Trade-off of dynamic fragility but not of robustness in metabolic pathways in silico

Selective robustness is a key feature of biochemical networks. It confers a fitness benefit to organisms living in dynamic environments. The (in-)sensitivity of a network to external perturbations results from the interplay between network dynamics, structure and enzyme kinetics. In this work, we focus on the subtle interplay between robustness and control (fragility). We describe a quantitative method for defining the fragility and robustness of system fluxes to perturbations. We find that for many mathematical models of metabolic pathways, the robustness of fluxes vis-a-vis perturbations of all the enzyme activities is captured by a broad distribution of the robustness coefficients. We find that in cases where a metabolic pathway flux is made less robust with respect to the perturbation of a particular network step, the average robustness may still be increased. We then show that fragility is conserved upon a perturbation of network processes and equate fragility with control as defined in metabolic control analysis. This highlights the non-intuitive nature of the interplay between fragility and robustness and the need for a dynamic network understanding.