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.     

Use of 13Calpha chemical shifts in protein structure determination

A physics-based method aimed at determining protein structures by using NOE-derived distances together with observed and computed 13C chemical shifts is proposed. The approach makes use of 13Calpha chemical shifts, computed at the density functional level of theory, to obtain torsional constraints for all backbone and side-chain torsional angles without making a priori use of the occupancy of any region of the Ramachandran map by the amino acid residues. The torsional constraints are not fixed but are changed dynamically in each step of the procedure, following an iterative self-consistent approach intended to identify a set of conformations for which the computed 13Calpha chemical shifts match the experimental ones. A test is carried out on a 76-amino acid, all-alpha-helical protein; namely, the Bacillus subtilis acyl carrier protein. It is shown that, starting from randomly generated conformations, the final protein models are more accurate than an existing NMR-derived structure model of this protein, in terms of both the agreement between predicted and observed 13Calpha chemical shifts and some stereochemical quality indicators, and of similar accuracy as one of the protein models solved at a high level of resolution. The results provide evidence that this methodology can be used not only for structure determination but also for additional protein structure refinement of NMR-derived models deposited in the Protein Data Bank.     

The Structure of Some Phenol-Formaldehyde Condensates for Wood Adhesives

The probable minimum-energy structures of three dimeric, three tri-meric, and two hexameric phenol-formaldehyde (PF) condensates were determined by using a simplified model where the total energy was calculated as the sum of the van der Waals, hydrogen bonding, torsional, and electrostatic energies. The minimum-energy conformation was defined as that with internal angles of rotation that correspond to the overall minimum in the total energy. Representations of the structures of these PF condensates in the minimum-energy conformations were obtained. The results obtained indicated that the van der Waals energy, and in some cases the hydrogen bonding energy, make the most important contributions to the total energy. The phenol-formaldehyde dimers and trimers are predicted by this model to have nonplanar structures, and the longer phenol-formaldehyde condensates, such as the hexamers, probably exist in helical conformations.     

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.     

Quantum mechanical calculations of tryptophan and comparison with conformations in native proteins

We report a detailed analysis of the potential energy surface of N-acetyl-l-tryptophan-N-methylamide, (NATMA) both in the gas phase and in solution. The minima are identified using the density-functional-theory (DFT) with the 6-31g(d) basis set. The full potential energy surface in terms of torsional angles is spanned starting from various initial configurations. We were able to locate 77 distinct L-minima. The calculated energy maps correspond to the intrinsic conformational propensities of the individual NATMA molecule. We show that these conformations are essentially similar to the conformations of tryptophan in native proteins. For this reason, we compare the results of DFT calculations in the gas and solution phases with native state conformations of tryptophan obtained from a protein library. In native proteins, tryptophan conformations have strong preferences for the beta sheet, right-handed helix, tight turn, and bridge structures. The conformations calculated by DFT, the solution-phase results in particular, for the single tryptophan residue are in agreement with native state values obtained from the Protein Data Bank.     

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.     

Efficient generation,storage, and manipulation of fully flexible pharmacophore multiplets and their use in 3-D similarity searching

Pharmacophore triplets and quartets have been used by many groups in recent years, primarily as a tool for molecular diversity analysis. In most cases, slow processing speeds and the very large size of the bitsets generated have forced researchers to compromise in terms of how such multiplets were stored, manipulated, and compared, e.g., by using simple unions to represent multiplets for sets of molecules. Here we report using bitmaps in place of bitsets to reduce storage demands and to improve processing speed. Here, a bitset is taken to mean a fully enumerated string of zeros and ones, from which a compressed bitmap is obtained by replacing uniform blocks ("runs") of digits in the bitset with a pair of values identifying the content and length of the block (run-length encoding compression). High-resolution multiplets involving four features are enabled by using 64 bit executables to create and manipulate bitmaps, which "connect" to the 32 bit executables used for database access and feature identification via an extensible mark-up language (XML) data stream. The encoding system used supports simple pairs, triplets, and quartets; multiplets in which a privileged substructure is used as an anchor point; and augmented multiplets in which an additional vertex is added to represent a contingent feature such as a hydrogen bond extension point linked to a complementary feature (e.g., a donor or an acceptor atom) in a base pair or triplet. It can readily be extended to larger, more complex multiplets as well. Database searching is one particular potential application for this technology. Consensus bitmaps built up from active ligands identified in preliminary screening can be used to generate hypothesis bitmaps, a process which includes allowance for differential weighting to allow greater emphasis to be placed on bits arising from multiplets expected to be particularly discriminating. Such hypothesis bitmaps are shown to be useful queries for database searching, successfully retrieving active compounds across a range of structural classes from a corporate database. The current implementation allows multiconformer bitmaps to be obtained from pregenerated conformations or by random perturbation on-the-fly. The latter application involves random sampling of the full range of conformations not precluded by steric clashes, which limits the usefulness of classical fingerprint similarity measures. A new measure of similarity, The Stochastic Cosine, is introduced here to address this need. This new similarity measure uses the average number of bits common to independently drawn conformer sets to normalize the cosine coefficient. Its use frees the user from having to ensure strict comparability of starting conformations and having to use fixed torsional increments, thereby allowing fully flexible characterization of pharmacophoric patterns.     

An ab initio study of the geometries and rotational barriers of 1-, 2-, and 5-phenylimidazole

The torsional barrier was calculated in the 3-21G basis set for 1-, 2-, and 5-phenylimidazole. Full geometry optimization was carried out at inter-ring torsional angles of 0°, 30°, 60°, 90°, 120°, 150°, 180°, and additional intermediate angles. All torsional potential energies were found to be symmetric with respect to the 90° conformation. The 2-phenylimidazole torsional energy exhibits a minimum at 0° (and 180°) and a maximum at 90° with a barrier height of 5.83 kcal/mol relative to the 0° conformation. The minima in the 1- and 5-phenylimidazole torsional potential energies correspond to non-planar conformations, resulting in a double-well potential with maxima at 0° (180°) and 90°. The 1-phenylimidazole minima are located at 46.5 and 133.5°; the 5-phenylimidazole minima, at 35.3 and 144.7°. In the 0° (180°) and 90° conformations, 1-phenylimidazole exhibits torsional barriers of 1.84 and 0.75 kcal/mol, respectively, relative to the energy of the 46.5° conformation. For 5-phenylimidazole, these barriers are 0.94 and 1.89 kcal/mol, relative to the energy of the 35.3° conformation. The energy of 5-phenylimidazole in the 35.3° conformation corresponds to a relative tautomeric energy difference of 1.80 kcal/mol compared to the 0° conformer of the 4-phenylimidazole tautomer.     

Polystyrene models. III. modeling backbone/side-group interactions by an ab initio study of 2,4-diphenylpentane

The Structure and the energy of the stable conformations of the two possible stereochemical configurations of 2,4-diphenylpentane are obtained using the ab initio molecular orbital theory. The objective was to mimic the possible structures and determine the corresponding energies of the dyads of syndiotactic and isotactic polystyrene and, consequently, to study the interactions between the phenyl groups. The results of complete geometry optimization showed significant changes in geometrical parameters compared with those expected from the ideal hydrocarbon structure. The steric strain is most pronounced in some of the gauche conformations where large (approximately 40°) distortions of the backbone torsional angles and/or simultaneous phenyl group rotations in the range of 30°–40° away from its global minimum position may occur. In addition to the discussion of the geometrical parameters, the corresponding dipole moments are also calculated and differences related to the various structures and discussed. © 1993 John Wiley & Sons. Inc.     

Conformational memories with variable bond angles

Conformational Memories (CM) is a simulated annealing/Monte Carlo method that explores peptide and protein dihedral conformational space completely and efficiently, independent of the original conformation. Here we extend the CM method to include the variation of a randomly chosen bond angle, in addition to the standard variation of two or three randomly chosen dihedral angles, in each Monte Carlo trial of the CM exploratory and biased phases. We test the hypothesis that the inclusion of variable bond angles in CM leads to an improved sampling of conformational space. We compare the results with variable bond angles to CM with no bond angle variation for the following systems: (1) the pentapeptide Met-enkephalin, which is a standard test case for conformational search methods; (2) the proline ring pucker in a 17mer model peptide, (Ala)(8)Pro(Ala)(8); and (3) the conformations of the Ser 7.39 chi(1) in transmembrane helix 7 (TMH7) of the cannabinoid CB1 receptor, a 25-residue system. In each case, analysis of the CM results shows that the inclusion of variable bond angles results in sampling of regions of conformational space that are inaccessible to CM calculations with only variable dihedral angles, and/or a shift in conformational populations from those calculated when variable bond angles are not included. The incorporation of variable bond angles leads to an improved sampling of conformational space without loss of efficiency. Our examples show that this improved sampling leads to better exploration of biologically relevant conformations that have been experimentally validated.     

A knowledge-based approach to generating diverse but energetically representative ensembles of ligand conformers

This paper describes a new and efficient stochastic conformational sampling method for generating a range of low-energy molecule conformations. Sampling can be tailored to a specific structural domain (e.g., peptides) by extracting torsional profiles from specific datasets and subsequently applying them to target molecules outside the reference set. The programs that handle creation of the knowledge-based torsional profiles and conformer generation per se are separate and so can be used independently or sequentially, depending on the task at hand. The conformational ensembles produced are contrasted with those generated using local minimization approaches. They are also quantitatively compared with a broader range of techniques in terms of speed and the ability to reproduce bound ligand conformations found in complexes with proteins.     

Steric trigger as a mechanism for CB1 cannabinoid receptor activation

To determine the moiety that behaves as the steric trigger to activate the CB(1) cannabinoid receptor, conformational properties of the nonclassical cannabinoid CP55244, one of the most potent CB(1) receptor agonists, were characterized by conformational analysis, rotational barrier calculations, and molecular dynamics (MD) simulations. It was shown from the present MD simulations that the torsion angles phi1 and phi4 of the C3 side chain showed the most dramatic change when compared with the ground-state receptor-bound conformation, indicating that rotation around these torsion angles is responsible for releasing the ligand strain energy. Multiple stages would be involved in the ligand conformational change. As a molecular mechanism for the ligand-induced CB(1) receptor conformational change, we propose that the C3 side chain serves as the steric trigger, while the ACD-ring moiety of CP55244 serves as the plug. Steric clash with helices within the binding pocket would induce microconformational adaptation within the protein. This mechanism would suggest that rotational flexibility in a ligand may be as important a determinant of agonist activity as the pharmacophoric elements that can be identified.     

Seven- and Eight-Membered Ring Conformations of Phosphorus Containing Heterocycles

Abstract

The conformational behaviour of seven- and eight-membered heterocycles based on their NMR spectrum and on a theoretical investigation is described. All possible basic conformations and their quantitative parameters have been considered. A molecular mechanics approach is applied to the calculation of the multidimensional maps of potential energy dependence on torsional angles.     

Steric effects—III: Composition of the E's parameter. Variation of alkyl steric effects with substitution. Role of conformation in determining sterically active and inactive sites

The steric effect of alkyl groups as parameterized by E'_s covers a range of over seven powers of ten. In this article an attempt is made to portray in mechanism terms the manifold nature of the steric effect as a function of substitution, i.e. the composition of the steric effect. One most consider the contribution of the topological carbon sites as a function of the true coordinates of these atoms. To this end, we evaluate the geometry of these alkyl groups in carboxylic acid indirectly by a search for the probable conformations of these acids. The starting point in this study is the determination of the minimum energy conformations in carboxylic acids using the empirical force field method based on analogous alkylmethyl ketone models.This approach to the ground state behaviour of these acids leads directly to a division of the complete set of alkyl groups into two subsets within which a Conformational sequence or filitation is associated with the substitution process which generates the successive alkyl groups of that subset. It is shown that eclipsed conformations are preferred in the case of secondary and tertiary groups bearing Et and Me sub-groups, giving way to preferred bisected conformations when t-Bu and i-Pr sub-groups are present. For further elucidation of steric perturbation terms these two subsets must be considered independently. These important observations lead to an overall coherent interpretation of steric effects.Three regions of distinct behaviour as a function of substitution have been identified. In Region I (the so-called “mormal” region, where the contribution of the introduction of successive methyl groups to the overall E'_s increases monotonically), besides excellent topological site correlations, an excellent hybrid correlation is proposed. For a conformationally homogeneous (i.e. eclipsed) set of alkyl groups the overall E'_s of groups is well expressed by a linear combination of the weighted contribution of sub-groups and the Newman six-number. This correlation leads to an interpretation of the composition of the overall steric effect of an alkyl group, as measured by the E'_s parameter, in terms of conformationally defined sites and stresses the steric importance of certain privileged sites. This result is consistent with the molecular mechanics viewpoint of preferred conformations but at variance with previous assumptions.The levelling effect (Region II), in the light of conformational information, is understood in terms of sterically active and inactive sites, while the inversion effect (Region III) is considered to be the result of molecular distortion brought about by relief of local internal steric strain within the alkyl groups. The X-ray structure of i-Pr₃CCO₂H illustrates this point.     

Acidity of ortho-substituted benzoic acids: an infrared and theoretical study of the intramolecular hydrogen bonds

The structures of ortho-substituted benzoic acids with substituents bearing hydrogen atoms (OH, NH2, COOH and SO2NH2) were investigated by means of IR spectroscopy and of density functional theory at the B3LYP/6-311 + G(d,p) level. All possible conformations, hydrogen bonds, tautomeric forms and zwitterions were taken into consideration and particular attention was given to intramolecular H-bonds and their effect on acidity. Strong H-bonds in the anions of all four acids, were revealed by calculations. In three cases they were confirmed by the IR spectra of the tetrabutylammonium salts in tetrachloromethane solution, while the salt of 1,2-benzenedicarboxylic acid was not sufficiently soluble. The H-bonds are of different strengths but in all cases they are the main cause of the strengthened acidity of these acids in the gas phase and also in solution, although their effect is opposed by weaker H-bonds present in the undissociated acid molecules. The substituent effect on the acidity was evaluated in terms of isodesmic reactions, separately in the acid molecules and in the anions. While the acidity of the 2-OH and 2-NH2 acids is determined essentially by the H-bonds, that of the 2-COOH and 2-SO2NH2 acids is strengthened by the polar effect operating in the undissociated molecule in addition to the H-bond in the anion. The steric inhibition of resonance (SIR), estimated from model conformations with fixed torsional angles, is of little importance. This analysis goes significantly beyond the classical explanation obtained from the acidities in solution but essentially conforms with it.     

Singular value decomposition of torsional angles of analogs of the dopamine reuptake inhibitor GBR 12909

Analysis of large, flexible molecules, such as the dopamine reuptake inhibitor GBR 12909 (1), is complicated by the fact that they can take on a wide range of closely related conformations. The first step in the analysis is to classify the conformers into groups. Here, Singular Value Decomposition (SVD) was used to group conformations of GBR 12909 analogs by the similarity of their nonring torsional angles. The significance of the present work, the first application of SVD to the analysis of very flexible molecules, lies in the development of a novel scaling technique for circular data and in the grouping of molecular conformations using a technique that is independent of molecular alignment. Over 700 conformers each of a piperazine (2) and piperidine (3) analog of 1 were studied. Analysis of the score and loading plots showed that the conformers of 2 separate into three large groups due to torsional angles on the naphthalene side of the molecule, whereas those of 3 separate into nine groups due to torsional angles on the bisphenyl side of the molecule. These differences are due to nitrogen inversion at the unprotonated piperazinyl nitrogen of 2, which results in a different ensemble of conformers than those of 3, where no inversion is possible at the corresponding piperidinyl carbon.     

The Structure of Cellulose by Conformational Analysis. 1. Cellobiose and Methyl-β-cellobioside

Conformational analysis studies on the tertiary structure of cellobiose and methyl-β-cellobioside were carried out by using calculations of van der Waals, H-bond, electrostatic, and torsional energy interactions between the atoms and groups of the molecules. Energy maps as functions of the rotational anglesΨo and Φ° of the glucosidic bond were obtained in increments of 20° and refined in increments of 1°. Two “primary” and one “secondary” conformations of minimum energy were obtained for both cellobiose and methyl-β-cellobioside, some of which are equivalent to results obtained by x-ray diffraction. The H-bond forces are shown to be, together with the van der Waals forces, the predominant factors in the fixation of the conformations of minimum energy. The position and energy contributions of the H-bonds patterns for the favored conformations are identified.     

Systematic drug receptor mapping: A new approach to the analysis of conformational energy calculations of flexible molecules with application to dopaminergic and adrenergic agonists

The computer program PRODIS is used to find low energy conformations of flexible molecules by searching the potential energy surface(s) of one or more torsion angles via rigid rotation. The n-dimensional grid of energy versus torsion angles is then converted to a Boltzman probability distribution, with the probability being represented not as a function of torsion angle, but rather a distance between two atoms. These atoms are chosen by comparison with a known, active analogue in which certain atoms have previously been determined as requirements for drug activity. PRODIS produces a list of low energy conformations, their corresponding interatomic distances and the Boltzman probability for each distance ±0.125, as well as the total probability for each conformation. The user also specifies a target interatomic distance and range (usually derived from a more rigid analogue) for which PRODIS lists all conformations and their Boltzman probability that meet this distance.     

Non-Boltzmann sampling and Bennett's acceptance ratio method: how to profit from bending the rules

The exact computation of free energy differences requires adequate sampling of all relevant low energy conformations. Especially in systems with rugged energy surfaces, adequate sampling can only be achieved by biasing the exploration process, thus yielding non-Boltzmann probability distributions. To obtain correct free energy differences from such simulations, it is necessary to account for the effects of the bias in the postproduction analysis. We demonstrate that this can be accomplished quite simply with a slight modification of Bennett's Acceptance Ratio method, referring to this technique as Non-Boltzmann Bennett. We illustrate the method by several examples and show how a creative choice of the biased state(s) used during sampling can also improve the efficiency of free energy simulations.