Application of Dynamic Metabolic Flux Analysis for Process Modeling: Robust Flux Estimation with Regularization, Confidence Bounds and Selection of Elementary Modes

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) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly in order 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 stoichiometric model, the DMFA for EM method is combined with a multi-objective genetic algorithm (GA). The method is applied to real data from a CHO fed-batch process. From measurements of 6 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. This article is protected by copyright. All rights reserved.