Protein Sequence Comparison and DNA-binding Protein Identification with Generalized PseAAC and Graphical Representation

Li, Chun; Zhao, Jialing; Wang, Changzhong; Yao, Yuhua

In this section, we give a numerical characterization of a protein sequence that will facilitate quantitative comparisons of protein sequences. As is known, once a graphical representation is given, it can be transformed into some structural matrices, such as the matrices ED, GD, M/M, and L/L [6, 24, [29] [30] [31] [32] [33] [34] [35] [36] [37] . Here we employ the L/L matrix. L/L is a nonnegative symmetric matrix whose off-diagonal entries are defined as a quotient of the Euclidean distance between two vertices of the graph and the sum of geometrical lengths of edges between the two vertices. By definition all diagonal elements are zero. Obviously, the entries in a L/L matrix are less than or equal to one. The higher order k L/ k L matrix is the matrix whose (i,j)-entry is . As the exponent k approaches positive infinity, k L/ k L converges to a (0,1) matrix (denoted by b L/ b L). With respect to the proposed 2-D graph, [ b L/ b L] ij =1 if and only if the two corresponding vertices lie on a straight line in the curve, including the cases of adjacency and non-adjacency. In this sense, we call such a matrix a geometric line adjacency matrix (GLAM), or simply a generalized adjacency matrix (GAM), generated by a graph, and denote it by .