Feature extraction using molecular planes for fuzzy relational clustering of a flexible dopamine reuptake inhibitor

Six rigid-body parameters (Shift, Slide, Rise, Tilt, Roll, Twist) are commonly used to describe the relative displacement and orientation of successive base pairs in a nucleic acid structure. The present work adapts this approach to describe the relative displacement and orientation of any two planes in an arbitrary molecule-specifically, planes which contain important pharmacophore elements. Relevant code from the 3DNA software package (Nucleic Acids Res. 2003, 31, 5108-5121) was generalized to treat molecular fragments other than DNA bases as input for the calculation of the corresponding rigid-body (or "planes") parameters. These parameters were used to construct feature vectors for a fuzzy relational clustering study of over 700 conformations of a flexible analogue of the dopamine reuptake inhibitor, GBR 12909. Several cluster validity measures were used to determine the optimal number of clusters. Translational (Shift, Slide, Rise) rather than rotational (Tilt, Roll, Twist) features dominate clustering based on planes that are relatively far apart, whereas both types of features are important to clustering when the pair of planes are close by. This approach was able to classify the data set of molecular conformations into groups and to identify representative conformers for use as template conformers in future Comparative Molecular Field Analysis studies of GBR 12909 analogues. The advantage of using the planes parameters, rather than the combination of atomic coordinates and angles between molecular planes used in our previous fuzzy relational clustering of the same data set (J. Chem. Inf. Model. 2005, 45, 610-623), is that the present clustering results are independent of molecular superposition and the technique is able to identify clusters in the molecule considered as a whole. This approach is easily generalizable to any two planes in any molecule.     

Hierarchical clustering analysis of flexible GBR 12909 dialkyl piperazine and piperidine analogs

Pharmacophore modeling of large, drug-like molecules, such as the dopamine reuptake inhibitor GBR 12909, is complicated by their flexibility. A comprehensive hierarchical clustering study of two GBR 12909 analogs was performed to identify representative conformers for input to three-dimensional quantitative structure–activity relationship studies of closely-related analogs. Two data sets of more than 700 conformers each produced by random search conformational analysis of a piperazine and a piperidine GBR 12909 analog were studied. Several clustering studies were carried out based on different feature sets that include the important pharmacophore elements. The distance maps, the plot of the effective number of clusters versus actual number of clusters, and the novel derived clustering statistic, percentage change in the effective number of clusters, were shown to be useful in determining the appropriate clustering level.Six clusters were chosen for each analog, each representing a different region of the torsional angle space that determines the relative orientation of the pharmacophore elements. Conformers of each cluster that are representative of these regions were identified and compared for each analog. This study illustrates the utility of using hierarchical clustering for the classification of conformers of highly flexible molecules in terms of the three-dimensional spatial orientation of key pharmacophore elements.     

Novel feature extraction technique for fuzzy relational clustering of a flexible dopamine reuptake inhibitor

This paper describes a novel clustering methodology for classifying over 700 conformations of a flexible analogue of GBR 12909, a dopamine reuptake inhibitor that has completed phase I clinical trials as a treatment for cocaine abuse. The major aspect of the clustering methodology includes an efficient data-conditioning scheme where a systematic feature extraction procedure based on the structural properties of the molecule was used to reduce the associated feature space. This allowed region-specific clustering that focused on individual pharmacophore elements of the molecule. For clustering of the reduced feature set, the fuzzy clustering partitional method was utilized. Due to the relational nature of the feature data, fuzzy relational clustering was employed, and it successfully detected natural groups defined by rotational minima around N(sp(3))-C(sp(3)), O(sp(3))-C(sp(3)), and C(sp(3))-C(sp(2)) bonds. The proposed clustering methodology also employed several cluster validity measures, which corroborated the partitions produced by the clustering technique and agreed with the results of hierarchical clustering using the XCluster program. Representative structures which exhibited a reasonable spread of energies and showed good spatial coverage of the conformational space were identified for use as putative bioactive conformations in a future Comparative Molecular Field Analysis of GBR 12909 analogues. The clustering methodology developed here is capable of handling other computational chemistry problems, and the feature extraction technique can be easily generalized to other molecules.     

A fast and efficient method to generate biologically relevant conformations

Summary Mutual binding between a ligand of low molecular weight and its macromolecular receptor demands structural complementarity of both species at the recognition site. To predict binding properties of new molecules before synthesis, information about possible conformations of drug molecules at the active site is required, especially if the 3D structure of the receptor is not known. The statistical analysis of small-molecule crystal data allows one to elucidate conformational preferences of molecular fragments and accordingly to compile libraries of putative ligand conformations. A comparison of geometries adopted by corresponding fragments in ligands bound to proteins shows similar distributions in conformation space. We have developed an automatic procedure that generates different conformers of a given ligand. The entire molecule is decomposed into its individual ring and open-chain torsional fragments, each used in a variety of favorable conformations. The latter ones are produced according to the library information about conformational preferences. During this building process, an extensive energy ranking is applied. Conformers ranked as energetically favorable are subjected to an optimization in torsion angle space. During minimization, unfavorable van der Waals interactions are removed while keeping the open-chain torsion angles as close as possible to the experimentally most frequently observed values. In order to assess how well the generated conformers map conformation space, a comparison with experimental data has been performed. This comparison gives some confidence in the efficiency and completeness of this approach. For some ligands that had been structurally characterized by protein crystallography, the program was used to generate sets of some 10 to 100 conformers. Among these, geometries are found that fall convincingly close to the conformations actually adopted by these ligands at the binding site.     

Conformational variety for the ansa chain of rifamycins: Comparison of observed crystal structures and molecular dynamics simulations

The antibiotic activity (via inhibition of DNA-dependent RNA polymerase, DDRP) of rifamycins has been correlated to the conformation of the ansa chain, which can be described by means of 17 torsion angles defined along the ansa backbone. It has been shown that favourable or unfavourable conformations of the ansa chain in rifamycin crystals are generally diagnostic of activity or inactivity against isolated DDRP. The principles of structure correlation suggest that the torsional variety observed in rifamycin crystals should mimic the dynamic flexibility of the ansa chain in solution. Twenty-six crystal structures of rifamycins are grouped into two classes (active and non-active). For each class the variance of the 17 ansa backbone torsion angles is analysed. Active compounds show a well-defined common pattern, while non-active molecules are more scattered, mainly due to steric constraints forcing the molecules into unfavourable conformations. The experimental distributions of torsion angles are compared to the torsional freedom of the ansa chain simulated by molecular dynamics calculations performed at different temperatures and conditions on rifamycin S and rifamycin O, which represent a typical active and a typical sterically constrained molecule, respectively. It is shown that the torsional variety found in the crystalline state samples the dynamic behaviour of the ansa chain for active compounds. The methods of circular statistics are illustrated to describe torsion angle distributions.     

A new method for fast and accurate derivation of molecular conformations

During molecular simulations, three-dimensional conformations of biomolecules are calculated from the values of their bond angles, bond lengths, and torsional angles. In this paper we study how to efficiently derive three-dimensional molecular conformations from the values of torsional angles. This case is of broad interest as torsional angles greatly affect molecular shape and are always taken into account during simulations. We first review two widely used methods for deriving molecular conformations, the simple rotations scheme and the Denavit-Hartenberg local frames method. We discuss their disadvantages which include extensive bookkeeping, accumulation of numerical errors, and redundancies in the local frames used. Then we introduce a new, fast, and accurate method called the atomgroup local frames method. This new method not only eliminates the disadvantages of earlier approaches but also provides lazy evaluation of atom positions and reduces the computational cost. Our method is especially useful in applications where many conformations are generated or updated such as in energy minimization and conformational search.     

Determination of the major solution conformation of tyrocidine A,using molecular mechanics energy minimization and NMR-derived distance and torsion angle constraints

Molecular mechanics energy calculations coupled with nuclear magnetic resonance-determined distance and torsion angle constraints have been used to determine the three-dimensional structure of tyrocidine A, a cyclic decapeptide which exists largely as a single conformation in solution. Two open-chain polyalanine models were used to represent separate halves of the peptide backbone and a combinatorial method of searching conformation space used to generate candidate structures consistent with experimental distance constraints. These structures were energy-minimized using the AMBER molecular mechanics forcefield and the resulting conformations classified by factor analysis of their Cartesian coordinates. Representative low-energy conformers of the two halves of the backbone were fused together and two candidate conformations of the completed backbone refined by further minimization using both distance and torsional constraints. Side chains were then added as their experimentally preferred rotamers and the whole molecule minimized without constraints to give the final model structure. This shows type II' and III ß turns at residues 4–5 and 9–10, respectively, coupled by twisted antiparallel strands which show hydrogen bonds between all four pairs of opposing peptide groups. The backbone conformation of residues 2–6 closely resembles that found in the crystal structure of gramicidin S.     

Exhaustive Conformational Search for Sialyl Cation Reveals Possibility of Remote Participation of Acyl Groups

Finding convenient ways for the stereoselective α-sialylation is important due to the high practical significance of α-sialic acid-containing glycans and neoglycoconjugates. It was proposed that sialylation stereoselectivity is determined by the structure of the sialyl cation (also known in biochemistry as “sialosyl cation”), a supposed intermediate in this reaction. Here we design a new approach for studying the conformational space of highly flexible sialyl cation and find 1625 unique conformers including those stabilized by covalent remote participation (also known as long-range participation) of 4-O-acetyl (4-OAc), 5-N-trifluoroacetyl (5-NTFA), as well as 7,8,9-OAc from both α and β sides. The most energetically stable sialyl cation conformers are featured by 4-OAc participation, closely followed by 5-NTFA- and 7-OAc-stabilized conformers; unstabilized sialyl cation conformers are ∼10 kcal mol⁻¹ less stable than the 4-OAc-stabilized ones. Analysis of all the obtained conformers by means of substituents positions, side chain conformations and ring puckering led us to a new “eight-conformer hypothesis” which describes interconversions among the most important sialyl cation conformers and predicts that stronger remote participation of acyl groups favors β-anomers. Thus, selective synthesis of the desired α-sialosides requires minimization of acyl groups participation.     

A general treatment of the configuration statistics of polysaccharides.

A treatment of the configurational statistics of polysaccharides is given in the isomeric state approximation. All classes of linear polysaccharides of specifiec chemical sequence are treated simultaneously. Chain tortuosity arising from torsional motions about the chemical bonds of the glycosidic linkages is recognized explicitly as is the possibility for conformational isomerism of the sugar residues. Valence angles and lengths are taken to be fixed at the equilibrium values, and pyranose residues in their chair conformations are treated as inflexible constituents of the skeletal structure. Pyranose and furanose forms capable of pseudorotation may be incorporated as rigid skeletal entities as well, provided suitable attention is given to the selection and interpretation of the conformational isomeric states included. Separation of the configuration energy into independent contributions is shown to be impossible in general. Methods are described for assessing the influence of neighbor interactions on the populations of the several conformers of the sugar residues. The relative conformational free energy of the flexible and chair form conformers of pyranose sugars is discussed, and appropriate measures of polysaccharide chain flexibility and stiffness are suggested.     

Electronic structure and conformational properties of the amide linkage Part 5. Internal rotation and inversion in 1-formylaziridine

Internal rotation and nitrogen inversion in 1-formylaziridine (1) have been investigated by quantum mechanical (ab initio and MNDO) calculations, especially with respect to the variation of the geometry of the aziridine ring. While conformational stability is mainly determined by the n(N)/π(CO) interaction, the bond lengths within the ring are affected by the amount of interaction between the π(CO) orbital and the Walsh orbital ω_A. To separate the two types of interaction, calculations were also performed on formylcyclopropane (9). The torsional potential of 1 has a minimum close to the perpendicular conformation 1b. The two bisected conformations, 1a and 1c, are transition states for internal rotation. For nitrogen inversion, a barrier of 1.44 kcal mol⁻¹ (ab initio) was calculated. Calculations on 1-cyanoaziridine (7) gave inversion barriers of 5.81 (ab initio) and 12.31 kcal mol⁻¹ (MNDO). Probably due to methodical reasons the ab initio values seem to be too low, as calculations with different basis sets for aziridine indicate.     

Konformative Beweglichkeit Flexibler Ringsysteme–XII Modellrechnungen zur Ringinversion bei Methylsubstituierten Cyclohexanen

For the interpretation of experimental data on the activation energy and free activation enthalpy for the inversion of cyclohexane and its di-, tetra- and hexa-methyl derivatives, model calculations were made to determine the ‘relative’ energies of the ground, intermediate and transition states of the molecules. For this purpose Hendrickson's model was extended so that with internal molecular variables (bond lengths, valence and torsional angles) the topography and the ‘relative’ energy of every possible unsymmetrical conformation could be included. To obtain optimal agreement between the calculated values and the experimental results a total of 17 different combinations of potential functions for deformation of valence angles, torsional angles and H? H interactions were used. By application of the extended calculating procedure it was found that for cyclohexane the half-chair conformation is not, as until now assumed, the only transition conformation in chair inversion, but that there are numerous other unsymmetrical transition conformations with similar energies. The calculations for methyl cyclohexanes showed that for molecules with synaxial arrangement of methyl groups the relative energy of the chair form is considerably increased. The chair form is however still the most stable, even in the case of 1,1,3,3,5,5-hexamethylcyclohexane. The most favourable twist conformations are about 2.6 to 6.5 kcal/mole energy richer. Calculation of activation energies showed that, with synaxial arrangement of two or more methyl groups, the relative energy of the transition conformation is less markedly increased than is that of the ground state, with the result that the activation energy is reduced in comparison with that for cyclohexane.     

Conformational behaviour, hydrogen bond competition and intramolecular dynamics in vanillin derivatives: acetovanillone and 6-hydroxy-3-methoxyacetophenone

The conformational landscape of the structural isomers acetovanillone (apocynin, AV) and 6-hydroxy-3-methoxyacetophenone (HMAP) has been investigated in a supersonic jet using Fourier transform microwave spectroscopy. Two conformers have been detected in the jet-cooled expansion for each molecule (s-cis and s-trans in AV; s-trans and a-trans for HMAP), differing in the relative orientation of the acetyl and methoxy groups. Both molecules are stabilized by O-H···O or O-H···O=C hydroxyl intramolecular hydrogen bonds, either constraining the local conformations of the methoxy group in AV, or that of the acetyl group in HMAP. Internal rotation splittings have been observed in both conformers of each molecule, originated by the acetyl group, that yield information on the influence of the intramolecular hydrogen bonds on the methyl torsion. The similar internal rotation barriers in both molecules (6.6 and 7.4 kJ mol(-1) in AV; 7.3 and 7.0 kJ mol(-1) in HMAP) suggest that the acetyl torsion is only slightly affected by intramolecular hydrogen bonding. The absence of torsional tunnellings due to the methoxy group indicates torsional barriers above 10.2 and 8.9 kJ mol(-1) for AV conformers, 10.1 and 10.4 kJ mol(-1) for HMAP. Conformational ratios and relative free energies have been estimated from relative intensity measurements of the spectral lines. Ab initio (MP2) and density functional calculations using the recent M05-2X empirical functional have been used to aid the experimental work in describing the structures, internal rotation barriers and isomerization potentials.     

Conformational studies of 5-acetyl-10-cyano-10,11-dihydro-5H-dibenz[b,f]azepine

5 - Acetyl - 10 - cyano - 10,11 - dihydro - 5H - dibenz[b,f]azepine, 3, has been synthesized and its conformations in solution have been studied by variable temperature NMR. At ?55° in CDCl₃ solution, 3 shows the signals due to four different conformational isomers. At 55°, signals due to only two conformers can be seen. The ABX pattern of each of the four conformers was analyzed using double resonance experiments and the LAOCN3 computer program. The relative abundances of the isomers in the mixtures were estimated by computer additions of different proportions of the spectra calculated for the separate isomers. These spectral observations are discussed in detail and interpreted in terms of slow inversion of the seven-membered ring by torsion of the 4a55a bonds and restricted twisting of the C10C11 ethylene bridge.     

Rotationally resolved electronic spectra of 2- and 3-methylanisole in the gas phase: a study of methyl group internal rotation

Rotationally resolved fluorescence excitation spectra of several torsional bands in the S1 <-- S0 electronic spectra of 2-methylanisole (2MA) and 3-methylanisole (3MA) have been recorded in the collision-free environment of a molecular beam. Some of the bands can be fit with rigid rotor Hamiltonians; others exhibit perturbations produced by the coupling between the internal rotation of the methyl group and the overall rotation of the entire molecule. Analyses of these data show that 2MA and 3MA both have planar heavy-atom structures; 2MA has trans-disposed methyl and methoxy groups, whereas 3MA has both cis- and trans-disposed substituents. The preferred orientations (staggered or eclipsed) in two of the conformers and the internal rotation barriers of the methyl groups in all three conformers change when they are excited by light. Additionally, the values of the barriers opposing their motion depend on the relative positions of the substituent groups, in both electronic states. In contrast, no torsional motions of the attached methoxy groups were detected. Possible reasons for these behaviors are discussed.     

Single molecule spectroscopy as a probe for dye-polymer interactions

Experimental (Single Molecule Spectroscopy) and theoretical (quantum-chemical calculations and Monte Carlo and molecular dynamics simulations) techniques are combined to investigate the behavior and dynamics of a polymer-dye molecule system. It is shown that the dye molecule of interest (1,1'-dioctadecyl-3,3,3',3'-tetramethylindo-dicarbocyanine) adopts two classes of conformations, namely planar and nonplanar ones, when embedded in a poly(styrene) matrix. From an in-depth analysis of the fluorescence lifetime trajectories, the planar conformers can be further classified according to the way their alkyl side chains interact with the surrounding poly(styrene) chains.     

Cages, baskets, ladders, and tubes: conformational studies of polyhedral oligomeric silsesquioxanes

The conformational flexibility of a series of cage, basket, ladder, and tube polyhedral oligomeric silsesquioxanes (POSS) has been examined using the Low Mode:Monte Carlo conformational search method in conjunction with the MM3/GBSA(CHCl3) surface. An ensemble of low energy structures was generated and used to explore the molecular shape and flexibility of each system. The results indicate that, except for the ladder molecule, the incompletely condensed systems that are studied are relatively rigid. Even in cases where the molecule is able to adopt numerous low energy conformations, the overall shape remains cage-like and the conformations differ only by small angles or substituent orientations. The ladder molecule is the most flexible and this ensemble clusters into two families: one that is cage-like and the other that is more open and ladder-like. The conformational flexibilities in the gas and solvent phases, as approximated using the GBSA continuum solvent model, are very similar.     

Relevance of torsional effects to the conformational equilibria of 1,5-diaza-cis-decalins: a theoretical and experimental study

1,5-Diaza-cis-decalin populates two conformations in which the nitrogen atoms are either gauche (N-in) or anti (N-out) to one another. The equilibrium mixture of the two conformers depends on the substituents at the nitrogen atom, as well as the reaction conditions. Ab initio (HF/6-31G, B3LYP/6-31+G) and molecular mechanics (Amber) calculations have been performed to examine the possible role of stereoelectronics and steric effects in controlling the equilibrium of substituted 1,5-diaza-cis-decalins. In the present study, N,N'-diethyl- and N,N'-bistrifluoroethyl-1,5-diaza-cis-decalins have been synthesized, and the equilibrium mixtures have been measured using 1H and 13C NMR experiments. Steric effects appear to control the equilibria between the two conformational isomers of 1,5-diaza-cis-decalin while torsional effects appear to dominate the equilibria for the N,N'-dialkyl derivatives.     

Conformational analysis of vitamin K<Subscript>1</Subscript> model molecule: a theoretical study

Isomerism, conformations, and molecular structure of a model molecule of vitamin K₁ with a truncated side chain have been studied by the density functional theory calculations using B3LYP method and double- and triple-ζ correlation consistent basis sets. The conformations of two possible (E and Z) isomers, formed by the rotations around three single C–C bonds closest to the naphthoquinone ring, have been studied. The lowest energy conformers are stabilized by additional hydrogen bonds between hydrogen atoms of the side chain and an oxygen atom in the naphthoquinone subunit. It is interesting to note that the structure of the energetically preferred conformer of the E-isomer (3c) has been found to be similar to the solid state structures of phylloquinones in the photosystem I of cyanobacterium Synechococcus elongatus. The excited electronic states of two lowest energy conformers have also been investigated.     

Conformational Analysis of C‐Trehaloses Using Molecular Mechanics Calculations

Relaxed‐residue energy maps based on the MM3 force field were computed for the three C‐linked (1‐1) d‐glucosyl disaccharides, C‐trehaloses: the axial–axial linked α,α‐trehalose, the axial–equatorial α,β‐trehalose and the equatorial–equatorial linked β,β‐trehalose. Optimized structures were calculated on a 20°‐grid spacing of the torsional angles about the C‐glycosidic bonds. Boltzman weighted ³J coupling constants were calculated and compared to the experimental values; they are satisfactory. The general shape of the energy maps indicates that α,α‐trehalose is a quite rigid molecule adopting only one conformation around the C‐glycosidic linkage, whereas the other two isomers are rather flexible. Compared to the corresponding O‐disaccharides α,β‐ and β,β‐trehaloses exhibit a larger number of low energy conformers and a larger area of the map energy < 8 kcal/mol. The preferred conformations of the axial C‐glycosidic bond are in agreement with the exo‐anomeric effect. Equatorial C‐ glycosidic bonds are rather flexible, influenced by the polarity of the milieu and the formation of interresidue hydrogen bonds.