Diastereomer configurations from joint experimental-computational analysis

The potential of the approach combining nuclear magnetic resonance (NMR) spectroscopy, relaxed grid search (RGS), molecular dynamics (MD) simulations, and quantum mechanical (QM) calculations for the determination of diastereomer configurations is demonstrated using four diastereomers of a trisubstituted epoxide. Since the change in configuration of the chiral center is expected to change the distribution of conformer populations (including those of side-chain rotamers), changes in NMR parameters [chemical shifts, J couplings, and nuclear Overhauser effects (NOEs)] are expected. The method therefore relies on (1) identification of possible conformations in each diastereomer using relaxed grid search analysis and MD simulations; (2) geometry optimizations of conformers selected from step (1), followed by calculations of their relative energies (populations) using QM methods; (3) calculations of averaged NMR parameters using QM methods; (4) matching calculated and experimental values of NMR parameters of diastereomers. The diastereomer configurations are considered resolved, if three NMR parameters different in nature, chemical shifts, J couplings, and NOEs, are in agreement. A further advantage of this method is that full structural and dynamics characterization of each of the diastereomers is achieved based on the joint analysis of experimental and computational data.     

Dynamic structures of phosphodiesterase-5 active site by combined molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical calculations

Various quantum mechanical/molecular mechanical (QM/MM) geometry optimizations starting from an x-ray crystal structure and from the snapshot structures of constrained molecular dynamics (MD) simulations have been performed to characterize two dynamically stable active site structures of phosphodiesterase-5 (PDE5) in solution. The only difference between the two PDE5 structures exists in the catalytic, second bridging ligand (BL2) which is HO- or H2O. It has been shown that, whereas BL2 (i.e. HO-) in the PDE5(BL2 = HO-) structure can really bridge the two positively charged metal ions (Zn2+ and Mg2+), BL2 (i.e. H2O) in the PDE5(BL2 = H2O) structure can only coordinate Mg2+. It has been demonstrated that the results of the QM/MM geometry optimizations are remarkably affected by the solvent water molecules, the dynamics of the protein environment, and the electronic embedding charges of the MM region in the QM part of the QMM/MM calculation. The PDE5(BL2 = H2O) geometries optimized by using the QM/MM method in different ways show strong couplings between these important factors. It is interesting to note that the PDE5(BL2 = HO-) and PDE5(BL2 = H2O) geometries determined by the QM/MM calculations neglecting these three factors are all consistent with the corresponding geometries determined by the QM/MM calculations that account for all of these three factors. These results suggest the overall effects of these three important factors on the optimized geometries can roughly cancel out. However, the QM/MM calculations that only account for some of these factors could lead to considerably different geometries. These results might be useful also in guiding future QM/MM geometry optimizations on other enzymes.     

Simulation of 59Co NMR chemical shifts in aqueous solution

59Co chemical shifts were computed at the GIAO-B3LYP level for [Co(CN)6]3-, [Co(H2O)6]3+, [Co(NH3)6]3+, and [Co(CO)4]- in water. The aqueous solutions were modeled by Car-Parrinello molecular dynamics (CPMD) simulations, or by propagation on a hybrid quantum-mechanical/molecular-mechanical Born-Oppenheimer surface (QM/MM-BOMD). Mean absolute deviations from experiment obtained with these methods are on the order of 400 and 600 ppm, respectively, over a total delta(59Co) range of about 18,000 ppm. The effect of the solvent on delta(59Co) is mostly indirect, resulting primarily from substantial metal-ligand bond contractions on going from the gas phase to the bulk. The simulated solvent effects on geometries and delta(59Co) values are well reproduced by using a polarizable continuum model (PCM), based on optimization and perturbational evaluation of quantum-mechanical zero-point corrections.     

QM/MM calculation of solvent effects on absorption spectra of guanine

Electronic spectra of guanine in the gas phase and in water were studied by quantum mechanical/molecular mechanical (QM/MM) methods. Geometries for the excited‐state calculations were extracted from ground‐state molecular dynamics (MD) simulations using the self‐consistent‐charge density functional tight binding (SCC‐DFTB) method for the QM region and the TIP3P force field for the water environment. Theoretical absorption spectra were generated from excitation energies and oscillator strengths calculated for 50 to 500 MD snapshots of guanine in the gas phase (QM) and in solution (QM/MM). The excited‐state calculations used time‐dependent density functional theory (TDDFT) and the DFT‐based multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke, in combination with two basis sets. Our investigation covered keto‐N7H and keto‐N9H guanine, with particular focus on solvent effects in the low‐energy spectrum of the keto‐N9H tautomer. When compared with the vertical excitation energies of gas‐phase guanine at the optimized DFT (B3LYP/TZVP) geometry, the maxima in the computed solution spectra are shifted by several tenths of an eV. Three effects contribute: the use of SCC‐DFTB‐based rather than B3LYP‐based geometries in the MD snapshots (red shift of ca. 0.1 eV), explicit inclusion of nuclear motion through the MD snapshots (red shift of ca. 0.1 eV), and intrinsic solvent effects (differences in the absorption maxima in the computed gas‐phase and solution spectra, typically ca. 0.1–0.3 eV). A detailed analysis of the results indicates that the intrinsic solvent effects arise both from solvent‐induced structural changes and from electrostatic solute–solvent interactions, the latter being dominant. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Lennard-Jones parameters for the combined QM/MM method using the B3LYP/6-31G*/AMBER potential

A combined DFT quantum mechanical and AMBER molecular mechanical potential (QM/MM) is presented for use in molecular modeling and molecular simulations of large biological systems. In our approach we evaluate Lennard-Jones parameters describing the interaction between the quantum mechanical (QM) part of a system, which is described at the B3LYP/6-31+G* level of theory, and the molecular mechanical (MM) part of the system, described by the AMBER force field. The Lennard-Jones parameters for this potential are obtained by calculating hydrogen bond energies and hydrogen bond geometries for a large set of bimolecular systems, in which one hydrogen bond monomer is described quantum mechanically and the other is treated molecular mechanically. We have investigated more than 100 different bimolecular systems, finding very good agreement between hydrogen bond energies and geometries obtained from the combined QM/MM calculations and results obtained at the QM level of theory, especially with respect to geometry. Therefore, based on the Lennard-Jones parameters obtained in our study, we anticipate that the B3LYP/6-31+G*/AMBER potential will be a precise tool to explore intermolecular interactions inside a protein environment.     

Interpreting protein structural dynamics from NMR chemical shifts

In this investigation, semiempirical NMR chemical shift prediction methods are used to evaluate the dynamically averaged values of backbone chemical shifts obtained from unbiased molecular dynamics (MD) simulations of proteins. MD-averaged chemical shift predictions generally improve agreement with experimental values when compared to predictions made from static X-ray structures. Improved chemical shift predictions result from population-weighted sampling of multiple conformational states and from sampling smaller fluctuations within conformational basins. Improved chemical shift predictions also result from discrete changes to conformations observed in X-ray structures, which may result from crystal contacts, and are not always reflective of conformational dynamics in solution. Chemical shifts are sensitive reporters of fluctuations in backbone and side chain torsional angles, and averaged (1)H chemical shifts are particularly sensitive reporters of fluctuations in aromatic ring positions and geometries of hydrogen bonds. In addition, poor predictions of MD-averaged chemical shifts can identify spurious conformations and motions observed in MD simulations that may result from force field deficiencies or insufficient sampling and can also suggest subsets of conformational space that are more consistent with experimental data. These results suggest that the analysis of dynamically averaged NMR chemical shifts from MD simulations can serve as a powerful approach for characterizing protein motions in atomistic detail.     

Modelling zwitterions in solution: 3-fluoro-γ-aminobutyric acid (3F-GABA)

The conformations and relative stabilities of folded and extended 3-fluoro-γ-aminobutyric acid (3F-GABA) conformers were studied using explicit solvation models. Geometry optimisations in the gas phase with one or two explicit water molecules favour folded and neutral structures containing intramolecular NH···O-C hydrogen bonds. With three or five explicit water molecules zwitterionic minima are obtained, with folded structures being preferred over extended conformers. The stability of folded versus extended zwitterionic conformers increases on going from a PCM continuum solvation model to the microsolvated complexes, though extended structures become less disfavoured with the inclusion of more water molecules. Full explicit solvation was studied with a hybrid quantum-mechanical/molecular-mechanical (QM/MM) scheme and molecular dynamics simulations, including more than 6000 TIP3P water molecules. According to free energies obtained from thermodynamic integration at the PM3/MM level and corrected for B3LYP/MM total energies, the fully extended conformer is more stable than folded ones by about -4.5 kJ mol(-1). B3LYP-computed (3)J(F,H) NMR spin-spin coupling constants, averaged over PM3/MM-MD trajectories, agree best with experiment for this fully extended form, in accordance with the original NMR analysis. The seeming discrepancy between static PCM calculations and experiment noted previously is now resolved. That the inexpensive semiempirical PM3 method performs so well for this archetypical zwitterion is encouraging for further QM/MM studies of biomolecular systems.     

Quantum mechanics/fluctuating charge calculations for absorption spectra of aqueous green fluorescent protein chromophore

We applied the quantum mechanics/fluctuating charges (QM/FQ) method to simulate the absorption spectra of three protonated forms of p-hydroxybenzylidene imidazolone (p-HBDI) in water. Configurations of solute-solvent were generated from molecular dynamics (MD) simulation within the context of a hybrid scheme in which solute and solvents were treated at QM and molecular mechanics, respectively. Nonperiodic spherical boundary condition was used. To examine the influence on simulated spectra coming from the geometrical relaxation of solute, the MD simulations were carried out for two cases: frozen and flexible molecular geometry of solute. As a result of our calculations, the simulations using the flexible solute's structure delivered vertical excitation energies closer to experimental data than those of a frozen solute, especially for the neutral case. For spectral broadening, changing from fixed geometry of solute to a flexible one led to a significant increase for both neutral and anionic forms of p-HBDI, but no effect happened for the cationic one.     

Conformational analysis of L-prolines in water

The results of the ring conformational analysis of L-proline, N-acetyl-L-proline, and trans-4-hydroxy-L-proline by NMR combined with calculations using density functional theory (DFT) and molecular dynamics (MD) are reported. Accurate values of 1H-1H J-couplings in water and other solvents have been determined. Using a two-site equilibrium model, the Cgamma-endo conformer of L-proline in water has been identified as intermediate between gammaTdelta [twist(Cgamma-endo, Cdelta-exo)] and gammaE [envelope(Cgamma-endo)] and the Cgamma-exo conformer as betaTgamma. Both conformers were equally populated at room temperature. The N-acetyl [cis-rotamer gammaTbeta(80%)/gammaE(20%) and trans-rotamer gammaTbeta(61%)/gammaE(39%)] and 4-hydroxy (gammaEpsilon) derivatives showed significant changes in both the population and the geometries of the preferred ring conformers. The combination of NMR predicted populations with the DFT B3LYP/6-311+G(2d,p)/IEFPCM calculations proved successful, resulting in fairly accurate predictions of J-couplings. Simulations using MD were mostly in favor of the two-site equilibrium model between Cgamma-endo and Cgamma-exo conformers, similar to that used for the analysis of NMR J-couplings. Various force fields examined for MD simulations failed to reproduce the ring conformational geometries and populations of L-proline in water accurately, while significantly better agreement with NMR was found for trans-N-acetyl-L-proline using GROMOS and AMBER force fields.     

Development of massive multilevel molecular dynamics simulation program,platypus (PLATform for dYnamic protein unified simulation), for the elucidation of protein functions

A massively parallel program for quantum mechanical‐molecular mechanical (QM/MM) molecular dynamics simulation, called Platypus (PLATform for dYnamic Protein Unified Simulation), was developed to elucidate protein functions. The speedup and the parallelization ratio of Platypus in the QM and QM/MM calculations were assessed for a bacteriochlorophyll dimer in the photosynthetic reaction center (DIMER) on the K computer, a massively parallel computer achieving 10 PetaFLOPs with 705,024 cores. Platypus exhibited the increase in speedup up to 20,000 core processors at the HF/cc‐pVDZ and B3LYP/cc‐pVDZ, and up to 10,000 core processors by the CASCI(16,16)/6‐31G** calculations. We also performed excited QM/MM‐MD simulations on the chromophore of Sirius (SIRIUS) in water. Sirius is a pH‐insensitive and photo‐stable ultramarine fluorescent protein. Platypus accelerated on‐the‐fly excited‐state QM/MM‐MD simulations for SIRIUS in water, using over 4000 core processors. In addition, it also succeeded in 50‐ps (200,000‐step) on‐the‐fly excited‐state QM/MM‐MD simulations for the SIRIUS in water. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Using MD snapshots in ab initio and DFT calculations: OH vibrations in the first hydration shell around Li+(aq)

The average OH stretching vibrational frequency for the water molecules in the first hydration shell around a Li(+) ion in a dilute aqueous solution was calculated by a hybrid molecular dynamics + quantum-mechanical ("MD + QM") approach. Using geometry configurations from a series of snapshots from an MD simulation, the anharmonic, uncoupled OH stretching frequencies were calculated for 100 first-shell OH oscillators at the B3LYP and HF/6-31G(d,p) levels of theory, explicitly including the first shell and the relevant second shell water molecules into charge-embedded supermolecular QM calculations. Infrared intensity-weighting of the density-of-states (DOS) distributions by means of the squared dipole moment derivatives (which vary by a factor of 20 over the OH stretching frequency band at the B3LYP level), changes the downshift from approximately -205 to -275 cm(-1) at the B3LYP level. Explicit inclusion of relevant third-shell water molecules in the supermolecular cluster leads to a further downshift by approximately -30 cm(-1). Our final estimated average downshift is approximately -305 cm(-1). The experimental value lies somewhere in the range between -290 and -420 cm(-1). Also, the absolute nu(OH) frequency is well reproduced in our calculations. "In-liquid" instantaneous correlation curves between nu(OH) and various typical H-bond strength parameters such as R(O...O), R(H...O), the intramolecular OH bond length, and the IR intensity are presented. Some of these correlations are robust and persist also for the rather distorted instantaneous geometries in the liquid; others are less so.     

The Jahn-Teller effect of the Cr(2+) ion in aqueous solution: Ab initio QM/MM molecular dynamics simulations

The hydration structure of Cr(2+) has been studied using molecular dynamics (MD) simulations including three-body corrections and combined ab initio quantum mechanical/molecular mechanical (QM/MM) MD simulations at the Hartree-Fock level. The structural properties are determined in terms of radial distribution functions, coordination numbers, and several angle distributions. The mean residence time was evaluated for describing ligand exchange processes in the second hydration shell. The Jahn-Teller distorted octahedral [Cr(H(2)O)(6)](2+) complex was pronounced in the QM/MM MD simulation. The first-shell distances of Cr(2+) are in the range of 1.9-2.8 A, which are slightly larger than those observed in the cases of Cu(2+) and Ti(3+). No first-shell water exchange occurred during the simulation time of 35 ps. Several water-exchange processes were observed in the second hydration shell with a mean residence time of 7.3 ps.     

Correlation effects on the structure and dynamics of the H3O+ hydrate: B3LYP/MM and MP2/MM MD simulations

Two combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations, namely B3LYP/MM and MP2/MM, have been performed to investigate the possible influence of electron correlation on the structure and dynamics of the H(3)O(+) hydrate. In comparison to the previously published HF/MM results, both B3LYP/MM and MP2/MM simulations clearly reveal stronger H(3)O(+)-water hydrogen bond interactions, which are reflected in a slightly greater compactness of the H(3)O(+) hydrate. However, the B3LYP/MM simulation, although providing structural details very close to the MP2/MM data, shows an artificially slow dynamic nature of some first shell water molecules as a consequence of the formation of a long-lived H(3)O(+)···H(2)O hydrogen bonding structure.     

An extensible interface for QM/MM molecular dynamics simulations with AMBER

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface. © 2013 Wiley Periodicals, Inc.     

A molecular mechanics and ab initio prediction of the 1H chemical shifts of pinanes

Molecular mechanics calculations plus the application of a refined Karplus equation gave the conformations of 19 pinanes. These range from a Y‐shaped geometry in the apopinene and α‐pinene series to a pseudo chair conformation in β‐pinene, nopinone and verbanone, a flattened chair in pinocarvone and the pinocarveols and a distorted Y shape for iso‐verbanone. These structures were then used as input to predict the ¹H chemical shifts of these compounds by semi‐empirical (¹H‐NMR spectra (HSPEC)) and ab initio gauge‐invariant atomic orbital (GIAO) calculations, the latter at the B3LYP hybrid density functional theory level using 6‐31++G** basis set. The two methods gave generally good agreement with the 184 observed shifts with root mean square (RMS) errors 0.07 ppm (HSPEC) and 0.10 ppm (GIAO), but the GIAO calculations gave several significant (>0.25 ppm) errors. One was for the H₃ proton in apopinenone and other α,β unsaturated ketones; the others occurred for protons in close proximity to hydroxyl groups. To provide more information, smaller analogues of known geometry and chemical shifts were subject to the same analysis. In cyclopentenone, the Gaussian geometry gave good agreement with the observed shifts, but the MMFF94, MMX and MM3 geometries all gave errors for different protons. These results show clearly that the molecular geometries of the α,β unsaturated ketones are responsible for the errors. The errors for the alcohols were examined using ethanol as model and were shown to be due to the different possible conformations of the OH group. Similar GIAO calculations on substituted methanes gave good agreement for the methyl compounds but poor agreement for di and tri halosubstituted methanes. The aforementioned method of molecular mechanics plus GIAO calculations is shown to be a very useful tool for the investigation of molecular geometries and conformations. However, multihalogen compounds may require different basis sets for accurate calculations. Copyright © 2017 John Wiley & Sons, Ltd.