Abstract:-The purpose of this paper is to report on the development of a procedure for inferring black-box, yet biologically interpretable, dynamic models of bioprocesses based on sets of measurements of a few external components (biomass, substrates, and products of interest). The procedure has three main steps: (a) the determination of the number of macroscopic biological reactions linking the measured components; (b) the estimation of a first reaction scheme, which has interesting mathematical properties, but might … Show more
“…Alternative modeling approaches use empirical qualitative reaction schemes as macro reactions and fit the corresponding stoichiometric coefficients to data (Herold & King, 2014; Mailier & Wouwer, 2009). The complexity of these models is comparable with the complexity of models which use EM as macro reactions, as internal balances and reactions are lumped onto a few macroscopic pathways.…”
In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745–755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed‐batch process. From measurements of six fed‐batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.
“…Alternative modeling approaches use empirical qualitative reaction schemes as macro reactions and fit the corresponding stoichiometric coefficients to data (Herold & King, 2014; Mailier & Wouwer, 2009). The complexity of these models is comparable with the complexity of models which use EM as macro reactions, as internal balances and reactions are lumped onto a few macroscopic pathways.…”
In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745–755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed‐batch process. From measurements of six fed‐batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.
“…Some methods for the objective determination of macroscopic reaction scheme and stoichiometric identification have been developed [2][3][4][5][6][7][8] while the determination of the kinetic structure seems to remain based on arbitrary choices. Indeed, there exists in the literature a profusion of apparently equivalent laws allowing the description of specific kinetic phenomena (e.g.…”
This study presents an effective procedure for the determination of a biologically inspired, black-box model of cultures of microorganisms (including yeasts, bacteria, plant and animal cells) in bioreactors. This procedure is based on sets of experimental data measuring the time-evolution of a few extracellular species concentrations, and makes use of maximum likelihood principal component analysis to determine, independently of the kinetics, an appropriate number of macroscopic reactions and their stoichiometry. In addition, this paper provides a discussion of the geometric interpretation of a stoichiometric matrix and the potential equivalent reaction schemes. The procedure is carefully evaluated within the stoichiometric identification framework of the growth of the yeast Kluyveromyces marxianus on cheese whey. Using Monte Carlo studies, it is also compared with two other previously published approaches.
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