Approaches to charge calculations in molecular mechanics

Alternative methods of estimating atomic charges in haloalkanes are presented, derived from quantum mechanical and classical treatments. A scheme based on a breakdown of the transmission of charge by polar atoms into one-bond, two-bond, and three-bond additive contributions is given, in which the one-bond effect is proportional to the difference in the electronegativities of the bonded atoms, and the two- and three-bond effects functions of the atomic electronegativity and polarizability. Suitable developments of the basic scheme, including an iterative self-consistent process, give calculated dipole moments for a variety of haloalkanes in good agreement with the observed values. The atomic charges obtained by this scheme are compared with other estimates of these charges. They are similar to those derived from a simple LCAO –MO scheme but differ from those obtained by population analysis of more refined quantum mechanical calculations.     

1,4-Interactions in molecular mechanics calculations of Ethers

Van der Waals and electrostatic interactions are found to be insufficient for the calculation of conformational energies of ethers by molecular mechanics. Low order torsional potential functions must be added for the potential about C-O bonds. A onefold term necessary for the CCOC-fragment is interpreted to be a substitute for gauche interactions present in CCCC-, but missing in CCOC-fragments. For the COCO fragment the anomeric effect must be included explicitly as another torsional energy term, but no such term is required to stabilize the gauche conformation for OCCO. With the resulting ether force field the geometries and energies of model compounds, many of them 1,3-dioxanes, are calculated with good accuracy.     

Comparison of inter- and intramolecular cyclodextrin complexes

Abstract

We present the first comparative steady-state and time-resolved fluorescence studies of inter- and intramolecular cyclodextrin complexes. Specifically, we report equilibrium and kinetic results for dansyl-glycine complexed with β-cyclodextrin (intermolecular) and the dansyl-glycine-β-cyclodextrin adduct (intramolecular). The fluorescence intensity decay profile for the intermolecular system is best described by a discrete triple exponential decay law. This is consistent with stepwise 1:1 and 2:1 (β-cyclodextrin:guest) inclusion complexation. Equilibrium constants are in line with previous results on similar species. In contrast, we found that the intramolecular case was described by a doubly exponential decay law—consistent with a single intramolecular inclusion complex. Displacement experiments, with borneol, confirm the simplicity of the intramolecular complex. In all cases, continuous distribution models failed to fit the experimental data.     

Forces in molecular recognition: Comparison of experimental data and molecular mechanics calculations

Summary NMR studies of the rotation barrier of the disaccharide of the glycopeptide antibiotic vancomycin have been used to test the performance of computer simulation techniques using molecular mechanics. In the absence of any solvated water, no correlation could be found between experiment and calculation. By introducing solvent water molecules into the binding region of the antibiotic, the NMR results could be simulated both qualitatively and quantitatively within experimental error without using massive computational resources.     

Prediction of polymer miscibility from molecular mechanics calculations

A new computational method is presented for the rapid estimation of polymer miscibility. The algorithm (coined FLEXIBLEND) uses molecular mechanics calculations on a pair of polymer segments and takes into account the effects of local chain flexibility to estimate heats of mixing. This paper shows miscibility predictions in agreement with experiment for blends of poly(ethyleneoxide) (PEO) with isotactic poly(propylene) (PP) as an immiscible system and of PEO with poly(acrylic acid) (PAA) as a miscible system.     

Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By separating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described.     

The inclusion of electrostatic hydration energies in molecular mechanics calculations

Summary The problem of including solvent effects in molecular mechanics calculations is discussed. It is argued that the neglect of charge-solvent (solvation) interactions can introduce significant errors. The finite difference Poisson-Boltzmann (FDPB) method for calculating electrostatic interactions is summarized and is used as a basis for introducing a new pairwise energy term which accounts for charge-solvent interactions. This term acts between all pairs of atoms usually considered in molecular mechanics calculations and can be easily incorporated into existing force fields. As an example, a parameterization is developed for the CHARMm force field and the results compared to the predictions of the FDPB method. An approach to the realistic incorporation of solvent screening into force fields is also outlined.     

MoBioTools: A toolkit to setup quantum mechanics/molecular mechanics calculations

We present a toolkit that allows for the preparation of QM/MM input files from a conformational ensemble of molecular geometries. The package is currently compatible with trajectory and topology files in Amber, CHARMM, GROMACS and NAMD formats, and has the possibility to generate QM/MM input files for Gaussian (09 and 16), Orca (≥4.0), NWChem and (Open)Molcas. The toolkit can be used in command line, so that no programming experience is required, although it presents some features that can also be employed as a python application programming interface. We apply the toolkit in four situations in which different electronic-structure properties of organic molecules in the presence of a solvent or a complex biological environment are computed: the reduction potential of the nucleobases in acetonitrile, an energy decomposition analysis of tyrosine interacting with water, the absorption spectrum of an azobenzene derivative integrated into a voltage-gated ion channel, and the absorption and emission spectra of the luciferine/luciferase complex. These examples show that the toolkit can be employed in a manifold of situations for both the electronic ground state and electronically excited states. It also allows for the automatic correction of the active space in the case of CASSCF calculations on an ensemble of geometries, as it is shown for the azobenzene derivative photoswitch case.     

Structural forms of green fluorescent protein by quantum mechanics/molecular mechanics calculations

The molecular modeling of structural forms of the green fluorescent protein (GFP) with the Ser65Thr single-site mutation was performed by the quantum mechanics/molecular mechanics (QM/MM) method. Two model systems were constructed based on the crystallographic structure from the Protein Data Bank (PDB entry code 1EMA.) The model systems differ in the initial protonation state of the side chain of the amino acid residue Glu222 near the chromophore. The atomic coordinates of the protein macromolecule corresponding to the equilibrium geometric configurations were determined by total energy minimization using the QM/MM method within the density functional theory approximation PBE0/cc-pVDZ for the quantum subsystem that consists of the chromophore, a water molecule, and the side chains of Arg96, Glu222, and Ser205, and with the parameters of the AMBER force field for the molecular mechanics subsystem. In the analysis of the results, particular attention was given to the hydrogen bond redistribution in the chromophore-containing region of the protein caused by a change in the protonation state of the chromophore. The results obtained from the model containing the initially protonated side chain of Glu222 suggest a new interpretation of the photophysical processes in the green fluorescent protein.     

B-spline method for energy minimization in grid-based molecular mechanics calculations

A method is described for molecular mechanics calculations based on a cubic B-spline approximation of the potential energy. This method is useful when parts of the system are allowed to remain fixed in position so that a potential energy grid can be precalculated and used to approximate the interaction energy between parts of a molecule or between molecules. We adapted and modified the conventional B-spline method to provide an approximation of the Empirical Conformational Energy Program for Peptides (ECEPP) potential energy function. The advantage of the B-spline method over simpler approximations is that the resulting B-spline function is C2 continuous, which allows minimization of the potential energy by any local minimization algorithm. The standard B-spline method provides a good approximation of the electrostatic energy; but in order to reproduce the Lennard–Jones and hydrogen-bonding functional forms accurately, it was necessary to modify the standard B-spline method. This modification of the B-spline method can also be used to improve the accuracy of trilinear interpolation for simulations that do not require continuous derivatives. As an example, we apply the B-spline method to rigid-body docking energy calculations using the ECEPP potential energy function. Energies are calculated for the complex of Phe-Pro-Arg with thrombin. For this system, we compare the performance of the B-spline method to that of the standard pairwise summation in terms of speed, accuracy, and overhead costs for a variety of grid spacings. In our rigid-body docking calculations, the B-spline method provided an accurate approximation of the total energy of the system, and it resulted in an 180-fold reduction in the time required for a single energy and gradient calculation for this system. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 71–85, 1998     

Charge calculations in molecular mechanics. Part 8 Partial atomic charges from classical calculations

Summary The CHARGE2 programme, which involves the classical calculation of both the inductive and resonance contributions to the partial atomic charges in molecules is described, and the charges and electrostatic potentials obtained presented for some illustrative examples.In substituted methanes (CH₃X, CF₃X, CCl₃X) the effects of varying the electronegativity of the substituents and the - and -substituent contributions are clearly illustrated for a variety of substituent groups X.The problems involved in the inclusion of silicon into this scheme are detailed, together with the methods of overcoming them. The partial atomic charges ( and contributions) and electrostatic potentials for some silicon oxygen compounds are presented and discussed.The partial atomic charges from CHARGE2 for all the natural amino acids as their N-acetyl, N-methyl-amides are given and compared with those obtained from the AMBER and ECEPP/2 force fields. Considerable differences in these figures are observed, with the AMBER charges consistently much larger than those from the other two methods.The CHARGE2 partial atomic charges and electrostatic potentials for the four common nucleic acids, adenine, cytosine, guanine and thymine, are given and compared with those derived from other calculations. Again there is general similarity but also there are considerable differences, with those from the AMBER force field somewhat larger than the other methods.For previous parts in this series, see Refs. 1-7.     

On a semiclassical interpretation of inter- and intramolecular interactions

The semiclassical models considered here are composed by charge distributions coming from ab initio quantum-mechanical calculations on actual molecular systems. These charge distributions interact with one another according to the laws of classical electrostatics. This article describes some results of a systematic examination of the performances of this model in a variety of cases, with the aim of putting in evidence the usefulness and the limits of this inherently approximate representation of chemical interactions. Intermolecular interactions are examined first; the test cases are interactions of neutral molecules with H⁺, Li⁺, and C1^?, and the formation of H-bonded complexes. Attention is paid mainly to the energetics of the processes; each interacting molecule is considered as a unique entity and classical molecular reactivity indexes (electrostatic potential V, polarization term P) are introduced to compute the interaction energy, to interpret the details of the interaction process, and then to elaborate on less expensive computational procedures. Intramolecular interactions are considered. Attention is paid to the question of defining chemical groups starting from SCF molecular wavefunctions. The transferability and conservation degree of groups derived from localized orbitals of actual molecules is examined in detail, taking as tests their ability to reproduce charge distribution, one-electron observables, and energy. The effect of classical fields on these groups is then examined, taking into consideration external fields originated either by a point charge or by a solvent, and internal fields deriving from substitution of chemical groups. The intergroup analysis is then extended to the case of bimolecular reaction acts by considering the whole system as a supermolecule. Approximate computational procedures able to reproduce the main features of these interactions are proposed and tested. All through the article the performances of the classical models are compared with ab initio SCF calculations (mainly of low or intermediate quality).     

Charge calculations in molecular mechanics. III: Amino acids and peptides

Atomic charges obtained with a previously published charge scheme are given for amino acids and peptides. In order to do this, a method of handling charged species with the basic scheme^2,3 has been developed. The charges obtained for alkylammonium ions and carboxylate ions with the scheme are presented and compared with CNDO and ab initio values. The calculated experimental dipole moments of the zwitterionic forms of glycine, alanine and β-alanine are then discussed. Finally, the atomic charges obtained for the naturally occurring amino acids are given, both in the form of the N-acetyl-N′-methyl amino acid amides, used as models for the amino acid residues in enzymes, and as the free zwitterionic amino acids. The charges obtained show a good correlation with n. m. r. chemical shifts of both carbon and hydrogen atoms.     

Mechanisms of inter- and intramolecular communication in GPCRs and G proteins

This study represents the first attempt to couple, by computational experiments, the mechanisms of intramolecular and intermolecular communication concerning a guanidine nucleotide exchange factor (GEF), the thromboxane A2 receptor (TXA2R), and the cognate G protein (Gq) in its heterotrimeric GDP-bound state. Two-way pathways mediate the communication between the receptor-G protein interface and both the agonist binding site of the receptor and the nucleotide binding site of the G protein. The increase in solvent accessibility in the neighborhoods of the highly conserved E/DRY receptor motif, in response to agonist binding, is instrumental in favoring the penetration of the C-terminus of Gqalpha in between the cytosolic ends of H3, H5, and H6. The arginine of the E/DRY motif is predicted to be an important mediator of the intramolecular and intermolecular communication involving the TXA2R. The receptor-G protein interface is predicted to involve multiple regions from the receptor and the G protein alpha-subunit. However, receptor contacts with the C-terminus of the alpha5-helix seem to be the major players in the receptor-catalyzed motion of the alpha-helical domain with respect to the Ras-like domain and in the formation of a nucleotide exit route in between the alphaF-helix and beta6/alpha5 loop of Gqalpha. The inferences from this study are of wide interest, as they are expected to apply to the whole rhodopsin family, given also the considerable G protein promiscuity.     

Carbocycles via enantioselective inter- and intramolecular iridium-catalysed allylic alkylations

Carbocycles with > 90% ee were prepared via Ir-catalysed asymmetric allylic alkylation/ring closing metathesis sequences or enantioselective Ir-catalysed intramolecular allylic alkylations.     

Using molecular dynamics and quantum mechanics calculations to model fluorescence observables

We provide a critical examination of two different methods for generating a donor-acceptor electronic coupling trajectory from a molecular dynamics (MD) trajectory and three methods for sampling that coupling trajectory, allowing the modeling of experimental observables directly from the MD simulation. In the first coupling method we perform a single quantum-mechanical (QM) calculation to characterize the excited state behavior, specifically the transition dipole moment, of the fluorescent probe, which is then mapped onto the configuration space sampled by MD. We then utilize these transition dipoles within the ideal dipole approximation (IDA) to determine the electronic coupling between the probes that mediates the transfer of energy. In the second method we perform a QM calculation on each snapshot and use the complete transition densities to calculate the electronic coupling without need for the IDA. The resulting coupling trajectories are then sampled using three methods ranging from an independent sampling of each trajectory point (the independent snapshot method) to a Markov chain treatment that accounts for the dynamics of the coupling in determining effective rates. The results show that the IDA significantly overestimates the energy transfer rate (by a factor of 2.6) during the portions of the trajectory in which the probes are close to each other. Comparison of the sampling methods shows that the Markov chain approach yields more realistic observables at both high and low FRET efficiencies. Differences between the three sampling methods are discussed in terms of the different mechanisms for averaging over structural dynamics in the system. Convergence of the Markov chain method is carefully examined. Together, the methods for estimating coupling and for sampling the coupling provide a mechanism for directly connecting the structural dynamics modeled by MD with fluorescence observables determined through FRET experiments.     

A study on the anisole-water complex by molecular beam-electronic spectroscopy and molecular mechanics calculations

An experimental and theoretical study is made on the anisole-water complex. It is the first van der Waals complex studied by high resolution electronic spectroscopy in which the water is seen acting as an acid. Vibronically and rotationally resolved electronic spectroscopy experiments and molecular mechanics calculations are used to elucidate the structure of the complex in the ground and first electronic excited state. Some internal dynamics in the system is revealed by high resolution spectroscopy.