Landscape topography determines global stability and robustness of a metabolic network

Metabolic networks have gained broad attention in recent years as a result of their important roles in biological systems. However, how to quantify the global stability of the metabolic networks is still challenging. We develop a probabilistic landscape approach to investigate the global natures of the metabolic system under external fluctuations. As an example, we choose a model of the carbohydrate metabolism and the anaplerotic synthesis of oxalacetate in Aspergillus niger under conditions of citric acid accumulation to explore landscape topography. The landscape has a funnel shape, which guarantees the robustness of system under fluctuations and perturbations. Robustness ratio (RR), defined as the ratio of gap between lowest potential and average potential versus roughness measured by the dispersion or square root of variations of potentials, can be used to quantitatively evaluate the global stability of metabolic networks, and the larger the RR value, the more stable the system. Results of the entropy production rate imply that nature might evolve such that the network is robust against perturbations from environment or network wirings and performs specific biological functions with less dissipation cost. We also carried out a sensitivity analysis of parameters and uncovered some key network structure factors such as kinetic rates or wirings connecting the protein species nodes, which influence the global natures of the system. We found there is a strong correlation between the landscape topography and the input-output response. The more stable and robust the metabolic network is, the sharper the response is.