effects. Here, this challenging problem is approached by combining the fragment molecular orbital (FMO) method with the polarizable continuum model (PCM). The method is applied to compute excitonic couplings between chlorophyll a (Chl a) pigments of the water-soluble chlorophyll-binding protein (WSCP). By calibrating the vacuum dipole strength of the 0-0 transition of the Chl a chromophores according to experimental data, an excellent agreement between calculated and experimental linear absorption and circular dichroism spectra of WSCP is obtained. The effect of the mutual polarization of the pigment ground states is calculated to be very small. The simple Poisson-Transition-charge-from-Electrostatic-potential (Poisson-TrEsp) method is found to accurately describe the screening part of the excitonic coupling, obtained with FMO/PCM. Taking into account that the reaction field effects of the latter method can be described by a scalar constant leads to an improvement of Poisson-TrEsp that is expected to provide the basis for simple and realistic calculations of optical spectra and energy transfer in photosynthetic light-harvesting complexes. In addition, we present an expression for the estimation of Huang-Rhys factors of high-frequency pigment vibrations from experimental fluorescence line-narrowing spectra that takes into account the redistribution of oscillator strength by the interpigment excitonic coupling. Application to WSCP results in corrected Huang-Rhys factors that are less than one third of the original values obtained by the standard electronic two-state analysis that neglects the above redistribution. These factors are important for the estimation of the dipole strength of the 0-0 transition of the chromophores and for the development of calculation schemes for the spectral density of the exciton-vibrational coupling.

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For gaining insights into interactions in periodic systems, an analysis is developed based on the fragment molecular orbital method combined with periodic boundary conditions. The adsorption energy is decomposed into guest and surface polarization and deformation energy, guest-surface and guest-guest interactions, and the vibrational free energy. The analysis is applied to the adsorption of guest molecules to Ih (001) ice surface. The cooperativity effects result in a non-linear change in the adsorption energy with coverage due to many-body effects. The role of dispersion is found to be dominant for guests with long hydrophobic tails. A rule is proposed relating the length of the alkyl tail with the formation of the guest layer. The computed binding enthalpies are in good agreement with experimental values. For high coverage, adsorbed molecules can form an ordered layer known as self-assembled monolayer.

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Aptamer selection against novel infections is a complicated and time-consuming approach. Synergy can be achieved by using computational methods together with experimental procedures. This study aims to develop a reliable methodology for a rational aptamer in silico et vitro design. The new approach combines multiple steps: (1) Molecular design, based on screening in a DNA aptamer library and directed mutagenesis to fit the protein tertiary structure; (2) 3D molecular modeling of the target; (3) Molecular docking of an aptamer with the protein; (4) Molecular dynamics (MD) simulations of the complexes; (5) Quantum-mechanical (QM) evaluation of the interactions between aptamer and target with further analysis; (6) Experimental verification at each cycle for structure and binding affinity by using small-angle X-ray scattering, cytometry, and fluorescence polarization. By using a new iterative design procedure, structure- and interaction-based drug design (SIBDD), a highly specific aptamer to the receptor-binding domain of the SARS-CoV-2 spike protein, was developed and validated. The SIBDD approach enhances speed of the high-affinity aptamers development from scratch, using a target protein structure. The method could be used to improve existing aptamers for stronger binding. This approach brings to an advanced level the development of novel affinity probes, functional nucleic acids. It offers a blueprint for the straightforward design of targeting molecules for new pathogen agents and emerging variants.

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A fast quantum-mechanical approach, density-functional tight-binding combined with the fragment molecular orbital method and periodic boundary conditions, is used to optimize atomic coordinates and cell parameters for a set of protein crystals: 1ETL, 5OQZ, 3Q8J, 1CBN, and 2VB1. Good agreement between experimental and calculated structures is obtained for both atomic coordinates and cell parameters. Sterical clashes present in the experimental structures are corrected by simulations. The partition analysis is extended to treat periodic boundary conditions and applied to analyze protein-solvent interactions in crystals.

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Aptamers are short, single-stranded DNA or RNA oligonucleotide molecules that function as synthetic analogs of antibodies and bind to a target molecule with high specificity. Aptamer affinity entirely depends on its tertiary structure and charge distribution. Therefore, length and structure optimization are essential for increasing aptamer specificity and affinity. Here, we present a general optimization procedure for finding the most populated atomistic structures of DNA aptamers. Based on the existed aptamer LC-18 for lung adenocarcinoma, a new truncated LC-18 (LC-18t) aptamer LC-18t was developed. A three-dimensional (3D) shape of LC-18t was reported based on small-angle X-ray scattering (SAXS) experiments and molecular modeling by fragment molecular orbital or molecular dynamic methods. Molecular simulations revealed an ensemble of possible aptamer conformations in solution that were in close agreement with measured SAXS data. The aptamer LC-18t had stronger binding to cancerous cells in lung tumor tissues and shared the binding site with the original larger aptamer. The suggested approach reveals 3D shapes of aptamers and helps in designing better affinity probes.

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Vibrational energies are partitioned into the contributions of molecular parts called segments, for instance, residues in proteins. The fragment molecular orbital method is used to facilitate vibrational calculations of large systems at the DFTB and HF-3c levels. The vibrational analysis is combined with the partitioning of the electronic energy, yielding free-energy contributions of segments to the binding energy, pinpointing hot spots for drug discovery and other studies. The analysis is illustrated on two protein-ligand complexes in solution.