Efficient extraction of mapping rules of atoms from enzymatic reaction data

Many computational problems and methods have been proposed for analysis of biological pathways. Among them, this paper focuses on extraction of mapping rules of atoms from enzymatic reaction data, which is useful for drug design, simulation of tracer experiments, and consistency checking of pathway databases. Most of existing methods for this problem are based on maximal common subgraph algorithms. In this paper, we propose a novel approach based on graph partition and graph isomorphism. We show that this problem is NP-hard in general, but can be solved in polynomial time for wide classes of enzymatic reactions. We also present an O(n(1.5)) time algorithm for a special but fundamental class of reactions, where n is the maximum size of compounds appearing in a reaction. We develop practical polynomial-time algorithms in which the Morgan algorithm is used for computing the normal form of a graph, where it is known that the Morgan algorithm works correctly for most chemical structures. Computational experiments are performed for these practical algorithms using the chemical reaction data stored in the KEGG/LIGAND database. The results of computational experiments suggest that practical algorithms are useful in many cases.