Exact quantification of cellular robustness in genome-scale metabolic networks

Motivation: Robustness, the ability of biological networks to uphold their functionality in spite of perturbations, is a key characteristic of all living systems. Although several theoretical approaches have been developed to formalize robustness, it still eludes an exact quantification. Here, we present a rigorous and quantitative approach for the structural robustness of metabolic networks by measuring their ability to tolerate random reaction (or gene) knockouts. Results: In analogy to reliability theory, based on an explicit consideration of all possible knockout sets, we exactly quantify the probability of failure for a given network function (e.g. growth). This measure can be computed if the network's minimal cut sets (MSCs) are known. We show that even in genome-scale metabolic networks the probability of (network) failure can be reliably estimated from MSCs with lowest cardinalities. We demonstrate the applicability of our theory by analyzing the structural robustness of multiple Enterobacteriaceae and Blattibacteriaceae and show a dramatically low structural robustness for the latter. We find that structural robustness develops from the ability to proliferate in multiple growth environments consistent with experimentally found knowledge. Conclusion: The probability of (network) failure provides thus a reliable and easily computable measure of structural robustness and redundancy in (genome-scale) metabolic networks.