On 3-D graphical representation of proteomics maps and their numerical characterization

We consider numerical characterization of proteomics maps by representing a map as a three-dimensional graphical object based on x, y coordinates of the spots and using their relative abundance as the z coordinate. In our representation the protein spots are first ordered based on their relative abundance and labeled accordingly. In the next step a 3-D path is constructed connecting spots having adjacent labels. Finally a matrix is constructed by assigning to each pairs of labels (i, j) matrix element, the numerical value of which is based on the quotients of the Euclidean distance and the distance along the 3-D zigzag between the two points. The approach has been illustrated on a fragment of a proteomics map and compared with 2-D graphical representation of proteomics maps.     

Partitioning of <Emphasis Type="Italic">π</Emphasis> -electrons in rings of polycyclic conjugated hydrocarbons: Part 6. Comparison with other methods for estimating the local aromaticity of rings in polycyclic benzenoids

By adopting the convention that shared double bonds in polycyclic conjugated hydrocarbons contribute with one -electron and unshared ones with two -electrons, a partition of -electrons in each ring (-electron content, EC) can be obtained by averaging over all Kekulé structures, which are assumed to have equal weights. This affords a simple measure of local aromaticity that is comparable with other such local aromaticity indices in polycyclic benzenoids.     

Novel matrix invariants for characterization of changes of proteomics maps

Previous studies on mathematical characterization of proteomics maps by sets of map invariants were based on the construction of a set of distance-related matrices obtained by matrix multiplication of a single matrix by itself. Here we consider an alternative characterization of proteomics maps based on a set of matrices characterizing local features of an embedded zigzag curve over the map. It is shown that novel invariants can well characterize proteomics maps. Advantages of the novel approach are discussed.     

Algorithm for coding DNA sequences into "spectrum-like" and "zigzag" representations

An algorithm for encoding long strings of building blocks, like 4 DNA bases (adenine-A, cytosine-C, thymine-T, and guanidine-G), 20 natural amino acids (from Alanine Ala to Valine-Val, plus the stop triplet), or all 64 possible base triplets (from AAA to TTT), into "zigzag" or "spectrum-like" representations is suggested. The new encoding scheme can be derived in the 3-, 2-, or 1-dimensional form depending on the user's wishes. The only information, besides the string for which the "spectrum-like" representation is sought, is the initial positioning of the complete set of units from which the string is composed, i.e., four positions for A, C, G, and T, or 20 positions for natural amino acids plus stop, etc. This initial positioning can be initialized in either the 3-, 2-, or 1-D form. As an illustration of the suggested encoding scheme of the visual and chemometric comparison of the first 10 exon strings of the beta globin gene of 10 different species, each string consisting of about 100 basic amino acids long is shown.     

π-Electron currents in fixed π-sextet aromatic benzenoids

In view of different patterns of π-electron density currents in benzenoid aromatic compounds it is of interest to investigate the pattern of ring currents in various classes of compounds. Recently such a study using a graph theoretical approach to calculating CC bond currents was reported for fully benzenoid hydrocarbons, that is, benzenoid hydrocarbons which have either π-sextets rings or “empty” rings in the terminology of Clar. In this contribution we consider π-electron currents in benzenoid hydrocarbons which have π-electron sextets and C=C bonds fully fixed. Our approach assumes that currents arise from contributions of individual conjugated circuits within the set of Kekulé valence structures of these molecules.     

A convenient oxazole C-2 protecting group: the synthesis of 4- and 5-substituted oxazoles via metalation of 2-triisopropylsilyloxazoles

[reaction: see text] Metalation of oxazoles at the 4 and 5 position was achieved after regioselective C-2 silyl protection. Removal of the protecting group was then accomplished under mild conditions allowing for a straightforward preparation of C-5 monosubstituted and C-4,5 disubstituted oxazoles. The first practical C-2 protecting group of oxazoles has been demonstrated.