Calculations of the φ -ψ Conformational Contour Maps for N-Acetyl Alanine N'-Methyl Amide and of the Characteristic Ratios of Poly-L-alanine Using Various Molecular Mechanics Forcefields

Abstract

We generated φ -ψ conformational energy contour maps for the of N-acetyl alanine N'-methyl amide using the molecular mechanics forcefields AMBER, AMBER3, BI085, CFF91, CVFF, MM2, MM3, MM+, and SYBYL. With MM2, MM3, and MM+, we used a dielectric constant of ? = 1.5, the default effective value for these forcefields. With the other forcefields we used ? = 1 and 4, except with SYBYL, which, in Spartan 3.1, has no electrostatic term. All forcefields yielded the C^eq ₇ conformation as a low-energy minimum or the global minimum. Most of the forcefields also yielded a minimum-energy conformation in the C₅,α_R, and α_t. regions of the φ -ψ contour map. Fewer of the forcefields yielded a minimum in the C^ax ₇ region; however, adiabatic relaxation frequently lowered the relative energy of this region. Based on the appearance of the φ -ψ maps, the following pairs of forcefields were broadly similar (but not identical) to each other but dissimilar to the other pairs: AMBER3 and AMBER, BI085 and CHARMM, MM+ and MM2, SYBYL and ECEPP, and CFF91 and MM3. We used the data from the φ -ψ contour maps to compute the characteristic ratio of poly-L-alanine. Most of the computed values deviated significantly from the experimental value. Only the computed characteristic ratio of CFF91 without adiabatic relaxation at ? = 4 and MM3 without adiabatic relaxation at ? = 1.5 agreed with the experimental value.     

Calculation of protein backbone geometry from alpha-carbon coordinates based on peptide-group dipole alignment.

An algorithm is proposed for the conversion of a virtual-bond polypeptide chain (connected C alpha atoms) to an all-atom backbone, based on determining the most extensive hydrogen-bond network between the peptide groups of the backbone, while maintaining all of the backbone atoms in energetically feasible conformations. Hydrogen bonding is represented by aligning the peptide-group dipoles. These peptide groups are not contiguous in the amino acid sequence. The first dipoles to be aligned are those that are both sufficiently close in space to be arranged in approximately linear arrays termed dipole paths. The criteria used in the construction of dipole paths are: to assure good alignment of the greatest possible number of dipoles that are close in space; to optimize the electrostatic interactions between the dipoles that belong to different paths close in space; and to avoid locally unfavorable amino acid residue conformations. The equations for dipole alignment are solved separately for each path, and then the remaining single dipoles are aligned optimally with the electrostatic field from the dipoles that belong to the dipole-path network. A least-squares minimizer is used to keep the geometry of the alpha-carbon trace of the resulting backbone close to that of the input virtual-bond chain. This procedure is sufficient to convert the virtual-bond chain to a real chain; in applications to real systems, however, the final structure is obtained by minimizing the total ECEPP/2 (empirical conformational energy program for peptides) energy of the system, starting from the geometry resulting from the solution of the alignment equations. When applied to model alpha-helical and beta-sheet structures, the algorithm, followed by the ECEPP/2 energy minimization, resulted in an energy and backbone geometry characteristic of these alpha-helical and beta-sheet structures. Application to the alpha-carbon trace of the backbone of the crystallographic 5PTI structure of bovine pancreatic trypsin inhibitor, followed by ECEPP/2 energy minimization with C alpha-distance constraints, led to a structure with almost as low energy and root mean square deviation as the ECEPP/2 geometry analog of 5PTI, the best agreement between the crystal and reconstructed backbone being observed for the residues involved in the dipole-path network.     

Theoretical ab Initio Study of the Effects of Methylation on Structure and Stability of G:C Watson-Crick Base Pair

Abstract

Methylation of DNA occurs most readily at N(3), N(7), and O(6) of purine bases and N(3) and O(2) of pyrimidines. Methylated bases are continuously formed through endogenous and exogenous mechanisms. The results of a theoretical ab initio study on the methylation of G:C base pair components are reported. The geometries of the local minima were optimized without symmetry restrictions by the gradient procedure at DFT level of theory and were verified by energy second derivative calculations. The standard 6–31G(d) basis set was used. The single-point calculations have been performed at the MP2/6–31G(d,p), MP2/6–31₊₊G(d,p), and MP2/6–311₊₊G(2d,2p) levels of theory. The geometrical parameters, relative stability and counterpoise corrected interaction energies are reported. Also, using a variation-perturbation energy decomposition scheme we have found the vital contributions to the total interaction energy.     

Influence of local interactions on protein structure. I. Conformational energy studies of N-acetyl-N′-methylamides of pro-X and X-pro dipeptides

Conformational energy calculations using an Empirical Conformational Energy Program for Peptides (ECEPP) were carried out on the N-acetyl-N′-methylamides of Pro-X, where X = Ala, Asn, Asp, Gly, Leu, Phe, Ser, and Val, and of X-Pro, where X = Ala, Asn, Gly, and Pro. The conformational energy was minimized from starting conformations which included all combinations of low-energy single-residue minima and several standard bend structures. It was found that almost all resulting minima are combinations of low-energy single-residue minima, suggesting that intra residue interactions predominate in determining conformation. The calculations also indicate, however, that inter residue interactions can be important. In addition, librational entropy was found to influence the relative stabilities of some minima. Because of the existence of 10–100 low-energy minima for each dipeptide, the normalized statistical weight of an individual minimum rarely exceeds 0.3, suggesting that these dipeptides have considerable conformational flexibility and exist as statistical ensembles of low-energy structures. The propensity of each dipeptide to form bend conformations was calculated, and the results were compared with available experimental data. It was found that bends are favored in Pro-X dipeptides because ?_Pro is fixed by the pyrrolidine ring in a conformation which is frequently found in bends, but that bends are not favored in X-Pro dipeptides because interactions between the X residue and the pyrrolidine ring restrict the X residue to conformations which are not usually found in bends.     

Identification of novel small molecule non-peptidomimetic inhibitor for prolyl oligopeptidase through in silico and in vitro approaches

Abstract

Prolyl oligopeptidase (POP) enzyme has been studied for various disorders, viz. Schizophrenia, Alzheimer’s, Parkinson’s, Depression, Inflammation, etc., for three decades, but no drug has passed through the clinical trials, possibly because of indigent pharmacokinetics. This might have been a result of similar structures of drug candidates. This study aimed at identifying novel small non-peptidomimetic inhibitors for POP enzyme that could serve as a lead for developing newer drugs. Structure-based virtual screening of molecules of MolMall database was conducted on the POP enzyme (PDB ID 3DDU) to identify potential hits. The hits identified were subjected to computational pharmacokinetic screening followed by molecular mechanics/generalized Born and surface area studies to estimate the binding free energy of the docked complexes. After that, nine hits were selected and tested for POP inhibitory activity, among which one compound MM 4 was found to be most potent with EC₅₀ of 100 µM. Compound MM 4 was further subjected to molecular dynamics simulations to study the overall stability of the ligand–protein complex. The compound interacted strongly with catalytic amino acid Arg643 by forming salt and water bridges; it also interacted well with amino acids Phe173, Arg252 and Met235. This study provides a lead molecule for further development of POP inhibitors.

Communicated by Ramaswamy H. Sarma     

Theoretical Study of the Conformations of Pustulan [(1⇒6)-β-D)-Glucan]

Abstract

The total potential energy including nonbondedJuntorsional and hydrogen bond contributions has been computed for pustulan, a (1?6) linked β-D-glucan polysaccharide, as a function of rotational angles φ, ψ, and ω The (φ, ψ, ω)-space contains many local minima and at least three distinct deep minima. Two minima at (φ, ψ, ω)=(25°,190°,gg) and (φ, ψ, ω)=(65°,150°,gg) of almost equal energies have helical parameters (n=5.2, A=1.0Å) and (n=3.2, h= 1.5Å), respectively. A third minimum at (φ, ψ, ω)=(40°,70°gt) leads to an extended zig-zag structure (n=2.2, h=2.2Å). Energy maps obtained for gentiobiose, the disaccharide of pustulan, also reveal many local minima and the small energy differences among them indicate that gentiobiose is extremely flexible. Gentiodextrins, a family of cyclic molecules of (l?6)-β-D- glucose residues, were also studied. Conformations free from steric hindrance were found for cyclic molecules with three to six glucose residues.     

Hydration of cis and trans N-methylformamide as revealed by the use of 17O-NMR,molecular mechanics,and ab initio calculations

The solvation of cis and trans N-methylformamide (NMF) by water was investigated using a combination of ¹⁷O-nmr spectroscopy, classical molecular mechanics [MM2(77) and MM2(87)] force field, and ab initio 4-31G* gradient optimization calculations. In dilute aqueous solution, the ¹⁷O-nmr spectra of NMF indicate strong shielding by 66.9 and 66.1 ppm for the cis and trans amide oxygens, respectively, compared to those values obtained in dilute toluene solution. This demonstrates that both isomers are equally solvated by molecules of water, which are further hydrogen bonded to molecules of water of the bulk solvent. Molecular mechanics simulations were carried out for cis and trans NMF in a cluster of water molecules. Radial distribution functions show structural contacts by several water molecules at the amide CO and NH group, which are significantly more pronounced with MM2 (87) calculations. Ab initio 4-31G* gradient optimization calculations on the supermolecule trans NMF-(H₂O)₃ indicates the presence of more than two hydrogen-bond contacts at the carbonyl oxygen. This is in agreement with MM2 calculations and provides further evidence for multiple acceptor properties of the amide oxygen and an out of the amide plane arrangement of the bound molecules of water. Comparison of the integration data to the first radial distribution function (rdf) minima shows that the local solvation of the CO and NH groups is very similar for both cis and trans isomers. The intermolecular geometric parameters of the supermolecule trans NMA–(H₂O)₃ and the first rdf maxima resulting from MM2 (87) and MM2 (77) calculations are compared with distribution of water molecules around the CO and NH groups of peptides and proteins resulting from x-ray and neutron diffraction experiments. The rdfs involving the methyl group of NMF demonstrate the nonrandom distribution of solvent sites with first maxima in reasonable agreement with distribution of water molecules around the apolar side chain of amino acid residues in proteins. © 1995 John Wiley & Sons, Inc.     

The Asymmetry of (−)α‐Pinene as Revealed from its Raman Optical Activity Spectrum

An algorithm is employed to retrieve the differential bond polarizabilities of the C‐C bonds from the Raman optical activity (ROA) spectrum of (?)α‐pinene. (?)α‐pinene possesses two asymmetric centers (carbon atoms) and a local mirror symmetry. These differential bond polarizabilities show the characteristics of the asymmetry around the asymmetric carbons with respect to the mirror reflection. This analysis is accompanied along with the ROA mode signatures and the calculated β(G ')² and β(A)²which show the ROA coupling mechanisms involving the electric/magnetic dipoles and the electric dipole/quadrupole, respectively. Chirality 25:600–605, 2013. © 2013 Wiley Periodicals, Inc.     

Conformations of Cyclobut-A and Cyclobut-G: Structural Resemblance to Nucleosides and Incorporation into Double Helical DNA

Abstract

Conformational energy calculations have been carried out on two modified nucleosides Cyclobut-A and Cyclobut-G using the methods of molecular mechanics (MM2) obtainable in the computational software MacroModel. Conformations were generated as a function of the torsion angles equivalent to the glycosidic and backbone torsions in deoxyribonucleotides. The structural resemblance of the energy minimized models of the modified nucleosides to their corresponding deoxyribonucleosides has been investigated. It is found that conformations which lie within 3 kcal/mole of the global minimum do resemble the overall shape and volume of the B-DNA nucleoside. Following this result, two deoxypentanucleotides d(GCGCG) · d(CGCGC) and d(ATATA) · d(TATAT) were model built incorporating cyclobut-G and cyclobut-A, respectively. These were then energy refined using the molecular mechanics package AMBER. The resultant structures demonstrate that cyclobut-A and cyclobut-G can be easily accommodated in double helical polynucleotides with minimal overall distortions.     

The multiple-minima problem in the conformational analysis of polypeptides. III. An Electrostatically Driven Monte Carlo Method: Tests on enkephalin

The three-dimensional conformation of Met-enkephalin, corresponding to the lowest minimum of the empirical potential energy function ECEPP/2 (empirical conformational energy program for peptides), has been determined using a new algorithm, viz. the Electrostatically Driven Monte Carlo Method. This methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. These features are included in the algorithm that produces a Monte Carlo search in the conformational hyperspace of the polypeptide, using electrostatic predictions and a random sampling technique to locate low-energy conformations. In addition, we have incorporated an alternative mechanism that allows the structure to escape from some conformational regions representing metastable local energy minima and even from regions of the conformational space with great stability. In 33 test calculations on Met-enkephalin, starting from arbitrary or completely random conformations, the structure corresponding to the global energy minimum was found inall the cases analyzed, with a relatively small search of the conformational space. Some of these starting conformations wereright orleft-handed -helices, characterized by good electrostatic interactions involving their backbone peptide dipoles; nevertheless, the procedure was able to convert such locally stable structures to the global-minimum conformation.On leave from the National University of San Luis, Faculty of Sciences and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Instituto de Matemática Aplicada, San Luis, Ejército de los Andes 950, 5700 San Luis, Argentina.     

Absolute binding free energy calculations: On the accuracy of computational scoring of protein–ligand interactions

Calculating the absolute binding free energies is a challenging task. Reliable estimates of binding free energies should provide a guide for rational drug design. It should also provide us with deeper understanding of the correlation between protein structure and its function. Further applications may include identifying novel molecular scaffolds and optimizing lead compounds in computer‐aided drug design. Available options to evaluate the absolute binding free energies range from the rigorous but expensive free energy perturbation to the microscopic linear response approximation (LRA/β version) and related approaches including the linear interaction energy (LIE) to the more approximated and considerably faster scaled protein dipoles Langevin dipoles (PDLD/S‐LRA version) as well as the less rigorous molecular mechanics Poisson–Boltzmann/surface area (MM/PBSA) and generalized born/surface area (MM/GBSA) to the less accurate scoring functions. There is a need for an assessment of the performance of different approaches in terms of computer time and reliability. We present a comparative study of the LRA/β, the LIE, the PDLD/S‐LRA/β, and the more widely used MM/PBSA and assess their abilities to estimate the absolute binding energies. The LRA and LIE methods perform reasonably well but require specialized parameterization for the nonelectrostatic term. The PDLD/S‐LRA/β performs effectively without the need of reparameterization. Our assessment of the MM/PBSA is less optimistic. This approach appears to provide erroneous estimates of the absolute binding energies because of its incorrect entropies and the problematic treatment of electrostatic energies. Overall, the PDLD/S‐LRA/β appears to offer an appealing option for the final stages of massive screening approaches. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Average local ionization energy: A review

The average local ionization energy [`I] ( r ) \overline {\hbox{I}} \left( {\mathbf{r}} \right) is the energy necessary to remove an electron from the point r in the space of a system. Its lowest values reveal the locations of the least tightly-held electrons, and thus the favored sites for reaction with electrophiles or radicals. In this paper, we review the definition of [`I] ( r ) \overline {\hbox{I}} \left( {\mathbf{r}} \right) and some of its key properties. Apart from its relevance to reactive behavior, [`I] ( r ) \overline {\hbox{I}} \left( {\mathbf{r}} \right) has an important role in several fundamental areas, including atomic shell structure, electronegativity and local polarizability and hardness. All of these aspects of [`I] ( r ) \overline {\hbox{I}} \left( {\mathbf{r}} \right) are discussed.     

Geospatial analysis of population-based incidence of multiple myeloma in the United States

BackgroundWe investigated the spatial patterns of multiple myeloma (MM) incidence in the United States (US) between 2013 and 2017 to improve understanding of potential environmental risk factors for MM.MethodsWe analyzed the average county-level age-adjusted incidence rates (“ASR”) of MM between 2013 and 2017 in 50 states and the District of Columbia using the U.S. Cancer Statistics Public Use Databases. We firstly divided the ASR into quintiles and described spatial patterns using a choropleth map. To identify global and local clusters of the ASR, we performed the Spatial Autocorrelation (Global Moran’s I) analysis and the Anselin’s Local Indicator of Spatial Autocorrelation (LISA) analysis. We compared the means of selected demographic and socioeconomic factors between the clusters and counties of the whole US using Welch one-sided t-test.ResultsWe identified distinct spatial dichotomy of the ASR across counties. High ASR were observed in counties in the Southeast of the US as well as the Capital District (metropolitan areas surrounding Albany) and New York City in the state of New York, while low ASR were observed in counties in the Southwest and West of the US. The ASR showed a significant positive spatial autocorrelation. We identified two major high-high local clusters of the ASR in Georgia and Southern Carolina and five major low-low local clusters of the ASR in Alabama, Arizona, New Hampshire, Ohio, Oregon, and Tennessee. The racial population distribution may partly explain the spatial distribution of MM incidence in the US.ConclusionFindings from this study showed distinct spatial distribution of MM in the US and two high-high and five low-low local clusters. The non-random distribution of MM suggests that environmental exposures in certain regions may be important for the risk of MM.     

The electrostatically driven Monte Carlo method: application to conformational analysis of decaglycine

The Electrostatically Driven Monte Carlo (EDMC) method was applied in a study of a decamer of glycine whose conformational behavior is described by the Empirical Conformational Energy Program for Peptides (ECEPP/2) potential energy model. When free neutral end groups were used, it was found that conformations that were not alpha-helical had significantly lower potential energies than fully alpha-helical ones. However, when the N- and C-termini were blocked by acetyl and methyl amide groups, respectively, the number of unsatisfied hydrogen-bond donors and acceptors at the helix termini was diminished from 8 to 6; in this case, the possibility of forming two additional alpha-helical hydrogen bonds was an important enough factor in making the alpha-helical conformation the one with the lowest energy. The EDMC method was used as a global energy optimizer since it does not often become trapped in high-energy local minima.     

Conformational-energy calculations for oligosaccharides: a comparison of methods and a strategy of calculation

A theoretical conformational analysis of dimethoxymethane, 2-methoxytetrahydropyran, cellobiose, and maltose has been performed. The validity of several commonly used classical approaches to conformational energy, assuming non-bonded interactions, torsional terms, and the exo-anomeric contribution, and the MM2CARB method (a modified version of the MM2 force-field program using the Jeffrey-Taylor parameters) was tested against available experimental data or previous quantum-chemical calculations. The MM2CARB method correctly reproduces the energies and the variations in bond lengths and bond angles for conformers of dimethoxymethane and 2-methoxytetrahydropyran. Prediction of the observed conformers with simple potential functions appears to be less satisfactory. In particular, calculations that take into account non-bonded interactions and the exo-anomeric contribution based on dimethoxymethane give predicted energy differences that are 2–3 times higher than the experimental values. The general shapes of the (Φ, Ψ) potential-energy surfaces for cellobiose and maltose provided by potential-function calculations suggest the presence of several minima whose energies depend, to a great extent, on the choice of molecular geometry. The MM2CARB-calculated structures of seven cellobiose and five maltose conformers demonstrate clearly the variation of disaccharide geometry with change of conformation around the glycosidic linkage. The relative energies calculated by simple methods differ from MM2CARB energies and indicate that the simple potential-functions methods give only a qualitative estimate of oligosaccharide conformers. Based on these results, we propose a general strategy and two different approaches for the investigation of conformational properties of oligosaccharides.     

AM1 Study of N-2-Acetylaminofluorene bonded to Deoxyguanosine at the Minor Adduct Site

We have computed the total energy as a function of six important torsion angles of the carcinogen N-2-acetylaminofluorene (AAF) bonded to thenitrogen N2 of deoxyguanosine using the semiempirical quantum mechanical method AM1. One global minimum and one local minimum are found separated by a modest barrier. We have computed the normal-mode frequencies of the relevant torsional motions and have determined the rate of conversion betweenthe two minima.     

Discovery of potential sclerostin inhibitors from plants with loop2 region of sclerostin inhibition by interacting with residues outside Pro-Asn-Ala-Ile-Gly motif

Abstract

Sclerostin, an antagonist of the Wnt/β-catenin signaling pathway, was discovered as a potential therapeutic target for stimulating bone formation in osteoporosis. In this study, molecular docking was employed to predict the binding of 29 herbal compounds, which were reported as bone formation stimulators, to the loop2 region of sclerostin. Then, the 50 ns molecular dynamics (MD) simulation of the complexes between sclerostin and the top 10 hits obtained from molecular docking were carried out. Root mean square deviations (RMSDs) analysis of MD trajectories pointed out that all ligands-complexes remain stable throughout the duration of MD simulations. In addition, the molecular mechanics/generalized born surface area (MM/GBSA) binding free energy and energy decomposition analyses were determined. The results here suggested that baicalin is the most promising inhibitor of sclerostin. Interestingly, baicalin binds to sclerostin via the hydrophobic interaction with the amino acid residues on loop2 region but outside the Pro-Asn-Ala-Ile-Gly (PNAIG) motif, particularly the Arg-Gly-Lys-Trp-Trp-Arg (RGKWWR) motif. This finding could be a novel strategy for developing new sclerostin inhibitors in the future.

Communicated by Ramaswamy H. Sarma