Homomorphisms of Multisource Trees into Networks with Applications to Metabolic Pathways

Network mapping is a convenient tool for comparing and exploring biological networks; it can be used for predicting unknown pathways, fast and meaningful searching of databases, and potentially establishing evolutionary relations. Unfortunately, existing tools for mapping paths into general networks (PathBlast) or trees into tree networks allowing gaps (MetaPathwayHunter) cannot handle large query pathways or complex networks. In this paper we consider homomorphisms, i.e., mappings allowing to map different enzymes from the query pathway into the same enzyme from the networks. Homomorphisms are more general than homeomorphism (allowing gaps) and easier to handle algorithmically. Our dynamic programming algorithm efficiently finds the minimum cost homomorphism from a multisource tree to directed acyclic graphs as well as general networks. We have performed pairwise mapping of all pathways for four organisms (E. coli, S. cerevisiae, B. subtilis and T. thermophilus species) and found a reasonably large set of statistically significant pathway similarities. Further analysis of our mappings identifies conserved pathways across examined species and indicates potential pathway holes in existing pathway descriptions.