Application of the shape group method to conformational processes: Shape and conjugation changes in the conformers of 2-phenyl pyrimidine

The shape group method (SGM) and the associated (a,b)-parameter maps provide a detailed shape characterization of molecular charge distributions. This method is applied to the study of the variations of shape and conjugation of conformers of 2-phenyl pyrimidine in their electronic ground state. Within the SGM framework, the method of (a,b)-parameter maps provides a concise, nonvisual, algorithmic technique for shape characterization of molecules with fixed nuclear geometries. Moreover, shape codes derived from the (a,b)-parameter maps afford a practical means for efficiently storing the shape properties of molecules in an electronic database. The shape codes of two or more charge distributions can be compared directly, and numerical measures of molecular shape similarity can be computed using a technique that is simple, fast, and inexpensive, especially in relation to direct, pairwise comparisons of electronic charge densities. The quantitative and automated nature of the method suggests applications in the field of computer-aided molecular design. In this study, the method is used for the first time to determine detailed numerical shape codes and shape similarity measures for a nontrivial conformational problem involving changes in energy and in conjugation. Numerical shape similarity measures of eight conformers of 2-phenyl pyrimidine are determined and correlated with variations in conformational energy and conjugation. The competing effects of steric repulsion and conjugation lead to important correlations between conformational energy and shape. © 1995 John Wiley & Sons, Inc.     

From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins

An improved scheme to help in the prediction of protein structure is presented. This procedure generates improved starting conformations of a protein suitable for energy minimization. Trivariate gaussian distribution functions for the π, ψ, and χ¹ dihedral angles have been derived, using conformational data from high resolution protein structures selected from the Protein Data Bank (PDB). These trivariate probability functions generate initial values for the π, ψ, and χ¹ dihedral angles which reflect the experimental values found in the PDB. These starting structures speed the search of the conformational space by focusing the search mainly in the regions of native proteins. The efficiency of the new trivariate probability distributions is demonstrated by comparing the results for the α-class polypeptide fragment, the mutant Antennapedia (C39 → S) homeodomain (2HOA), with those from two reference probability functions. The first reference probability function is a uniform or flat probability function and the second is a bivariate probability function for π and ψ. The trivariate gaussian probability functions are shown to search the conformational space more efficiently than the other two probability functions. The trivariate gaussian probability functions are also tested on the binding domain of Streptococcal protein G (2GB1), an α/β class protein. Since presently available energy functions are not accurate enough to identify the most native-like energy-minimized structures, three selection criteria were used to identify a native-like structure with a 1.90-Å rmsd from the NMR structure as the best structure for the Antennapedia fragment. Each individual selection criterion (ECEPP/3 energy, ECEPP/3 energy-plus-free energy of hydration, or a knowledge-based mean field method) was unable to identify a native-like structure, but simultaneous application of more than one selection criterion resulted in a successful identification of a native-like structure for the Antennapedia fragment. In addition to these tests, structure predictions are made for the Antennapedia polypeptide, using a Pattern Recognition-based Importance-Sampling Minimization (PRISM) procedure to predict the backbone conformational state of the mutant Antennapedia homeodomain. The ten most probable backbone conformational state predictions were used with the trivariate and bivariate gaussian dihedral angle probability distributions to generate starting structures (i.e., dihedral angles) suitable for energy minimization. The final energy-minimized structures show that neither the trivariate nor the bivariate gaussian probability distributions are able to overcome the inaccuracies in the backbone conformational state predictions to produce a native-like structure. Until highly accurate predictions of the backbone conformational states become available, application of these dihedral angle probability distributions must be limited to problems, such as homology modeling, in which only a limited portion of the backbone (e.g., surface loops) must be explored. © 1996 John Wiley & Sons, Inc.     

Hydrophobic Molecular Similarity from MST Fractional Contributions to the Octanol/water Partition Coefficient

Summary The use of a recently proposed hydrophobic similarity index for the alignment of molecules and the prediction of their differences in biological activity is described. The hydrophobic similarity index exploits atomic contributions to the octanol/water transfer free energy, which are evaluated by means of the fractional partitioning scheme developed within the framework of the Miertus-Scrocco-Tomasi continuum model. Those contributions are used to define global and local measures of hydrophobic similarity. The suitability of this computational strategy is examined for two series of compounds (ACAT inhibitors and 5-HT₃ receptor agonists), which are aligned to maximize the global hydrophobic similarity using a Monte Carlo-simulated protocol. Indeed, the concept of local hydrophobic similarity is used to explore structure–activity relationships in a series of COX-2 inhibitors. Inspection of the 3D distribution of hydrophobic/hydrophilic contributions in the aligned molecules is valuable to identify regions of very similar hydrophobicity, which can define pharmacophoric recognition patterns. Moreover, low similar regions permit to identify structural elements that modulate the differences in activity between molecules. Finally, the quantitative relationships found between the pharmacological activity and the hydrophobic similarity index points out that not only the global hydrophobicity, but its 3D distribution, is important to gain insight into the activity of molecules. J.M.M. and S.P. have contributed equally to this study.     

Conformational analysis of oligosaccharides in solution

A complete understanding of the role of carbohydrates in biological systems is to a large extent dependent on the information available about the equilibrium mixture and about the preferred conformation of the carbohydrate molecules in solution. The conformational analysis offers a tool which can determine all possible conformations which influence the solution behavior of carbohydrates. This paper attempts to survey the progress in the theoretical conformational analysis of saccharides in solution. The conformational analysis will be discussed in detail both with respect to the strategy for the investigation of conformational properties but also with regard to the quality of the method used for calculations of the energy of the isolated molecule and free energy of solvation. Finally, examples will be given to illustrate how the methods of conformational analysis can be used to estimate the solution behavior of cyclic model compounds of carbohydrates 2-methoxytetrahydropyran, monosaccharide D -glucopyranose, and two disaccharides; β-maltose and β-cellobiose.     

Conformational flexibility in open chain molecules: chiral and achiral alkanes

Conformational partition functions of chiral and achiral alkanes have been computed by using a continuum approach (instead of rotational isomeric state approximations). The accessible conformational space per bond depends upon the structure of the compound and is only in the range of 5–13% of the maximum accessible range. In order to partly overcome the intrinsic ambiguity of the term “conformational flexibility”, the distinction between number flexibility (a measure of the number of accessible energy minima) and space flexibility (a measure of the total allotted space) is proposed. Further, the conformational versatility of each bond of a molecule is evaluated in terms of the a priori probability density function of that bond, and it is shown that the use of this function permits a comparison of the relative conformational flexibilities of the individual bonds, which is particularly useful for molecules having more than two rotation angles (where the conventional energy maps cannot be used). Optical rotations are calculated for a series of chiral alkanes by combining the continuum approach for conformational analysis and a recent optical activity calculation scheme. Contributions of single bonds to the molar optical rotation are evaluated and discussed. The influence of temperature upon conformational and chiral properties is evaluated.     

Quantitative orbital analysis of ab initio SCF=MO computations : Part II. Conformational preferences in H2N---OH and H2N---SH

The results obtained in a quantitative orbital analysis of the ab initio SCF=MO computations performed on hydroxylamine and thiohydroxylamine are described. The analysis is based on the use of fragment localized MOs and the energy effects associated with their interactions are estimated, in the framework of the ab initio SCF—MO computations, using PMO expressions. In particular the factors are analyzed which control the conformational preference in these molecules, and the effect of the sulphur 3d orbitals upon conformational stability is discussed.     

Use of Molecular Electrostatic Potentials for Analysis of Anticonvulsant Activities of Phenylsuccinimides

Abstract

The present study was performed on a group of 27 derivatives of phenylsuccinimides, of which only 12 were active against maximal electrical shock in spite of the structural similarities of these compounds. The work consisted of four main parts: 1. crystallographic investigations of a subset of chosen compounds; 2. conformational analysis of characteristic molecules from the investigated series, performed by means of molecular mechanics calculations; 3. molecular orbital optimization of all the molecules using the MNDO method starting with conformations obtained in 2; 4. molecular electrostatic potential (MEP) analysis which was performed on the semiempirical (MNDO) and ab initio levels. This research showed that MEP maps provide a signature that distinguishes between active and inactive compounds. There are MEP minima close to the two carbonyl oxygens of the imide ring, and although the magnitude of the difference between the two minima is approximately constant, the sign of the difference provides an activity index. The initial orientations of phenylsuccinimide molecules in relation to the receptor are not equivalent and they depend on the potential distribution around both the succinimide molecules and around the receptor. In the active compounds the negative potential difference at the discussed points most probably influences the initial set-up of the molecules in relation to the receptor and results in a considerably higher probability of the molecules being bound at the right place on the receptor.     

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.     

Study of molecular quantum similarity of enantiomers of amino acids

Molecular quantum similarity is evaluated for enantiomers in the case of molecules showing conformational flexibility, using our earlier proposed Boltzmann weighted similarity index. The conformers of the enantiomers of the amino acids alanine, asparagine, cysteine, leucine, serine, and valine were examined. Next to studying global indices, the evaluation of local similarity is carried out using our earlier proposed local similarity index based on the Hirshfeld partitioning, to further illustrate Mezey's holographic electron density theorem in chiral systems and to quantify dissimilarity of enantiomers.     

Incorporating partial matches within multiobjective pharmacophore identification

This paper describes the extension of our earlier multiobjective method for generating plausible pharmacophore hypotheses to incorporate partial matches. Diverse sets of molecules rarely adopt exactly the same binding mode, and so allowing the identification of partial matches allows our program to be applied to larger and more diverse datasets. The method explores the conformational space of a series of ligands simultaneously with their alignment using a multiobjective genetic algorithm (MOGA). The principles of Pareto ranking are used to evolve a diverse set of pharmacophore hypotheses that are optimised on conformational energy of the ligands, the goodness of the overlay and the volume of the overlay. A partial match is defined as a pharmacophoric feature that is present in at least two, but not all, of the ligands in the set. The number of ligands that map to a given pharmacophore point is taken into account when evaluating an overlay. The method is applied to a number of test cases extracted from the Protein Data Bank (PDB) where the true overlay is known.     

Pattern recognition in the prediction of protein structure. III. An importance-sampling minimization procedure

A procedure that generates random conformations of a protein chain, and then applies energy minimization to find the structure of lowest energy, is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. Each state corresponds to a rectangular region in the ?, ψ map. The conformation of an entire chain is then represented by a sequence of single-residue conformational states. The distinct “chain-states” in this representation correspond to multidimensional rectangular regions in the conformational space of the whole protein. A set of highly-probable chain-states can be predicted from the amino acid sequence using the pattern recognition procedure developed in the first two articles of this series. The importance-sampling minimization procedure of the present article is then used to explore the regions of conformational space corresponding to each of these chain-states. The importance-sampling procedure generates a number of random conformations within a particular multidimensional rectangular region, sampling most densely from the most probable, or “important,” sections of the ?, ψ map. All values of ? and ψ are allowed, but the less-probable values are sampled less often. To achieve this, the random values of ? and Φ are generated from bivariate gaussian distributions that are determined from known X-ray structures. Separate gaussian distributions are used for proline residues in the α and ? states, for glycine residues in the α, ?, α*, and ?* states, and for ordinary residues involved in 29 different tripeptide conformations. Energy minimization is then applied to the randomly-generated structures to optimize interactions and to improve packing. The final energy values are used to select the best structures. The importance-sampling minimization procedure is tested on the avian pancreatic polypeptide, using chain-states predicted from the amino acid sequence. The conformation having the lowest energy is very similar to the X-ray conformation.     

Conformational searching methods for small molecules. II. Genetic algorithm approach

We demonstrate the use of a genetic algorithm (GA) search procedure for finding low-energy conformations of small to medium organic molecules (1–12 rotatable bonds). GAS are in a class of biologically motivated optimization methods that evolve a population of individuals where individuals who are more “fit” have a higher probability of surviving into subsequent generations. Here, an individual is a conformation of a given molecule and the fitness is the molecule's conformational energy. In the course of a simulated evolution, the population produces conformations having increasingly lower energy. We test the GA method on a suite of 72 molecules and compare the performance against the CSEARCH algorithm in Sybyl. For molecules with more than eight rotatable bonds, the GA method is more efficient computationally and as the number of rotatable bonds increases the relative efficiency of the GA method grows. The GA method also found energies equal to or lower than the energy of the relaxed crystal structure in the large majority of cases. © John Wiley & Sons, Inc.     

Conformation of polystyrene with special emphasis to the near all-trans extended-chain model relevant in polystyrene gels

In light of novel and problematic diffraction patterns arising through the thermoreversible gelation of isotactic polystyrene, the conformational possibilities were examined with particular reference to other conformational works published recently on this polymer. The specific objective was to ascertain whether highly extended, helical backbone geometries such as are required by the new x-ray patterns are possible or not with a purely isotactic arrangement of side groups. The first realization was that the recently announced low-energy, near-trans conformations are not relevant to the present issue as they do not provide the required extended geometry. Further, specific sampling of the conformational energy map revealed that the required high chain extension may be energetically feasible, contrary to traditional conceptions and to recent conformational calculations elsewhere. The divergences as regards the latter were traced to the specific choice of nonbonded atomic radii—all within generally accepted limits—which accordingly has a crucial effect even to the extent whether specific conformation types are forbidden or energetically stable. The implications this has for conformational analysis in general are being pointed out. While the novel crystal structure has not been solved, the present study at least eliminates the previously believed categoric objections to it being associated with isotactic chains and, beyond this, opens up new perspectives as regards conformational possibilities in polyolefins. The more general problems concerning the nature and origin of the gelation phenomenon nevertheless remain.     

Implementation and use of the method of prudent ascent in conformational analysis using molecular mechanics

In two-dimensional conformational analysis the current practice is to perform an energy minimization for all possible combinations of two dihedral angles in the molecule, in a fixed order, and apply a certain dihedral angle step-size. A newly developed method is presented in which the order of the evaluation points on the energy-surface is not fixed, but is dependent on all previous results in a way which we call “the method of prudent ascent.” In this method the most promising calculation is carried out first, thus minimizing the risk of atomic collisions. In order to be able to take care of the many additional degrees of conformational freedom present in, e.g., carbohydrate molecules, all minimizations are performed using a set of different promising starting conformations on the basis of previous calculations, and only the lowest energy result for each point is saved. An application of the method to conformational analysis of methyl-cellobiose and the artificial sweetener trichlorogalactosucrose is also presented.