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.     

Three pillars for achieving quantum mechanical molecular dynamics simulations of huge systems: Divide‐and‐conquer,density‐functional tight‐binding,and massively parallel computation

The linear‐scaling divide‐and‐conquer (DC) quantum chemical methodology is applied to the density‐functional tight‐binding (DFTB) theory to develop a massively parallel program that achieves on‐the‐fly molecular reaction dynamics simulations of huge systems from scratch. The functions to perform large scale geometry optimization and molecular dynamics with DC‐DFTB potential energy surface are implemented to the program called DC‐DFTB‐K. A novel interpolation‐based algorithm is developed for parallelizing the determination of the Fermi level in the DC method. The performance of the DC‐DFTB‐K program is assessed using a laboratory computer and the K computer. Numerical tests show the high efficiency of the DC‐DFTB‐K program, a single‐point energy gradient calculation of a one‐million‐atom system is completed within 60 s using 7290 nodes of the K computer. © 2016 Wiley Periodicals, Inc.     

Parallel implementation of efficient charge–charge interaction evaluation scheme in periodic divide‐and‐conquer density‐functional tight‐binding calculations

A low‐computational‐cost algorithm and its parallel implementation for periodic divide‐and‐conquer density‐functional tight‐binding (DC‐DFTB) calculations are presented. The developed algorithm enables rapid computation of the interaction between atomic partial charges, which is the bottleneck for applications to large systems, by means of multipole‐ and interpolation‐based approaches for long‐ and short‐range contributions. The numerical errors of energy and forces with respect to the conventional Ewald‐based technique can be under the control of the multipole expansion order, level of unit cell replication, and interpolation grid size. The parallel performance of four different evaluation schemes combining previous approaches and the proposed one are assessed using test calculations of a cubic water box on the K computer. The largest benchmark system consisted of 3,295,500 atoms. DC‐DFTB energy and forces for this system were obtained in only a few minutes when the proposed algorithm was activated and parallelized over 16,000 nodes in the K computer. The high performance using a single node workstation was also confirmed. In addition to liquid water systems, the feasibility of the present method was examined by testing solid systems such as diamond form of carbon, face‐centered cubic form of copper, and rock salt form of sodium chloride. © 2017 Wiley Periodicals, Inc.     

Performance of density‐functional tight‐binding models in describing hydrogen‐bonded anionic‐water clusters

Density‐functional tight‐binding (DFTB) models are computationally efficient approximations to density‐functional theory that have been shown to predict reliable structural and energetic properties for various systems. In this work, the reliability and accuracy of the self‐consistent‐charge DFTB model and its recent extension(s) in predicting the structures, binding energies, charge distributions, and vibrational frequencies of small water clusters containing polyatomic anions of the Hofmeister series (carbonate, sulfate, hydrogen phosphate, acetate, nitrate, perchlorate, and thiocyanate) have been carefully and systematically evaluated on the basis of high‐level ab initio quantum‐chemistry [MP2/aug‐cc‐pVTZ and CCSD(T)/aug‐cc‐pVQZ] reference data. Comparison with available experimental data has also been made for further validation. The self‐consistent‐charge DFTB model, and even more so its recent extensions, are shown to properly account for the structural properties, energetics, intermolecular polarization, and spectral signature of hydrogen‐bonding in anionic water clusters at a fraction of the computational cost of ab initio quantum‐chemistry methods. This makes DFTB models candidates of choice for investigating much larger systems such as seeded water droplets, their structural properties, formation thermodynamics, and infrared spectra. © 2014 Wiley Periodicals, Inc.     

Energy gradients in combined fragment molecular orbital and polarizable continuum model (FMO/PCM) calculation

The analytic energy gradients for the combined fragment molecular orbital and polarizable continuum model (FMO/PCM) method are derived and implemented. Applications of FMO/PCM geometry optimization to polyalanine show that the structures obtained with the FMO/PCM method are very close to those obtained with the corresponding full ab initio PCM methods. FMO/PCM (RHF/6‐31G* level) is used to optimize the solution structure of the 304‐atom Trp‐cage miniprotein and the result is in agreement with NMR experiments. The key factors determining the relative stability of the α‐helix, β‐turn and the extended form in solution are elucidated for polyalanine. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

The self‐consistent charge density functional tight‐binding theory study of carbon adatoms using tuned Hubbard U parameters

The self‐consistent charge density functional tight‐binding (DFTB) theory is a useful tool for realizing the electronic structures of large molecular complex systems. In this study, the electronic structure of C₆₁ formed by fullerene C₆₀ with a carbon adatom is analyzed, using the fully localized limit and pseudo self‐interaction correction methods of DFTB to adjust the Hubbard U parameter (DFTB + U). The results show that both the methods used to adjust U can significantly reduce the molecular orbital energy of occupied states localized on the defect carbon atom and improve the gap between highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) of C₆₁. This work will provide a methodological reference point for future DFTB calculations of the electronic structures of carbon materials.     

Fully analytic energy gradient in the fragment molecular orbital method

The Z-vector equations are derived and implemented for solving the response term due to the external electrostatic potentials, and the corresponding contribution is added to the energy gradients in the framework of the fragment molecular orbital (FMO) method. To practically solve the equations for large molecules like proteins, the equations are decoupled by taking advantage of the local nature of fragments in the FMO method and establishing the self-consistent Z-vector method. The resulting gradients are compared with numerical gradients for the test molecular systems: (H(2)O)(64), alanine decamer, hydrated chignolin with the protein data bank (PDB) ID of 1UAO, and a Trp-cage miniprotein construct (PDB ID: 1L2Y). The computation time for calculating the response contribution is comparable to or less than that of the FMO self-consistent charge calculation. It is also shown that the energy gradients for the electrostatic dimer approximation are fully analytic, which significantly reduces the computational costs. The fully analytic FMO gradient is parallelized with an efficiency of about 98% on 32 nodes.     

Less is more when simulating unsulfated glycosaminoglycan 3D‐structure: Comparison of GLYCAM06/TIP3P,PM3‐CARB1/TIP3P,and SCC‐DFTB‐D/TIP3P predictions with experiment

The 3D‐structure of extracellular matrix glycosaminoglycans is central to function, but is currently poorly understood. Resolving this will provide insight into their heterogeneous biological roles and help to realize their significant therapeutic potential. Glycosaminoglycan chemical isoforms are too numerous to study experimentally and simulation provides a tractable alternative. However, best practice for accurate calculation of glycosaminoglycan 3D‐structure within biologically relevant nanosecond timescales is uncertain. Here, we evaluate the ability of three potentials to reproduce experimentally observed glycosaminoglycan monosaccharide puckering, disaccharide 3D‐conformation, and characteristic solvent interactions. Temporal dynamics of unsulfated chondroitin, chondroitin‐4‐sulfate, and hyaluronan β(1→3) disaccharides were simulated within TIP3P explicit solvent unrestrained for 20 ns using the GLYCAM06 force‐field and two semi‐empirical quantum mechanics methods, PM3‐CARB1 and SCC‐DFTB‐D (both within a hybrid QM/MM formalism). Comparison of calculated and experimental properties (vicinal couplings, nuclear Overhauser enhancements, and glycosidic linkage geometries) showed that the carbohydrate‐specific parameterization of PM3‐CARB1 imparted quantifiable benefits on monosaccharide puckering and that the SCC‐DFTB‐D method (including an empirical correction for dispersion) best modeled the effects of hexosamine 4‐sulfation. However, paradoxically, the most approximate approach (GLYCAM06/TIP3P) was the best at predicting monosaccharide puckering, 3D‐conformation, and solvent interactions. Our data contribute to the debate and emerging consensus on the relative performance of these levels of theory for biological molecules. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Rapid QM/MM approach for biomolecular systems under periodic boundary conditions: Combination of the density‐functional tight‐binding theory and particle mesh Ewald method

A quantum mechanical/molecular mechanical (QM/MM) approach based on the density‐functional tight‐binding (DFTB) theory is a useful tool for analyzing chemical reaction systems in detail. In this study, an efficient QM/MM method is developed by the combination of the DFTB/MM and particle mesh Ewald (PME) methods. Because the Fock matrix, which is required in the DFTB calculation, is analytically obtained by the PME method, the Coulomb energy is accurately and rapidly computed. For assessing the performance of this method, DFTB/MM calculations and molecular dynamics simulation are conducted for a system consisting of two amyloid‐β(1‐16) peptides and a zinc ion in explicit water under periodic boundary conditions. As compared with that of the conventional Ewald summation method, the computational cost of the Coulomb energy by utilizing the present approach is drastically reduced, i.e., 166.5 times faster. Furthermore, the deviation of the electronic energy is less than . © 2016 Wiley Periodicals, Inc.     

Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method

A new energy expression is proposed for the fragment molecular orbital method interfaced with the polarizable continuum model (FMO/PCM). The solvation free energy is shown to be more accurate on a set of representative polypeptides with neutral and charged residues, in comparison to the original formulation at the same level of the many-body expansion of the electrostatic potential determining the apparent surface charges. The analytic first derivative of the energy with respect to nuclear coordinates is formulated at the second-order M?ller-Plesset (MP2) perturbation theory level combined with PCM, for which we derived coupled perturbed Hartree-Fock equations. The accuracy of the analytic gradient is demonstrated on test calculations in comparison to numeric gradient. Geometry optimization of the small Trp-cage protein (PDB: 1L2Y) is performed with FMO/PCM/6-31(+)G(d) at the MP2 and restricted Hartree-Fock with empirical dispersion (RHF/D). The root mean square deviations between the FMO optimized and NMR experimental structure are found to be 0.414 and 0.426 A? for RHF/D and MP2, respectively. The details of the hydrogen bond network in the Trp-cage protein are revealed.     

Establishing effective simulation protocols for β‐ and α/β‐peptides. III. Molecular mechanical model for acyclic β‐amino acids

All‐atom molecular mechanics (MM) force field parameters are developed for the backbone of acyclic β‐amino acid using an improved version of the multiobjective evolutionary algorithm (MOEA). The MM model is benchmarked using β³‐homo‐Alanine (β³‐hAla) diamide in water with SCC‐DFTB/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC‐DFTB/MM results regarding the distribution of key dihedral angles for the β³‐hAla diamide in water. The MM model is further applied to a β‐hepta‐peptide in methanol solution. The calculated NOE values and ³J coupling constants averaged over different trajectories are consistent with experimental data. By contrast, simulations using parameters directly transferred from the CHARMM22 force field for proteins lead to much worse agreement, which highlights the importance of careful parameterization for non‐natural peptides, for which the improved MOEA is particularly useful. Finally, as an initial application of the new force field parameters, the behaviors of a short random copolymer consisting of β amino acids in bulk solution and membrane/water interface are studied using a generalized Born implicit solvent model (GBSW). Results for four selected sequences show that segregation of hydrophobic and cationic groups occur easily at the membrane/solution interface for all sequences. The sequence that features alternating short blocks exhibits signs of lower stability at the interface compared to other sequences. These results confirm the hypothesis in recent experimental studies that β‐amino‐acid based random copolymers can develop a high degree of amphiphilicity without regular three‐dimensional structure. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Studies on structure and conformational stability of free canonical 2′‐deoxyribonucleosides: Approximate SCC‐DFTB and LMP2 methods

The molecular structure of free canonical 2′‐deoxyribonucleosides have been studied by applying the electron‐correlated local second‐order Møller–Plesset perturbation theory (LMP2) and self‐consistent‐charge density‐functional tight‐binding (SCC‐DFTB) methods. The variation of structural parameters for C2, C3 endo and exo conformations, and anti, syn orientation of the base unit with furanose ring have been discussed. The relative energies have been calculated for the anti and syn conformations of dT, dC, dG, and dA. Conformational analysis has been performed using the results of the LMP2 and SCC‐DFTB methods. Chemical hardness and chemical potential have been used to study the conformational stability of the conformers. The maximum hardness principle is obeyed for the furanose ring conformations and not for the nucleosides. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Development of Divide‐and‐Conquer Density‐Functional Tight‐Binding Method for Theoretical Research on Li‐Ion Battery

The density‐functional tight‐binding (DFTB) method is one of the useful quantum chemical methods, which provides a good balance between accuracy and computational efficiency. In this account, we reviewed the basis of the DFTB method, the linear‐scaling divide‐and‐conquer (DC) technique, as well as the parameterization process. We also provide some refinement, modifications, and extension of the existing parameters that can be applicable for lithium‐ion battery systems. The diffusion constants of common electrolyte molecules and LiTFSA salt in solution have been estimated using DC‐DFTB molecular dynamics simulation with our new parameters. The resulting diffusion constants have good agreement to the experimental diffusion constants.     

Hydrogen bonding in polyamino‐polyalcohols: a monohydrated cocrystal of 1,3‐diamino‐5‐azaniumyl‐1,3,5‐trideoxy‐cis‐inositol iodide and 1,3,5‐triamino‐1,3,5‐trideoxy‐cis‐inositol

In the title monohydrated cocrystal, namely 1,3‐diamino‐5‐azaniumyl‐1,3,5‐trideoxy‐cis‐inositol iodide–1,3,5‐triamino‐1,3,5‐trideoxy‐cis‐inositol–water (1/1/1), C₆H₁₆N₃O₃⁺·I⁻·C₆H₁₅N₃O₃·H₂O, the neutral 1,3,5‐triamino‐1,3,5‐trideoxy‐cis‐inositol (taci) molecule and the monoprotonated 1,3‐diamino‐5‐azaniumyl‐1,3,5‐trideoxy‐cis‐inositol cation (Htaci⁺) both adopt a chair conformation, with the three O atoms in axial and the three N atoms in equatorial positions. The cation, but not the neutral taci unit, exhibits intramolecular O—H...O hydrogen bonding. The entire structure is stabilized by a complex three‐dimensional network of intermolecular hydrogen bonds. The neutral taci entities and the Htaci⁺ cations are each aligned into chains along [001]. In these chains, two O—H...N interactions generate a ten‐membered ring as the predominant structural motif. The rings consist of vicinal 2‐amino‐1‐hydroxyethylene units of neighbouring molecules, which are paired via centres of inversion. The chains are interconnected into undulating layers parallel to the ac plane, and the layers are further held together by O—H...N hydrogen bonds and additional interactions with the iodide counter‐anions and solvent water molecules.     

Analytic gradient and molecular dynamics simulations using the fragment molecular orbital method combined with effective potentials

The completely analytic energy gradients are derived and implemented for the two-body fragment molecular orbital (FMO2) method combined with the model core potentials (MCP) and effective fragment potentials (EFP). The many-body terms in EFP require solving coupled-perturbed Hartree-Fock equations, which are derived and implemented. The molecular dynamics (MD) simulations are performed using the FMO2/MCP method for the capped alanine decamer and with the FMO2/EFP method for the zwitterionic conformer of glycine tetramer immersed in the water layer of 6.0 Å (135 water molecules). The results of the MD simulations using the FMO2/EFP and FMO2/MCP gradients show that the total energy is conserved at the time steps less than 1 fs.     

Shift‐and‐invert parallel spectral transformation eigensolver: Massively parallel performance for density‐functional based tight‐binding

The Shift‐and‐invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density‐functional based tight‐binding (DFTB) Hamiltonian and overlap matrices for single‐wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ～330,000 (～5600) eigenvalues and eigenfunctions are obtained in ～190 (～5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPs is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time‐to‐solution at the strong scaling limit. A parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated. © 2015 Wiley Periodicals, Inc.