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

TL;DR

This paper extends the branching process approximation to estimate the robustness of metabolic networks against multiple reaction knockouts, providing a theoretical framework validated by real-world network data.

Contribution

It introduces a novel extension of the branching process method to multiple knockouts and proposes an improved offspring definition for better impact degree estimation.

Findings

Theoretical predictions align well with numerical results on real metabolic networks.

The approach effectively estimates impact degree distributions for multiple knockouts.

The method enhances understanding of metabolic network robustness.

Abstract

In our previous study, we showed that the branching process approximation is useful for estimating metabolic robustness, measured using the impact degree. By applying a theory of random family forests, we here extend the branching process approximation to consider the knockout of {\it multiple} reactions, inspired by the importance of multiple knockouts reported by recent computational and experimental studies. In addition, we propose a better definition of the number of offspring of each reaction node, allowing for an improved estimation of the impact degree distribution obtained as a result of a single knockout. Importantly, our proposed approach is also applicable to multiple knockouts. The comparisons between theoretical predictions and numerical results using real-world metabolic networks demonstrate the validity of the modeling based on random family forests for estimating the impact degree distributions resulting from the knockout of multiple reactions.