Extraction of Correlated Gene Clusters from Multiple Graph Structures: Theory

Abstract

Correlated gene cluster. With respect to an organism whose genome sequence has been determined, we can totally order all the genes along the genome sequence. Besides such geometrical relationships among genes, similarity relationships based on ORF sequences or 3D structures, functional relationships with respect to a metabolic/regulatory pathway or degree of co-expression, and so on can be denoted by using a set of binary relationships in a general manner. Each set of binary relationships forms a graph structure called an adjacency graph of genes as a whole. Fig. 1 shows three adjacency graphs G1 (genome), G2 (pathway), and G3 (co-expression). Each graph node corresponds to a gene, and two nodes are connected by an edge (expressed by a solid line) when they are related by the binary relationship. When a set of such adjacency graphs is given, finding a set of genes is attracting interest where all or most of the genes reserve their mutual relationships in multiple adjacency graphs (e.g., the light gray nodes and the dark gray nodes in Fig. 1). We call such a set of genes a correlated gene cluster.