How Uncertainty in Kinetic Parameters Affects Metabolic Control Analysis of Optimally Grown E. coli

Large-scale kinetic models of metabolism are essential for understanding and predicting the behavior of cellular systems when subject to perturbations. Despite the advances in experimental measurement technologies, the numerous parameters that are required to build kinetic models remain scarce and involve uncertainty. Even after incorporating the partially available experimental data, models still have many degrees of freedom. Due to this parametric uncertainty, some reactions are able to operate in forward and reverse directions. An operational configuration consists of reactions that operate in a unique direction. This flexibility results in the existence of alternative operational configurations representing the same physiology, with very distinct regulatory properties. In this study, we focus on one operational configuration and we investigate how the underlying uncertainty in the kinetic parameters affects the robustness of the model predictions and regulatory capabilities.

To study this question, we used a large-scale non-linear kinetic model built using integrated fluxomics and metabolomics data describing the physiology for aerobically grown E. coli. Because of the under-determined nature of the system, there are multiple kinetic parameters that can render the model feasible within the selected operational configuration. To account for the variability of the kinetic parameters within the designated operational configuration, we selected a reference vector of fluxes and concentrations close to their nominal values. Then, we used the ORACLE (optimization and risk analysis of complex living entities) framework to build populations of kinetic models that are consistent with the given physiology, while satisfying the stoichiometric and thermodynamic constraints. From these, we built non-linear models to test how the system’s response to perturbations changed with respect to the chosen kinetic parameters. This allowed us to quantify the effect of the uncertainty in the kinetic parameters on the robustness of the regulatory properties of the system.