The elucidation of metabolic pathways and their improvements using stable optimization of large-scale kinetic models of cellular systems.

Metabolic engineering of cellular systems to maximize reaction fluxes or metabolite concentrations still presents a significant challenge by encountering unpredictable instabilities that can be caused by simultaneous or consecutive enhancements of many reaction steps. It can therefore be important to select carefully small subsets of key enzymes for their subsequent stable modification compatible with cell physiology. To address this important problem, we introduce a general mixed integer non-linear problem (MINLP) formulation to compute automatically which enzyme levels should be modulated and which enzyme regulatory structures should be altered to achieve the given optimization goal using non-linear kinetic models of relevant cellular systems. The developed MINLP formulation directly employs a stability analysis constraint and also includes non-linear biophysical constraints to describe homeostasis conditions for metabolite concentrations and protein machinery without any preliminary model simplification (e.g. linlog kinetics approximation). The framework is demonstrated on a well-established large-scale kinetic model of the Escherichia coli central metabolism used for the optimization of the glucose uptake through the phosphotransferase transport system (PTS) and serine biosynthesis. Computational results show that substantial stable improvements can be predicted by manipulating only small subsets of enzyme levels and regulatory structures. This means that while more efforts can be required to elucidate larger stable optimal enzyme level/regulation choices, no further significant increase in the optimized fluxes can be obtained and, therefore, such choices may not be worth the effort due to the potential loss of stability properties. The source for instability through saddle-node and Hopf bifurcations is identified, and all results are contrasted with predictions from metabolic control analysis.