Dimerization and bifunctionality confer robustness to the isocitrate dehydrogenase regulatory system in Escherichia coli

An important goal of systems biology is to develop quantitative models that explain how specific molecular features give rise to systems-level properties. Metabolic and regulatory pathways that contain multifunctional proteins are especially interesting to study from this perspective because they have frequently been observed to exhibit robustness: the ability for a system to perform its proper function even as levels of its components change. In this study, we use extensive biochemical data and algebraic modeling to develop and analyze a model that shows how robust behavior arises in the isocitrate dehydrogenase (IDH) regulatory system of Escherichia coli, which was shown in 1985 to experimentally exhibit robustness. E. coli IDH is regulated by reversible phosphorylation catalyzed by the bifunctional isocitrate dehydrogenase kinase/phosphatase (IDHKP), and the level of IDH activity determines whether carbon flux is directed through the glyoxylate bypass (for growth on two-carbon substrates) or the full tricarboxylic acid cycle. Our model, which incorporates recent structural data on IDHKP, identifies several specific biochemical features of the system (including homodimerization of IDH and bifunctionality of IDHKP) that provide a potential explanation for robustness. Using algebraic techniques, we derive an invariant that summarizes the steady-state relationship between the phospho-forms of IDH. We use the invariant in combination with kinetic data on IDHKP to calculate IDH activity at a range of total IDH levels and find that our model predicts robustness. Our work unifies much of the known biochemistry of the IDH regulatory system into a single quantitative framework and highlights the importance of constructing biochemically realistic models in systems biology.