A comparative study of proteomics maps using graph theoretical biodescriptors

This paper reports the development of new methods for mathematical characterization of effects of different toxic agents on the cellular proteome. We describe numerical characterization of proteomics maps based on mathematical invariants. A graph is first associated with a proteomics map by considering partial ordering of spots on 2-D gels by ordering proteins with respect to the mass and the charge, the two properties by which proteins are separated. The graph is then embedded over the map, and several graph theoretical invariants have been constructed. In particular we consider invariants that can be extracted from the Euclidean distance-adjacency matrix of the embedded graph, in which only Euclidean distances between adjacent vertices of a graph are considered. The approach is illustrated using proteomics patterns of normal liver cells of rats and those derived from liver cells of animals exposed to four peroxisome proliferators. In contrast to direct comparison of spot abundance our approach incorporates information on spots locations. The difference between the two approaches is that in the first case only changes in abundances are considered as a measure of perturbation of the proteome map, but in the second case not only the charge but also the mass of proteins are used for ordering protein spots.     

Novel shape descriptors for molecular graphs.

We report on novel graph theoretical indices which are sensitive to the shapes of molecular graphs. In contrast to the Kier's kappa shape indices which were based on a comparison of a molecular graph with graphs representing the extreme shapes, the linear graph and the "star" graph, the new shape indices are obtained by considering for all atoms the number of paths and the number of walks within a graph and then making the quotients of the number of paths and the number of walks the same length. The new shape indices show much higher discrimination among isomers when compared to the kappa shape indices. We report the new shape indices for smaller alkanes and several cyclic structures and illustrate their use in structure-property correlations. The new indices offer regressions of high quality for diverse physicochemical properties of octanes. They also have lead to a novel classification of physicochemical properties of alkanes.