Characterization and comparison of Escherichia coli transfer RNAs by graph theory based on secondary structure

We have developed a model to characterize the tRNA structures of Escherichia coli using graph theory. First of all, tRNAs were represented as graphs, whose vertices correspond to nucleotides and the edges to phosphodiester and hydrogen bond linkages. Vertices and edges were weighted using the results of a preliminary quantum study of the nucleotides and the possible coupling between pair bases using the semiempirical method AM1. For each vertex, we defined a nucleotide valence that measures the capability of forming hydrogen bonds. Edges were differentiated by using bond orders. We have proposed weighted structural descriptors-closely related to molecular Randic connectivity and Balaban distance indices-as a distinctive characteristic of each structure. Molecules were characterized by a set of weighted structural descriptors and classified by a clustering method and discriminant function analysis. Two main groups of tRNAs that correspond to the biosynthetic amino acid pathways, in agreement with Wong's coevolution theory of the genetic code, were obtained.