Parameter Estimation in Dynamic Metabolic Networks with Advanced Mathematical Programming Techniques

Dynamic models for metabolic networks comprise a nonlinear differential algebraic system of equations, which arise from mass balances for metabolites and have a large number of kinetic parameters that require tuning for a specific growth condition. We have formulated a large-scale differential algebraic system representing a dynamic model for the Embden-Meyerhof-Parnas pathway, the phosphotransferase system and the pentose phosphate pathway of Escherichia coli, based on the model proposed by Chassagnole et al. (2002), as well as the fermentation reactions. The model comprises twenty three dynamic mass balance equations for extracellular glucose, intracellular metabolites and fermentation products, thirty five kinetic rate expressions and seven additional algebraic ones. Experimental data are taken from the literature for both intracellular and extracellular concentration profiles (Diaz Ricci et al., 1991). We have formulated a parameter estimation problem subject to the resulting differential algebraic system within a simultaneous optimization approach in which the DAE system is discretized by orthogonal collocation on finite elements. Within this framework, the resulting large-scale nonlinear programming problem is solved with a simultaneous approach (Biegler et al., 2002; Raghunathan et al., 2004) applying an Interior Point method with reduced successive quadratic programming techniques, within program IPOPT (Kameswaran and Biegler, 2006).

References

Diaz Ricci, J. C., Hitzmann, B., and Bailey, J. E. (1991) Biotechnol. Prog. 7, 305–310

Kameswaran, S., L.T. Biegler (2006), Simultaneous dynamic optimization strategies: Recent advances and challenges, Comp. Chem. Eng., 30, 1560.

Raghunathan A., M.S. Diaz, L.T. Biegler, 2004, An MPEC Formulation for Dynamic Optimization of Distillation Operations, Comp. Chem.Eng., 28, 2037.