Efficient enumeration of stereoisomers of tree structured molecules using dynamic programming

Nonredundant and exhaustive generation of stereoisomers of a chemical compound with a specified constitution is one of the important tools for molecular structure elucidation and molecular design. In this paper, we deal with chemical compounds composed of carbon, hydrogen, oxygen and nitrogen atoms whose graphical structures are tree-like graphs because these compounds are most fundamental, and consider stereoisomers that can be generated by asymmetric carbon atoms and double bonds between two adjacent carbon atoms. Based on dynamic programming, we propose an algorithm of generating all stereoisomers without duplication. We treat a given tree-like graph as a tree rooted at its structural center. Our algorithm first computes recursively the numbers of stereoisomers of the subgraphs 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 the stereoisomers in O(n) space and in O(n) time per stereoisomer, where n is the number of atoms in a given structure. The source code of the program implementing the proposed algorithm is freely available for academic use upon request.     

Determination of the relative stereochemistry of flexible organic compounds by Ab initio methods: conformational analysis and Boltzmann-averaged GIAO 13C NMR chemical shifts

Ab initio calculations at the Hartree-Fock level with full-geometry optimization using the 6-31G(d) basis set, and GIAO (gauge including atomic orbitals) (13)C NMR chemical shifts, are presented here as a support in the study of the stereochemistry of low-polar organic compounds having an open-chain structure. Four linear stereoisomers, fragments of a natural product previously characterized by experimental (13)C NMR spectra, which possesses three stereogenic centers, 11 carbon atoms, and 38 atoms in total, were considered. Conformational searches, by empirical force-field molecular dynamics, pointed out the existence of 8-13 relevant conformers per stereoisomer. Thermochemical calculations at the ab initio level in the harmonic approximation of the vibrational modes, allowed the evaluation, at 298.15 K, of the standard Gibbs free energy of the conformers. The (13)C NMR chemical shift of a given carbon atom in each stereoisomer was considered as the average chemical shift value of the same atom in the different conformers. The averages were obtained by the Boltzmann distribution, using the relative standard free energies as weighting factors. Computed parameters related to linear correlation plots of experimental (13)C chemical shifts versus the corresponding computed average data allowed us to distinguish among the four stereoisomers.     

Development of a chemical structure comparison method for integrated analysis of chemical and genomic information in the metabolic pathways

Cellular functions result from intricate networks of molecular interactions, which involve not only proteins and nucleic acids but also small chemical compounds. Here we present an efficient algorithm for comparing two chemical structures of compounds, where the chemical structure is treated as a graph consisting of atoms as nodes and covalent bonds as edges. On the basis of the concept of functional groups, 68 atom types (node types) are defined for carbon, nitrogen, oxygen, and other atomic species with different environments, which has enabled detection of biochemically meaningful features. Maximal common subgraphs of two graphs can be found by searching for maximal cliques in the association graph, and we have introduced heuristics to accelerate the clique finding and to detect optimal local matches (simply connected common subgraphs). Our procedure was applied to the comparison and clustering of 9383 compounds, mostly metabolic compounds, in the KEGG/LIGAND database. The largest clusters of similar compounds were related to carbohydrates, and the clusters corresponded well to the categorization of pathways as represented by the KEGG pathway map numbers. When each pathway map was examined in more detail, finer clusters could be identified corresponding to subpathways or pathway modules containing continuous sets of reaction steps. Furthermore, it was found that the pathway modules identified by similar compound structures sometimes overlap with the pathway modules identified by genomic contexts, namely, by operon structures of enzyme genes.     

The application of empirical methods of 13C NMR chemical shift prediction as a filter for determining possible relative stereochemistry

The reliable determination of stereocenters contained within chemical structures usually requires utilization of NMR data, chemical derivatization, molecular modeling, quantum‐mechanical (QM) calculations and, if available, X‐ray analysis. In this article, we show that the number of stereoisomers which need to be thoroughly verified, can be significantly reduced by the application of NMR chemical shift calculation to the full stereoisomer set of possibilities using a fragmental approach based on HOSE codes. The applicability of this suggested method is illustrated using experimental data published for a series of complex chemical structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Templated synthesis of mesolamellar n-alkylamine borophosphates

A family of lamellar mesostructured n-alkylamine borophosphates, denoted C n A-BPO (BPO stands for inorganic borophosphate layer; n = 9-15, the number of carbon atoms in the n-alkylamine chain) has been prepared hydrothermally at 160 degrees C by using neutral n-alkylamines as templates. Those C n A-BPO compounds were characterized by powder X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), thermogravimetric measurements, and differential thermal analysis (TG-DTA) as well as chemical analyses. Interestingly, these compounds may form a bilayer, a monolayer, or mixed state of bilayer and monolayer structures depending on the content of n-alkylamine. Linear relationships for both bilayer and monolayer compounds were observed between the interlayer distances and the numbers of carbon atoms in the n-alkylamine chain. The thickness of the inorganic layers, the arrangement of n-alkylamine in the interlayer space, and the composition of the compounds are proposed.     

Computational validation of the importance of absolute stereochemistry in virtual screening

Consideration of stereochemistry early in the identification and optimization of lead compounds can improve the efficiency and efficacy of the drug discovery process and reduce the time spent on subsequent drug development. These improvements can result by focusing on specific enantiomers that have the desired potential therapeutic effect (eutomers), while removing from consideration enantiomers that may have no, or even undesirable, effects (distomers). A virtual screening campaign that correctly takes stereochemical information into account can, in theory, be utilized to provide information about the relative binding affinities of enantiomers. Thus, the proper enumeration of the relevant stereoisomers in general, and enantiomeric pairs in particular, of chiral compounds is crucial if one is to use virtual screening as an effective drug discovery tool. As is obvious, in cases where no stereochemical information is provided for chiral compounds in a 2D chemical database, then each possible stereoisomer should be generated for construction of the subsequent 3D database to be used for virtual screening. However, acute problems can arise in 3D database construction when relative stereochemistry is encoded in a 2D database for a chiral compound containing multiple stereogenic atoms but absolute stereochemistry is not implied. In this case, we report that generation of enantiomeric pairs is imperative in database development if one is to obtain accurate docking results. A study is described on the impact of the neglect of enantiomeric pairs on virtual screening using the human homolog of murine double minute 2 (MDM2) protein, the product of a proto-oncogene, as the target. Docking in MDM2 with GLIDE 4.0 was performed using the NCI Diversity Set 3D database and, for comparison, a set of enantiomers we created corresponding to mirror image structures of the single enantiomers of chiral compounds present in the NCI Diversity Set. Our results demonstrate that potential lead candidates may be overlooked when databases contain 3D structures representing only a single enantiomer of racemic chiral compounds.     

Manual construction and mathematics- and computer-aided counting of stereoisomers. The example of oligoinositols

Two methods to obtain numbers of stereoisomers and of achiral stereoisomers of a given molecular structure are detailed on the example of di- and triinositols. The first method is manual exhaustive construction free of redundance of all stereoisomers, which is rendered feasible by symmetry considerations despite the large number of isomeric triinositols (82176). The second method is counting without constructing, made possible by use of a mathematical tool, the Cauchy-Frobenius lemma, which actually is a formalized manner of considering symmetry. The results are compared to those obtained by computer-aided stereoisomer generation using the program MOLGEN 3.5. It is demonstrated that in their results all three methods agree.     

Encoding the core electrons with graph concepts

The core electron problem of atoms in chemical graph studies has always been considered as a minor problem. Usually, chemical graphs had to encode just a small set of second row atoms, i.e., C, N, O, and F, thus, graph and, in some cases, pseudograph concepts were enough to "graph" encode the molecules at hand. Molecular connectivity theory, together with its side-branch the electrotopological state, introduced two "ad hoc" algorithms for the core electrons of higher-row atoms based, mainly, on quantum concepts alike. Recently, complete graphs, and, especially, odd complete graphs have been introduced to encode the core electrons of higher-row atoms. By the aid of these types of graphs a double-valued algorithm has been proposed for the valence delta, deltav, of any type of atoms of the periodic table with a principal quantum number n > or =2. The new algorithm is centered on an invariant suggested by the hand-shaking theorem, and the values it gives rise to parallel in some way the values derived by the aid of the two old "quantum" algorithms. A thorough comparative analysis of the newly proposed algorithms has been undertaken for atoms of the group 1A-7A of the periodic table. This comparative study includes the electronegativity, the size of the atoms, the first ionization energy, and the electron affinity. The given algorithm has also been tested with sequential complete graphs, while the even complete graphs give rise to conceptual difficulties. QSAR/QSPR studies do not show a clear-cut preference for any of the two values the algorithm gives rise to, even if recent results seem to prefer one of the two values.     

Algorithm for naming molecular equivalence classes represented by labeled pseudographs

The emergence of large chemical databases imposes a need for organizing the compounds in these databases. Mapping the chemical graph in particular, and a molecular equivalence class represented by a labeled pseudograph in general, to a unique number or string facilitates high-throughput browsing, grouping, and searching of the chemical database. Computing this number using a naming adaptation of the Morgan algorithm, we observed a large classification noise in which nonisomorphic graphs were mapped to the same number. Our extensions to that algorithm greatly reduced the classification noise.     

A molecular orbital study of the interactions of acrylic polymers with aluminum: Implications for adhesion

We present results of molecular orbital thory calculations of the interactions of acrylic polymers with aluminum, with a view toward understanding the nature of chemical bonding at the corresponding polymer-metal interfaces. The reported results are for the interactions of polymer model compounds with metal atoms (as opposed to our ongoing studies with metal surfaces). As such, the results relate to experimental studies where small dosages of metal atoms are evaporated onto polymer surfaces in pristine high vacuum environments. Our studies have been conducted within the theoretical framework of Hartree-Fock molecular orbital theory. We find that aluminum atoms interact primarily with the carbonyl group of acrylic polymers. The reaction proceeds by the metal atoms interacting with both the carbon and the oxygen atoms of the carbonyl functionality. This weakens the C?O bond. Finally, the carbonyl bond loses double bond character, and strong AL—O bonds are formed. Our results are compared to experimental data, and the implications of the detailed nature of bonding for adhesion applications are discussed.     

The signature molecular descriptor. 2. Enumerating molecules from their extended valence sequences

We present a new algorithm that enumerates molecular structures matching a predefined extended valence sequence or signature. The algorithm can construct molecular structures composed of about 50 non-hydrogen atoms in CPU seconds time scale. The algorithm is run to produce all molecular structures matching the binding affinities (IC(50)) of some HIV-1 protease inhibitors. The algorithm is also used to compute the degeneracy, or the number of molecular structures, corresponding to a given signature. Signature degeneracy is systematically studied for varying signature heights on four molecular series, alkanes, alcohols, fullerene-type structures, and peptides. Signature degeneracy is compared with similar results obtained with popular topological indices (TIs). As a general rule, we find that signature degeneracy decreases as the signature height increases. We also find that alkanes, alcohols, and fullerene-type structures comprising n non-hydrogen atoms are uniquely characterized by signatures of height n/4, while peptides up to 4000 amino acids can be singled out with signatures of heights as small as 2 and 3.     

Symmetry calculation for molecules and transition states

The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three‐dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label‐stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules. © 2014 Wiley Periodicals, Inc.     

The hydrogen perturbation in molecular connectivity computations

A new algorithm for the delta(v) number, the basic parameter of molecular connectivity indices, is proposed. The new algorithm, which is centered on graph concepts like complete graphs and general graphs, encodes the information of the bonded hydrogen on different atoms through a perturbation parameter that makes use of no new graph concepts. The model quality of the new algorithm is tested with 13 properties of seven different classes of compounds, as well as with composite classes of compounds with the same property and with composite properties of the same class of compounds. Chosen properties and classes of compounds display different percentage of bonded hydrogen atoms, which allow a checking of the importance of this parameter. A comparison is drawn with previous results with zero contribution for the hydrogen perturbation as well as among results obtained by changing the number of compounds of a property but keeping constant the percentage of hydrogen atoms. Results underline the importance of the property as well as the importance of the number of compounds in determining the level of the hydrogen perturbation. Molecular connectivity terms are in some cases more critical than the combination of indices in detecting the perturbation introduced by the hydrogen atoms.     

Crystal-Packing-Driven Enrichment of Atropoisomers

Crystal-packing forces can have a significant impact on the relative stabilities of different molecules and their conformations. The magnitude of such effects is, however, not yet well understood. Herein we show, that crystal packing can completely overrule the relative stabilities of different stereoisomers in solution. Heating of atropoisomers (i.e. “frozen-out” conformational isomers) in solution leads to complex mixtures. In contrast, solid-state heating selectively amplifies minor (<25 mole %) components of these solution-phase mixtures. We show that this heating strategy is successful for compounds with up to four rotationally hindered σ bonds, for which a single stereoisomer out of seven can be amplified selectively. Our results demonstrate that common supramolecular interactions—for example, [methyl⋅⋅⋅π] coordination and [C−H⋅⋅⋅O] hydrogen bonding—can readily invert the relative thermodynamic stabilities of different molecular conformations. These findings open up potential new avenues to control the folding of macromolecules.     

Halogenation of N-substituted <Emphasis Type="Italic">p</Emphasis>-quinone monoimines and <Emphasis Type="Italic">p</Emphasis>-quinone monooxime esters: VII. Halogenation of 4-aroyl(arylsulfonyl)imino- and 4-aroyl(arylsulfonyl)-oxyimino-2,6-diisopropylcyclohexa-2,5-dien-1-ones

Halogenation of 4-aroyl(arylsulfonyl)imino-2,6-diisopropylcyclohexa-2,5-dien-1-ones gave 4-aroyl-(arylsulfonyl)imino-3-halo-2,6-diisopropylcyclohexa-2,5-dien-1-ones and 4-aroyl(arylsulfonyl)imino-3,5,6-trihalo-2,6-diisopropylcyclohex-2-en-1-ones. The latter were formed as mixtures of two stereoisomers, and the isopropyl group on the sp ³-hybridized carbon atom in one stereoisomer occupies axial position, which is untypical of such compounds. Halogenation of 4-aroyl(arylsulfonyl)oxyimino-2,6-diisopropylcyclohexa-2,5-dien-1-ones leads to the formation of the corresponding addition products with traditional trans-diaxial arrangement of the halogen atoms.