Finding Minimal Reaction Sets in Large Metabolic Pathways

In systems biology, identifying vital functions like glycolysis from a given metabolic pathway is important to understand living organisms. In this paper, we particularly focus on the problem of finding minimal sub-pathways producing target metabolites from source metabolites. We represent laws of biochemical reactions in propositional formulas and use a minimal model generator based on a state-of-the-art SAT solver. An advantage of our method is that it can treat reversible reactions represented in cycles. Moreover recent advances of SAT technologies enables us to obtain solutions for large pathways. We have applied our method to a whole Escherichia coli metabolic pathway. As a result, we found 5 sets of reactions including the conventional glycolysis sub-pathway described in a biological database EcoCyc.