Quantifying Cellular Robustness in Genome-Scale Metabolic Reconstructions

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 robustness of metabolic networks by measuring their ability to tolerate random reaction (or gene) knockouts.

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 are known. We show that even in genome-scale metabolic networks the probability of (network) failure can be reliably estimated from minimal cut sets with lowest cardinalities. We demonstrate the applicability of our theory by analyzing the robustness of multiple Enterobacteriaceae and Blattabacteriaceae and show a dramatically low robustness for the latter. We find that robustness develops from the ability to proliferate in multiple growth environments consistent with experimentally found knowledge.

The probability of (network) failure provides thus a reliable and easily computable measure of robustness and redundancy in (genome-scale) metabolic networks.