Use of caps in the auxiliary basis set formulation of the fragment molecular orbital method

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.

Analysis of Site Energies and Excitonic Couplings: The Role of Symmetry and Polarization

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.

Site-Specific Ionization Potentials and Electron Affinities in Large Molecular Systems at Coupled Cluster Level

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.

Multi-level parallelization of quantum-chemical calculations

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.

Analytic Gradient for Time-Dependent Density Functional Theory Combined with the Fragment Molecular Orbital Method

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).

Parametrized quantum-mechanical approaches combined with the fragment molecular orbital method

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.

Hotspot Identification and Drug Design of Protein-Protein Interaction Modulators Using the Fragment Molecular Orbital Method

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).

Polarization energies in the fragment molecular orbital method

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.

The catalytic activity and adsorption in faujasite and ZSM-5 zeolites: the role of differential stabilization and charge delocalization

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.

Structure- and Interaction-Based Design of Anti-SARS-CoV-2 Aptamers

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.

Towards a quantitative description of excitonic couplings in photosynthetic pigment-protein complexes: quantum chemistry driven multiscale approaches

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.

The importance of reaction field and screening effects on the excitonic couplings is demonstrated, and from quantum-chemical calculations a single scaling factor is derived that can be used to improve simple models based on the Poisson equation.

Free Energy Decomposition Analysis Based on the Fragment Molecular Orbital Method

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 S_N2 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.

Analysis of Guest Adsorption on Crystal Surfaces Based on the Fragment Molecular Orbital Method

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.

Quantum-Mechanical Structure Optimization of Protein Crystals and Analysis of Interactions in Periodic Systems

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.

The role of SAXS and molecular simulations in 3D structure elucidation of a DNA aptamer against lung cancer

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.

Partitioning of the Vibrational Free Energy

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.

Unusual shift in the visible absorption spectrum of an active ctenophore photoprotein elucidated by time-dependent density functional theory

Active hydromedusan and ctenophore Ca2+-regulated photoproteins form complexes consisting of apoprotein and strongly non-covalently bound 2-hydroperoxycoelenterazine (an oxygenated intermediate of coelenterazine). Whereas the absorption maximum of hydromedusan photoproteins is at 460-470 nm, ctenophore photoproteins absorb at 437 nm. Finding out a physical reason for this blue shift is the main objective of this work, and, to achieve it, the whole structure of the protein-substrate complex was optimized using a linear scaling quantum-mechanical method. Electronic excitations pertinent to the spectra of the 2-hydroperoxy adduct of coelenterazine were simulated with time-dependent density functional theory. The dihedral angle of 60° of the 6-(p-hydroxy)-phenyl group relative to the imidazopyrazinone core of 2-hydroperoxycoelenterazine molecule was found to be the key factor determining the absorption of ctenophore photoproteins at 437 nm. The residues relevant to binding of the substrate and its adopting the particular rotation were also identified.

The fragment molecular orbital method combined with density-functional tight-binding and periodic boundary conditions

The density-functional tight-binding (DFTB) formulation of the fragment molecular orbital method is combined with periodic boundary conditions. Long-range electrostatics and dispersion are evaluated with the Ewald summation technique. The first analytic derivatives of the energy with respect to atomic coordinates and lattice parameters are formulated. The accuracy of the method is established in comparison to numerical gradients and DFTB without fragmentation. The largest elementary cell in this work has 1631 atoms. The method is applied to elucidate the polarization, charge transfer, and interactions in the solution.

Partition Analysis for Density-Functional Tight-Binding

High-order charge transfer is incorporated into the fragment molecular orbital (FMO) method using a charge transfer state with fractional charges. This state is used for a partition analysis of properties based on segments that may be different from fragments in FMO. The partition analysis is also formulated for calculations without fragmentation. All development in this work is limited to density-functional tight-binding. The analysis is applied to a water cluster, crambin (PDB: 1CBN), and two complexes of Trp-cage (1L2Y) with ligands. The contributions of functional groups in ligands are obtained, providing useful information for drug discovery.

Recent developments in the general atomic and molecular electronic structure system

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

Characterizing Interhelical Interactions of G-Protein Coupled Receptors with the Fragment Molecular Orbital Method

G-protein coupled receptors (GPCRs) are the largest superfamily of membrane proteins, regulating almost every aspect of cellular activity and serving as key targets for drug discovery. We have identified an accurate and reliable computational method to characterize the strength and chemical nature of the interhelical interactions between the residues of transmembrane (TM) domains during different receptor activation states, something that cannot be characterized solely by visual inspection of structural information. Using the fragment molecular orbital (FMO) quantum mechanics method to analyze 35 crystal structures representing different branches of the class A GPCR family, we have identified 69 topologically equivalent TM residues that form a consensus network of 51 inter-TM interactions, providing novel results that are consistent with and help to rationalize experimental data. This discovery establishes a comprehensive picture of how defined molecular forces govern specific interhelical interactions which, in turn, support the structural stability, ligand binding, and activation of GPCRs.

FMOxFMO: Elucidating Excitonic Interactions in the Fenna-Matthews-Olson Complex with the Fragment Molecular Orbital Method

In order to study Förster resonance energy transfer (FRET), the fragment molecular orbital (FMO) method is extended to compute electronic couplings between local excitations via the excited state transition density model, enabling efficient calculations of nonlocal excitations in a large molecular system and overcoming the previous limitation of being able to compute only local excitations. The results of these simple but accurate models are validated against full quantum calculations without fragmentation. The developed method is applied to a very important photosynthetic pigment-protein complex, the Fenna-Matthews-Olson complex (FMOc), that is responsible for the energy transfer from a chlorosome to the reaction center in the green sulfur bacteria. Absorption and circular dichroism spectra of FMOc are simulated, and the role of the molecular environment on the excitations is revealed.

Aptamer-Conjugated Superparamagnetic Ferroarabinogalactan Nanoparticles for Targeted Magnetodynamic Therapy of Cancer

Nanotechnologies involving physical methods of tumor destruction using functional oligonucleotides are promising for targeted cancer therapy. Our study presents magnetodynamic therapy for selective elimination of tumor cells in vivo using DNA aptamer-functionalized magnetic nanoparticles exposed to a low frequency alternating magnetic field. We developed an enhanced targeting approach of cancer cells with aptamers and arabinogalactan. Aptamers to fibronectin (AS-14) and heat shock cognate 71 kDa protein (AS-42) facilitated the delivery of the nanoparticles to Ehrlich carcinoma cells, and arabinogalactan (AG) promoted internalization through asialoglycoprotein receptors. Specific delivery of the aptamer-modified FeAG nanoparticles to the tumor site was confirmed by magnetic resonance imaging (MRI). After the following treatment with a low frequency alternating magnetic field, AS-FeAG caused cancer cell death in vitro and tumor reduction in vivo. Histological analyses showed mechanical disruption of tumor tissues, total necrosis, cell lysis, and disruption of the extracellular matrix. The enhanced targeted magnetic theranostics with the aptamer conjugated superparamagnetic ferroarabinogalactans opens up a new venue for making biocompatible contrasting agents for MRI imaging and performing non-invasive anti-cancer therapies with a deep penetrated magnetic field.

Accurate Scoring in Seconds with the Fragment Molecular Orbital and Density-Functional Tight-Binding Methods

The accurate evaluation of receptor-ligand interactions is an essential part of rational drug design. While quantum mechanical (QM) methods have been a promising means by which to achieve this, traditional QM is not applicable for large biological systems due to its high computational cost. Here, the fragment molecular orbital (FMO) method has been combined with the density-functional tight-binding (DFTB) method to compute energy calculations of biological systems in seconds. FMO-DFTB outperformed GBVI/WSA in identifying a set of 10 binders versus a background of 500 decoys applied to human k-opioid receptor. The significant increase in the speed and the high accuracy achieved with FMO-DFTB calculations allows FMO to be applied in areas of drug discovery that were not previously accessible to traditional QM methodologies. For the first time, it is now possible to perform FMO calculations in a high-throughput manner.

Analyzing Interactions with the Fragment Molecular Orbital Method

Basic concepts in the analysis of binding using the fragment molecular orbital method are discussed at length: polarization, desolvation, and interaction. The components in the pair interaction energy decomposition analysis are introduced, and the analysis is illustrated for a water dimer and a protein-ligand complex.

Characterizing Protein-Protein Interactions with the Fragment Molecular Orbital Method

Proteins are vital components of living systems, serving as building blocks, molecular machines, enzymes, receptors, ion channels, sensors, and transporters. Protein-protein interactions (PPIs) are a key part of their function. There are more than 645,000 reported disease-relevant PPIs in the human interactome, but drugs have been developed for only 2% of these targets. The advances in PPI-focused drug discovery are highly dependent on the availability of structural data and accurate computational tools for analysis of this data. Quantum mechanical approaches are often too expensive computationally, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed and the ability to reveal key interactions that would otherwise be hard to detect. FMO provides essential information for PPI drug discovery, namely, identification of key interactions formed between residues of two proteins, including their strength (in kcal/mol) and their chemical nature (electrostatic or hydrophobic). In this chapter, we have demonstrated how three different FMO-based approaches (pair interaction energy analysis (PIE analysis), subsystem analysis (SA) and analysis of protein residue networks (PRNs)) have been applied to study PPI in three protein-protein complexes.

Solvent Screening in Zwitterions Analyzed with the Fragment Molecular Orbital Method

Based on induced solvent charges, a new model of solvent screening is developed in the framework of the fragment molecular orbital combined with the polarizable continuum model. The developed model is applied to analyze interactions in a prototypical zwitterionic system, sodium chloride in water, and it is shown that the large underestimation of the interaction in the original solvent screening based on local charges is successfully corrected. The model is also applied to a complex of the Trp-cage (PDB: 1L2Y ) miniprotein with an anionic ligand, and the physical factors determined protein-ligand binding in solution are unraveled.

The Fragment Molecular Orbital Method Based on Long-Range Corrected Density-Functional Tight-Binding

The presently available linear scaling approaches to density-functional tight-binding (DFTB) based on the fragment molecular orbital (FMO) method are severely impacted by the problem of artificial charge transfer due to the self-interaction error (SIE), which hampers the simulation of zwitterionic systems such as biopolymers or ionic liquids. Here we report an extension of FMO-DFTB where we included a long-range corrected (LC) functional designed to mitigate the DFTB SIE, called the FMO-LC-DFTB method, resulting in a robust method which succeeds in simulating zwitterionic systems. Both energy and analytic gradient are developed for the gas phase and the polarizable continuum model of solvation. The scaling of FMO-LC-DFTB with system size N is shown to be almost linear, O( N^1.13-1.28), and its numerical accuracy is established for a variety of representative systems including neutral and charged polypeptides. It is shown that pair interaction energies between fragments for two mini-proteins are in excellent agreement with results from long-range corrected density functional theory. The new method was employed in long time scale (1 ns) molecular dynamics simulations of the tryptophan cage protein (PDB: 1L2Y ) in the gas phase for four different protonation states and in stochastic global minimum structure searches for 1-ethyl-3-methylimidazolium nitrate ionic liquid clusters containing up to 2300 atoms.

Characterising GPCR-ligand interactions using a fragment molecular orbital-based approach

There has been fantastic progress in solving GPCR crystal structures. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanical approaches (QM) are often too computationally expensive, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule towards ligand binding, including an analysis of their chemical nature.

Simulations of infrared and Raman spectra in solution using the fragment molecular orbital method

Calculation of IR and Raman spectra in solution for large molecular systems made possible with analytic FMO/PCM Hessians.

Exploring GPCR-Ligand Interactions with the Fragment Molecular Orbital (FMO) Method

The understanding of binding interactions between any protein and a small molecule plays a key role in the rationalization of affinity and selectivity. It is essential for an efficient structure-based drug design (SBDD) process. FMO enables ab initio approaches to be applied to systems that conventional quantum-mechanical (QM) methods would find challenging. The key advantage of the Fragment Molecular Orbital Method (FMO) is that it can reveal atomistic details about the individual contributions and chemical nature of each residue and water molecule toward ligand binding which would otherwise be difficult to detect without using QM methods. In this chapter, we demonstrate the typical use of FMO to analyze 19 crystal structures of β1 and β2 adrenergic receptors with their corresponding agonists and antagonists.

Rapid and accurate assessment of GPCR-ligand interactions Using the fragment molecular orbital-based density-functional tight-binding method

The reliable and precise evaluation of receptor–ligand interactions and pair‐interaction energy is an essential element of rational drug design. While quantum mechanical (QM) methods have been a promising means by which to achieve this, traditional QM is not applicable for large biological systems due to its high computational cost. Here, the fragment molecular orbital (FMO) method has been used to accelerate QM calculations, and by combining FMO with the density‐functional tight‐binding (DFTB) method we are able to decrease computational cost 1000 times, achieving results in seconds, instead of hours. We have applied FMO‐DFTB to three different GPCR–ligand systems. Our results correlate well with site directed mutagenesis data and findings presented in the published literature, demonstrating that FMO‐DFTB is a rapid and accurate means of GPCR–ligand interactions. © 2017 Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Subsystem Analysis for the Fragment Molecular Orbital Method and Its Application to Protein-Ligand Binding in Solution

A subsystem analysis is derived incorporating interfragment interactions into the fragment properties, such as energies or charges. The relative stabilities of three alanine isomers, the α-helix, the β-turn, and the extended form are studied and the differences in fragment properties are elucidated. The analysis is further elaborated for studies of binding energies. The binding of the Trp-cage protein (PDB: 1L2Y ) to two ligands is studied in detail. Binding energies defined for each fragment can be used as a convenient descriptor for analyzing contributions to binding in solution.