Abstract
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.
Highlights
For model‐based optimization of fermentation processes, for example, for process design or control, simple dynamic models which are accurate enough to predict the process behavior under varying conditions are needed (Frahm et al, 2002; Neddermeyer, Rossner, & King, 2015; Teixeira, Alves, Alves, Carrondo, & Oliveira, 2007).Essential elements of models of fermentation processes are the stoichiometry of the biochemical conversion and the dependency of the reaction rates on the process conditions
We present methods for the analysis and selection of elementary modes (EM) for process modeling where measurement data is used directly: A method for the analysis of EM reaction rates is presented which is based on the approach for dynamic metabolic flux analysis (DMFA) by Leighty and Antoniewicz (2011) for the computation of internal flux distributions of a metabolic network
This paper presents methods for the selection of small sets of EMs and for the estimation of reaction rates from noisy concentration measurements
Summary
For model‐based optimization of fermentation processes, for example, for process design or control, simple dynamic models which are accurate enough to predict the process behavior under varying conditions are needed (Frahm et al, 2002; Neddermeyer, Rossner, & King, 2015; Teixeira, Alves, Alves, Carrondo, & Oliveira, 2007). Essential elements of models of fermentation processes are the stoichiometry of the biochemical conversion and the dependency of the reaction rates on the process conditions. For the derivation of efficient models—efficient meaning sufficiently accurate with predictive capabilities but not overly complex—the usage of small metabolic networks at steady state (Nolan & Lee, 2011) or selections of elementary modes (EM) as macro reactions (Gao, Gorenflo, Scharer, & Budman, 2007; Provost, 2006; Soons, Ferreira, & Rocha, 2011; Teixeira et al, 2007) have been shown to be a powerful approaches. Formal kinetics or black‐box models like multilayer perceptron networks (MLP) can be used to model the dependency of the reaction rates of the EM on the process conditions or on the concentrations of species in the reactor
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