Complex graph matrix representations and characterizations of proteomic maps and chemically induced changes to proteomes

We have presented a complex graph matrix representation to characterize proteomics maps obtained from 2D-gel electrophoresis. In this method, each bubble in a 2D-gel proteomics map is represented by a complex number with components which are charge and mass. Then, a graph with complex weights is constructed by connecting the vertices in the relative order of abundance. This yields adjacency matrices and distance matrices of the proteomics graph with complex weights. We have computed the spectra, eigenvectors, and other properties of complex graphs and the Euclidian/graph distance obtained from the complex graphs. The leading eigenvalues and eigenvectors and, likewise, the smallest eigenvalues and eigenvectors, and the entire graph spectral patterns of the complex matrices derived from them yield novel weighted biodescriptors that characterize proteomics maps with information of charge and masses of proteins. We have also applied these eigenvector and eigenvalue maps to contrast the normal cells and cells exposed to four peroxisome proliferators, namely, clofibrate, diethylhexyl phthalate (DEHP), perfluorodecanoic acid (PFDA), and perfluoroctanoic acid (PFOA). Our complex eigenspectra show that the proteomic response induced by DEHP differs from the corresponding responses of other three chemicals consistent with their chemical structures and properties.