Cells show remarkable resilience against genetic and environmental perturbations. However, its evolutionary origin remains obscure. In order to leverage methods of systems biology for examining cellular robustness, a computationally accessible way of quantification is needed. Here, we present an unbiased metric of structural robustness in genome-scale metabolic models based on concepts prevalent in reliability engineering and fault analysis. The probability of failure (PoF) is defined as the (weighted) portion of all possible combinations of loss-of-function mutations that disable network functionality. It can be exactly determined if all essential reactions, synthetic lethal pairs of reactions, synthetic lethal triplets of reactions etc. are known. In theory, these minimal cut sets (MCSs) can be calculated for any network, but for large models the problem remains computationally intractable. Herein, we demonstrate that even at the genome scale only the lowest-cardinality MCSs are required to efficiently approximate the PoF with reasonable accuracy. Building on an improved theoretical understanding, we analysed the robustness of 489 E. coli, Shigella, Salmonella, and fungal genome-scale metabolic models (GSMMs). In contrast to the popular “congruence theory”, which explains the origin of genetic robustness as a byproduct of selection for environmental flexibility, we found no correlation between network robustness and the diversity of growth-supporting environments. On the contrary, our analysis indicates that amino acid synthesis rather than carbon metabolism dominates metabolic robustness.

细胞对遗传和环境扰动表现出卓越的恢复能力。然而，它的进化起源仍然不清楚。为了利用系统生物学方法来检查细胞的稳健性，需要一种可计算的量化方法。在这里，我们基于可靠性工程和故障分析中普遍存在的概念，提出了基因组规模代谢模型中结构鲁棒性的无偏度量。失败概率 (PoF) 定义为禁用网络功能的功能丧失突变的所有可能组合的（加权）部分。如果已知所有基本反应、合成致死反应对、合成致死反应三联体等，则可以准确确定。理论上，可以为任何网络计算这些最小割集（MCS），但对于大型模型，该问题在计算上仍然难以解决。在此，我们证明，即使在基因组规模上，也只需要最低基数 MCS 即可以合理的精度有效地近似 PoF。基于改进的理论理解，我们分析了 489种大肠杆菌、志贺氏菌、沙门氏菌和真菌基因组规模代谢模型 (GSMM) 的稳健性。流行的“一致性理论”将遗传稳健性的起源解释为环境灵活性选择的副产品，与此相反，我们发现网络稳健性与支持增长的环境多样性之间没有相关性。相反，我们的分析表明氨基酸合成而不是碳代谢主导着代谢稳健性。