Measuring Structural Robustness of Metabolic Networks Under a Boolean Model Using Integer Programming and Feedback Vertex Sets

Robustness is one of the important features of living organisms. For example, many organisms have strong adaptability to environmental changes and many organisms can live even if some of their genes are mutated. Besides, it is considered that cancer cells are very robust and thus cancers are difficult to treat. Therefore, it is important to identify origins of robustness in various kinds of organisms. Though several methods have been proposed for measuring robustness in metabolic networks or signal transduction networks, most methods require large computation time or are not guaranteed to output optimal solutions. In this paper, we formalized the problem as an integer program, where an objective function is to minimize the number of reactions to be inactivated so that at least one of the target compounds cannot be synthesized. In order to cope with cycles and reversible reactions, we developed a novel integer programming formalization method using a feedback vertex set (FVS). When applied to an E. coli metabolic network consisting of Glycolysis/Glyconeogenesis, Citrate cycle and Pentose phosphate pathway obtained from KEGG database, we could find an optimal set of enzymes to be inactivated several times faster than a naive method.