Design of stable metabolic networks.

In this work, we propose eigenvalue optimization combined with Lyapunov theory concepts to ensure stability of the Embden-Meyerhof-Parnas pathway, the pentose-phosphate pathway, the phosphotransferase system and fermentation reactions of Escherichia coli. We address the design of a metabolic network for the maximization of different metabolite production rates. The first case study focuses on serine production, based on a model that consists of 18 differential equations corresponding to dynamic mass balances for extracellular glucose and intracellular metabolites, and thirty kinetic rate expressions. A second case study addresses the design problem to maximize ethanol production, based on a dynamic model that involves mass balances for 25 metabolites and 38 kinetic rate equations. The nonlinear optimization problem including stability constraints has been solved with reduced space Successive Quadratic Programming techniques. Numerical results provide useful insights on the stability properties of the studied kinetic models.

Modeling phytoplankton community in reservoirs. A comparison between taxonomic and functional groups-based models.

In this paper we address the formulation of two mechanistic water quality models that differ in the way the phytoplankton community is described. We carry out parameter estimation subject to differential-algebraic constraints and validation for each model and comparison between models performance. The first approach aggregates phytoplankton species based on their phylogenetic characteristics (Taxonomic group model) and the second one, on their morpho-functional properties following Reynolds' classification (Functional group model). The latter approach takes into account tolerance and sensitivity to environmental conditions. The constrained parameter estimation problems are formulated within an equation oriented framework, with a maximum likelihood objective function. The study site is Paso de las Piedras Reservoir (Argentina), which supplies water for consumption for 450,000 population. Numerical results show that phytoplankton morpho-functional groups more closely represent each species growth requirements within the group. Each model performance is quantitatively assessed by three diagnostic measures. Parameter estimation results for seasonal dynamics of the phytoplankton community and main biogeochemical variables for a one-year time horizon are presented and compared for both models, showing the functional group model enhanced performance. Finally, we explore increasing nutrient loading scenarios and predict their effect on phytoplankton dynamics throughout a one-year time horizon.

Simultaneous parameters identifiability and estimation of an E. coli metabolic network model.

This work proposes a procedure for simultaneous parameters identifiability and estimation in metabolic networks in order to overcome difficulties associated with lack of experimental data and large number of parameters, a common scenario in the modeling of such systems. As case study, the complex real problem of parameters identifiability of the Escherichia coli K-12 W3110 dynamic model was investigated, composed by 18 differential ordinary equations and 35 kinetic rates, containing 125 parameters. With the procedure, model fit was improved for most of the measured metabolites, achieving 58 parameters estimated, including 5 unknown initial conditions. The results indicate that simultaneous parameters identifiability and estimation approach in metabolic networks is appealing, since model fit to the most of measured metabolites was possible even when important measures of intracellular metabolites and good initial estimates of parameters are not available.