The multiple alignment algorithm for metabolic pathways without abstraction

Computational problems associated with metabolic pathways have been extensively studied in computational biology. The problem of aligning multiple metabolic pathways is very challenging. Tohsato et al.'s algorithm for aligning multiple metabolic pathways is based on similarities between enzymes, however, a metabolic pathway consists of three types of entities: reactions, compounds, and enzymes. In this paper, we propose the first algorithm for the problem of aligning multiple metabolic pathways based on the similarities among reactions, compounds, enzymes, and pathway topology. First, we compute a weight between each pair of like entities in different input pathways based on the entities' similarity score and topological structure using the methods by Ferhat Ay et al.. We then construct a weighted k-partite graph for the reactions, compounds, and enzymes. We extract a mapping between these entities by solving the maximum-weighted k-partite matching problem by applying a novel heuristic algorithm. By analyzing the alignment results of multiple pathways in different organisms, we show that the alignments found by our algorithm correctly identify common sub networks among multiple pathways.