Design of a large-scale E. coli network under stability constraints

JIMENA ANDREA DI MAGGIO; ANÍBAL BLANCO; JOSÉ ALBERTO BANDONI; MARÍA SOLEDAD DÍAZ

Buenos Aires

Congreso; ALIO-INFORMS Joint International Meeting; 2010

Metabolic network design can be formulated as an optimization problem aimed at optimizing a given objective typically the production of a certain metabolite, subject to mass balance equations in the network. Kinetic metabolic network models allow the analysis of the stability of the predicted equilibriums, which is of fundamental importance since biological systems may exhibit complex nonlinear behavior including steady state multiplicity, bifurcations and even chaos. Therefore, if no stability issues are considered in the formulation, the optimal operating point might result unstable, making the network vulnerable to external disturbances. In other words, in the face of even modest disturbances, an unstable network will reach physiological constraints and collapse. The design problem with stability constraints has been largely addressed by the process systems engineering community since it is traditional wisdom to avoid the operation of complex chemical processes at open-loop unstable equilibriums. Such ideas have been extended in the last years to address the biological network design problem (Chang and Sahinidis, 2004, Matallana et al.,2006). Recently Di Maggio et al. (2009) proposed an eigenvalue optimization approach (Blanco and Bandoni, 2007) to ensure steady state stability of the Embden-Meyerhof-Parnas pathway, the pentose-phosphate pathway and phosphotranferase system of Escherichia coli K-12 W3110 (Chassagnole et al. 2002). The studied model consists of eighteen differential equations that represent dynamic mass balances of extracellular glucose and intracellular metabolites, thirty kinetic rate expressions and seven additional algebraic equations for co-metabolites and involves around one hundred parameters (Di Maggio et al., 2008). The analyzed objective function was the serine production. In this work the adopted eigenvalue optimization approach is applied to an extended version of the network which includes the ethanol production pathway. Such sub-system significantly increases the model complexity since it introduces eight additional dynamic equations and forty one parameters. Serine and ethanol productions are considered as the objective functions of the proposed design problem. Evidence of the robustness of the calculated equilibriums is shown by dynamic simulation of the resulting network.