In systems biology, identifying vital functions like glycolysis from a given metabolic pathway is important to understand living organisms. In this paper, we focus on the problem of finding minimal sub-pathways producing target metabolites from source metabolites. We translate laws of biochemical reactions into propositional formulas and compute its minimal models to solve the problem. An advantage of our method is that it can treat reversible reactions. Moreover the translation enables us to obtain solutions for large pathways. We apply our method to a whole Escherichia coli metabolic pathway. As a result, we have found the conventional glycolysis sub-pathway described in a biological database EcoCyc.
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