Study on How Underlying Uncertainty in the Flux Values 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 [1]. 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 flux values affects the robustness of the model predictions and regulatory capabilities.

To study this question, we used a large-scale kinetic model and integrated fluxomics and metabolomics data [2, 3] describing the physiology for aerobically grown E. coli. Because of the under-determined nature of the system, there are infinite existing flux solutions within the selected operational configuration. To account for the flux variability within the designated operational configuration, we selected a reference vector of concentrations close to their nominal value. We used the ORACLE (optimization and risk analysis of complex living entities) framework to build populations of kinetic models [4, 5] that are consistent with the given physiology, while satisfying the stoichiometric and thermodynamic constraints. We next performed a systematic analysis of the effect that the flux profiles have on the robustness of the regulatory properties of the system. 

We used the mean PCA (principle component analysis) [6] value of the flux samples as reference when selecting flux profiles. Flux profiles across the main components of the PCA were studied. We used ORACLE to generate populations of kinetic models for these flux profiles. Then, we computed the distributions of their flux control coefficients (FCCs) along the dimensions with the highest variance. Finally, by comparing the changes among the distributions of the FCCs versus those corresponding to the reference flux profile, we were able to quantify the robustness of the regulatory predictions within a specific operational configuration.

References

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2.         McCloskey, D., et al., A model-driven quantitative metabolomics analysis of aerobic and anaerobic metabolism in E. coli K-12 MG1655 that is biochemically and thermodynamically consistent. Biotechnology and Bioengineering, 2014. 111(4): p. 803-815.

3.         Bennett, B.D., et al., Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli. Nat Chem Biol, 2009. 5(8): p. 593-599.

4.         Chakrabarti, A., et al., Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric, thermodynamic and physiological constraints. Biotechnology Journal, 2013. 8: p. 1043–1057.

5.         Miskovic, L. and V. Hatzimanikatis, Production of biofuels and biochemicals: in need of an {ORACLE}. Trends in Biotechnology, 2010. 28: p. 391 - 397.

6.         Jolliffe, I., Principal Component Analysis, in Wiley StatsRef: Statistics Reference Online. 2014, John Wiley & Sons, Ltd.