Design of Stable Large-Scale Metabolic Networks

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

Computer Aided Chemical Engineering

Elsevier

Lugar: Amsterdam; Año: 2009 vol. 27 p. 1755 - 1760

1570-7946

Metabolic network design can be formulated as an optimization problem aimed at optimizing a given objective, for example the production of a certain metabolite, subject to mass balance equations in the network. Kinetic metabolic network models allow the analysis of stability of the predicted states, which is of fundamental importance as biological systems may exhibit not only monotonic stable states but also bistable switching threshold phenomena, oscillations and chaotic behavior. In E. coli, multistability and oscillations have been observed in strains modified for different objectives. Due to the nonlinear kinetics of the biochemical reactions and their coupling through common metabolites, biological systems may undergo drastic changes in their qualitative behavior when a variation of the enzyme levels occurs. If no stability constraints are included 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-for-stability problem, an important sub problem of the general design-for-operability problem, has motivated many contributions from the process systems engineering community. The proposed strategies have been applied mainly to the design of open-loop stable chemical processes since it is traditional wisdom to avoid operation at open-loop unstable regions due to operability and safety reasons. In order to include stability considerations within the network design formulation different strategies have been reported (Chang and Sahinidis, 2004, Matallana et al., 2006). In this work, we propose an eigenvalue optimization approach (Matallana et al. 2008) 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 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 nonlinear optimization problem, corresponding to steady state equations and additional stability constraints, has been solved with reduced space Successive Quadratic Programming techniques within program IPOPT (Biegler et al., 2002). Numerical results provide useful insights on the stability properties of the kinetic model describing the metabolism of E. coli.