Analysis of Metabolic Pathways by Graph Transformation

Biochemical pathways, such as metabolic, regulatory, and signal transduction pathways, constitute complex networks of functional and physical interactions between molecular species in the cell. They are represented in a natural way as graphs, with molecules as nodes and processes as arcs. In particular, metabolic pathways are represented as directed graphs, with the substrates, products, and enzymes as nodes and the chemical reactions catalyzed by the enzymes as arcs. In this paper, chemical reactions in a metabolic pathway are described by edge relabeling graph transformation rules, as explicit chemical reactions and also as implicit chemical reactions, in which the substrate chemical graph, together with a minimal set of edge relabeling operations, determines uniquely the product chemical graph. Further, the problem of constructing all pathways that can accomplish a given metabolic function of transforming a substrate chemical graph to a product chemical graph using a set of explicit chemical reactions, is stated as the problem of finding an appropriate set of sequences of chemical graph transformations from the substrate to the product, and the design of a graph transformation system for the analysis of metabolic pathways is described, which is based on a database of explicit chemical reactions, a database of metabolic pathways, and a chemical graph transformation system.