Efficient enumeration of stereoisomers of outerplanar chemical graphs using dynamic programming

Exhaustive and nonredundant generation of stereoisomers of a chemical compound with a specified constitution is an important tool for molecular structure elucidation and molecular design. It is known that many chemical compounds have outerplanar graph structures. In this paper we deal with chemical compounds composed of carbon, hydrogen, oxygen, and nitrogen atoms whose graphical structures are outerplanar and consider stereoisomers caused only by asymmetry around carbon atoms. Based on dynamic programming, we propose an algorithm of generating all stereoisomers without duplication. We treat a given outerplanar graph as a graph rooted at its structural center. Our algorithm first recursively computes the number of stereoisomers of the subgraph induced by the descendants of each vertex and then constructs each stereoisomer by backtracking the process of computing the numbers of stereoisomers. Our algorithm correctly counts the number of stereoisomers in O(n) time and space and correctly enumerates all of the stereoisomers in O(n3) time per stereoisomer on average and in O(n) space, where n is the number of atoms in a given structure.     

Efficient overlay of small organic molecules using 3D pharmacophores

Aligning and overlaying two or more bio-active molecules is one of the key tasks in computational drug discovery and bio-activity prediction. Especially chemical-functional molecule characteristics from the view point of a macromolecular target represented as a 3D pharmacophore are the most interesting similarity measure when describing and analyzing macromolecule-ligand interaction. In this study, a novel approach for aligning rigid three-dimensional molecules according to their chemical-functional pharmacophoric features is presented and compared to the overlay of experimentally determined poses in a comparable macromolecule coordinate frame. The presented approach identifies optimal chemical feature pairs using distance and density characteristics obtained by correlating pharmacophoric geometries and thus proves to be faster than existing combinatorial alignment methods and creates more reasonable alignments than pure atom-based methods. Examples will be provided to demonstrate the feasibility, speed and intuitiveness of this method.     

Statistical mechanics of helix bundles using a dynamic programming approach

Despite much study, biomolecule folding cooperativity is not well understood. There are quantitative models for helix-coil transitions and for coil-to-globule transitions, but no accurate models yet treat both chain collapse and secondary structure formation together. We develop here a dynamic programming approach to statistical mechanical partition functions of foldamer chain molecules. We call it the ascending levels model. We apply it to helix-coil and helix-bundle folding and cooperativity. For 14- to 50-mer Baldwin peptides, the model gives good predictions for the heat capacity and helicity versus temperature and urea. The model also gives good fits for the denaturation of Oas's three-helix bundle B domain of protein A (F13W*) and synthetic protein alpha3C by temperature and guanidine. The model predicts the conformational distributions. It shows that these proteins fold with transitions that are two-state, although the transitions in the Baldwin helices are nearly higher order. The model shows that the recently developed three-helix bundle polypeptoids of Lee et al. fold anti-cooperatively, with a predicted value of DeltaHvH/DeltaHcal = 0.72. The model also predicts that two-helix bundles are unstable in proteins but stable in peptoids. Our dynamic programming approach provides a general way to explore cooperativity in complex foldable polymers.     

Discovery of network motifs based on induced subgraphs using a dynamic expansion tree

Biological networks are powerful representations of topological features in biological systems. Finding network motifs in biological networks is a computationally hard problem due to their huge size and abrupt increase of search space with the increase of motif size. Motivated by the computational challenges of network motif discovery and considering the importance of this topic, an efficient and scalable network motif discovery algorithm based on induced subgraphs in a dynamic expansion tree is proposed. This algorithm uses a pruning strategy to overcome the space limitation of the static expansion tree. The proposed algorithm can identify large network motifs up to size 15 by significantly reducing the computationally expensive subgraph isomorphism checks. Further, the present work avoids the unnecessary growth of patterns that do not have any statistical significance. The runtime performance of the proposed algorithm outperforms most of the existing algorithms for large network motifs.     

Pattern recognition in capillary electrophoresis data using dynamic programming in the wavelet domain

A novel approach for CE data analysis based on pattern recognition techniques in the wavelet domain is presented. Low-resolution, denoised electropherograms are obtained by applying several preprocessing algorithms including denoising, baseline correction, and detection of the region of interest in the wavelet domain. The resultant signals are mapped into character sequences using first derivative information and multilevel peak height quantization. Next, a local alignment algorithm is applied on the coded sequences for peak pattern recognition. We also propose 2-D and 3-D representations of the found patterns for fast visual evaluation of the variability of chemical substances concentration in the analyzed samples. The proposed approach is tested on the analysis of intracerebral microdialysate data obtained by CE and LIF detection, achieving a correct detection rate of about 85% with a processing time of less than 0.3 s per 25,000-point electropherogram. Using a local alignment algorithm on low-resolution denoised electropherograms might have a great impact on high-throughput CE since the proposed methodology will substitute automatic fast pattern recognition analysis for slow, human based time-consuming visual pattern recognition methods.     

Efficient method development strategy for challenging separation of pharmaceutical molecules using advanced chromatographic technologies

In this paper, we describe a strategy that can be used to efficiently develop a high-performance liquid chromatography (HPLC) separation of challenging pharmaceutical molecules. This strategy involves use of advanced chromatographic technologies, such as a computer-assisted chromatographic method development tool (ChromSword) and an automated column switching system (LC Spiderling). This process significantly enhances the probability of achieving adequate separations and can be a large time saver for bench analytical scientists. In our study, the ChromSword was used for mobile phase screening and separation optimization, and the LC Spiderling was used to identify the most appropriate HPLC columns. For proof of concept, the analytes employed in this study are the structural epimers betamethylepoxide and alphamethylepoxide (also known as 16-beta methyl epoxide and 16-alpha methyl epoxide). Both of these compounds are used in the synthesis of various active pharmaceutical ingredients that are part of the steroid pharmaceutical products. While these molecules are relatively large in size and contain various polar functional groups and non-polar cyclic carbon chains, their structures differ only in the orientation of one methyl group. To our knowledge, there is no reported HPLC separation of these two molecules. A simple gradient method was quickly developed on a 5 cm YMC Hydrosphere C(18) column that separated betamethylepoxide and alphamethylepoxide in 10 min with a resolution factor of 3.0. This high resolution provided a true baseline separation even when the concentration ratio between these two epimers was 10,000:1. Although outside of the scope of this paper, stability-indicating assay and impurity profile methods for betamethylepoxide and for alphamethylepoxide have also been developed by our group based on a similar method development strategy.     

The enumeration of reaction pathways using Burnside's lemma

A simplified method for the calculation of molecular correlation energies, developed previously, is applied to the study of the potential energy hypersurface related to the reaction O₂+H→HO₂→OH+O. The main parameters that characterize the topology of the surface have been determined: the equilibrium geometries and vibrational frequencies of HO₂ and of its dissociation products, the dissociation energies, the energy gap between the dissociation limits, the geometry of an activated complex, and the corresponding potential barrier height. The particular importance of including the correlation energy is discussed for each of the calculated parameters. In spite of the minimal computational effort required, the results are in good agreement with the experimental data on the one hand, and with the results proceeding from elaborate variational calculations on the other hand. Moreover the controverted existence of a potential barrier (0.19 eV) along the O₂+H→ HO₂ recombination path is discussed.     

Efficient algorithm for conformational search of macrocyclic molecules

A new algorithm, complementarity, is developed for conformational search of macrocyclic molecules. The algorithm scans a large number of candidate conformations and energy-minimizes only the promising ones. These candidates can be generated by two operators that construct new conformations from known minima. The candidates have similar bonded-interaction energy as the known minima and possibly lower nonbonded interaction energy. This algorithm is 9 to 11 times faster than the existing methods when tested on two large rings, cycloheptadecane and rifamycin SV. © 1997 by John Wiley & Sons, Inc.     

Separation of cocaine stereoisomers by capillary electrophoresis using sulfated cyclodextrins

A capillary electrophoretic method for the separation of cocaine and its stereoisomers was developed. In this study, the effect of organic modifier was also investigated. The separation was achieved using 1% sulfated cyclodextrin, 10 mmol L(-1) phosphate buffer, 10% methanol at pH 3. The method provides good reproducibility and easy application.     

Computer enumeration of polyhexes using the compact naming approach

The enumeration of polyhexes can be easily carried out by utilizing a compact name (CN) approach to code chemical structures. The Fortran program performing generation of benzenoid hydrocarbons with 1–10 rings is presented. The computed structures are divided into various classes according to their cata- or peri- as well and non- or radicaloid character. Use of the additive nodal increments (ANI) approach leads to algorithm producing representative samples of the polyhexes' sets which can be applicable in testing of various topological formulae.     

Ab initio calculations of nonlinear optical rotation by several small chiral molecules and by uridine stereoisomers

Expressions for nonlinear optical rotation are presented based on the quantum theory of optical birefringence of Atkins and Barron [Proc. R. Soc. London, Ser. A 304, 303 (1968); 306, 119 (1968)]. As concrete examples, the ordinary and nonlinear optical rotations are calculated with density functional theory (DFT) methodology for some simple single-ring molecules, namely, oxaziridine, diaziridine, and their derivatives, and for two, somewhat more complicated, conformations of uridine. For the single-ring molecules, (1) the angles of the ordinary optical rotation are mostly positive and (2) the contributions of the nonlinear effect to the total optical rotation depend both on the nature of the substituted species and of the host atom located on the ring. For the two conformations of uridine, (1) the signs of nonlinear optical rotation differ even though their ordinary optical rotations have the same sign and (2) whether the molecular structures are geometrically optimized with Hartree-Fock or DFT methodologies has no significant effect on the calculated nonlinear optical rotation when gauge-including atomic orbitals were used, even though the basis sets are small. These studies are expected to be helpful for interpretation of experimental results on nonlinear optical rotation by molecules underway in our research group.     

Controlling the formation of 1 out of 64 stereoisomers using organocatalysis

The formation of 1 out of 64 stereoisomers, i.e. controlling the creation of 6 stereocenters, of important optically active bicyclo[3.3.1]non-2-ene compounds, has been achieved using organocatalysis; the reaction proceeds with excellent stereocontrol and can be carried out with the generation of enantiopure products using chromatography-free procedures.     

Efficient and accurate local single reference correlation methods for high-spin open-shell molecules using pair natural orbitals

A production level implementation of the high-spin open-shell (spin unrestricted) single reference coupled pair, quadratic configuration interaction and coupled cluster methods with up to doubly excited determinants in the framework of the local pair natural orbital (LPNO) concept is reported. This work is an extension of the closed-shell LPNO methods developed earlier [F. Neese, F. Wennmohs, and A. Hansen, J. Chem. Phys. 130, 114108 (2009); F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009)]. The internal space is spanned by localized orbitals, while the external space for each electron pair is represented by a truncated PNO expansion. The laborious integral transformation associated with the large number of PNOs becomes feasible through the extensive use of density fitting (resolution of the identity (RI)) techniques. Technical complications arising for the open-shell case and the use of quasi-restricted orbitals for the construction of the reference determinant are discussed in detail. As in the closed-shell case, only three cutoff parameters control the average number of PNOs per electron pair, the size of the significant pair list, and the number of contributing auxiliary basis functions per PNO. The chosen threshold default values ensure robustness and the results of the parent canonical methods are reproduced to high accuracy. Comprehensive numerical tests on absolute and relative energies as well as timings consistently show that the outstanding performance of the LPNO methods carries over to the open-shell case with minor modifications. Finally, hyperfine couplings calculated with the variational LPNO-CEPA∕1 method, for which a well-defined expectation value type density exists, indicate the great potential of the LPNO approach for the efficient calculation of molecular properties.     

De novo peptide sequencing using exhaustive enumeration of peptide composition

We introduce the use of a peptide composition lookup table indexed by residual mass and number of amino acids for de novo sequencing of polypeptides. Polypeptides of 1600 Daltons (Da) or more can be sequenced effectively through exhaustive compositional analysis of MS/MS spectra obtained by unimolecular decomposition (without CID) in a MALDI TOF/TOF despite a fragment mass accuracy of 50 mDa. Peaks are referenced against the lookup table to obtain a complete profile of amino acid combinations, and combinations are assembled into series of increasing length. Concatenating the differences between successive entries in compositional series yields peptide sequences that can be scored and ranked according to signal intensity. While the current work involves measurements acquired on MALDI TOF-TOF, such general treatment of the data anticipates extension to other types of mass analyzers.     

Graphs to chemical structures 3. General theorems with the use of different sets of sphericity indices for combinatorial enumeration of nonrigid stereoisomers

The extended sphericity indices of k-cycles, which were defined in Part 2 of this series (S. Fujita, Theor Chem Acc, Online: http://www.springerlink.com/index/10.1007/s00214-004-0606-z) according to the enantiospheric, homospheric, or hemispheric nature of each k-cycle, are further extended to prove more general theorems for enumerating nonrigid stereoisomers with rotatable ligands. One of the extended points is the use of different sets of sphericity indices to treat one or more orbits contained in skeletons and ligands. Another is to take account of chirality in proligands and sub-proligands, the latter of which are introduced to consider further inner structures of ligands. Two theorems for enumerating nonrigid stereoisomers are proved by adopting two schemes of their derivation, i.e., the scheme ``positions of a skeleton ⇐ proligands ⇐ ligands (positions of a ligand ⇐ sub-proligands)' and the scheme ``(positions of a skeleton ⇐ proligands ⇐ ligands (positions of a ligand)) ⇐ sub-proligands'. The theorems are applied to the stereoisomerism of trihydroxyglutaric acids. Thereby, it is demonstrated where Pólya's theorem and other previous methods are deficient, when applied to the enumeration of stereoisomers.     

Efficient statistical mapping of energy surfaces of nanoclusters and molecules

A statistical technique to efficiently map out the energy surfaces of nanoclusters and molecules is described. Global energy minimizations are performed to reach of the catchment basins of the lowest energy stationary points. Saddle points are located by using a large value of the iterative energy change as the stopping criterion of a final local relaxation. Minima are derived from saddle points by simply tightening the stopping criterion and continuing the relaxation. A statistical approximation to the widths of the paths in phase space between saddle points and minima is obtained. Application is made to argon clusters of 7 and 38 atoms.     

Efficient crystallization-induced dynamic resolution of alpha-substituted carboxylic acids

Herein we present a novel route to enantiomerically enriched chiral alpha-substituted carboxylic acids by crystallization-induced dynamic resolution (CIDR) of their diastereomeric salts with chiral amines. Thus, the racemic alpha-bromo acid 3 is converted reliably with (1R,2S)-2-amino-1,2-diphenylethanol in the presence of a catalytic amount of tetrabutylammonium bromide into its R-enantiomer 4 in 90% yield with 88% ee. Similarly, the racemic alpha-thiobenzoyl acid 5 could be resolved to 90% ee in 74% yield. Further enrichment to enantiomeric homogeneity could be achieved in both cases by crystallization. In a telescoped, two-step process, S-alpha-thiobenzoyl acid 6 (>or=99.6% ee) was prepared from the racemic bromide 3 in 63% yield. State-of-the-art parallel experimentation enabled rapid screening for suitable dynamic resolution conditions. Kinetic studies defined the influence of temperature, tetrabutylammonium bromide concentration, molarity, and solvent polarity on the resolution rate, product yield, and enantiomeric excess.