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

Abstract

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.

Figure 1

Classical scheme of parameters identifiability procedures.

Figure 2

Numerical procedure proposed for parameter identifiability in metabolic networks.

Figure 3

Possibilities of numerical procedure for 3 parameters investigated; nP and nPSS represent, respectively, the number of parameters and the number of succeeded selected parameters.

Figure 4

Escherichia coli central carbon metabolism [2].

Figure 5

Collinearity angles among sensitivity vectors b _θi and b _θj for all parameters of the E. coli K-12 W3110 metabolic networks.

Figure 6

Experimental and predicted metabolites concentrations as function of the time: (○) experimental value, (-▲-) predicted value using initial estimates, and (-●-) predicted value after parameter identifiability using model of E. coli K-12 W3110 metabolic networks.

Box 1

Sequence proposed for modeling metabolic systems, based on Wiechert and Graaf [35] and Steuer and Junker [1].