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In our previous study, we showed that the branching process approximation isuseful for estimating metabolic robustness, measured using the impact degree.By applying a theory of random family forests, we here extend the branchingprocess approximation to consider the knockout of {\it multiple} reactions,inspired by the importance of multiple knockouts reported by recentcomputational and experimental studies. In addition, we propose a betterdefinition of the number of offspring of each reaction node, allowing for animproved estimation of the impact degree distribution obtained as a result of asingle knockout. Importantly, our proposed approach is also applicable tomultiple knockouts. The comparisons between theoretical predictions andnumerical results using real-world metabolic networks demonstrate the validityof the modeling based on random family forests for estimating the impact degreedistributions resulting from the knockout of multiple reactions.

Theoretical estimation of metabolic network robustness against multiple reaction knockouts using branching process approximation