Application of dynamic metabolic flux analysis for process modeling: Robust flux estimation with regularization, confidence bounds, and selection of elementary modes

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.

Development of a Dynamic Gray‐Box Model of a Fermentation Process for Spore Production

“…This is because once there is input-output-data for the submodels available, conventional input selection and model structure selection methods and parameter estimation approaches can be applied without having to consider the dynamics of the process. Using information about the metabolites of a cell, Hebing et al [9], estimate the values of the rates of cell internal reactions to analyze the suitability of a chosen set of reaction pathways for subsequent kinetic model development. This is based on the methodology of Leighty and Antoniewicz [13,14] called dynamic metabolic flux analysis (DMFA).…”

“…Besides the parameters of the model of the growth rate, the yield coefficient Y g is also optimized. This is contrast to some works based on DMFA, where these coefficients are computed from a metabolic network [9,13]. The parameter estimation problem is formulated as…”

“…Besides the parameters of the model of the growth rate, the yield coefficient Y g is also optimized. This is contrast to some works based on DMFA, where these coefficients are computed from a metabolic network 9, 13. The parameter estimation problem is formulated as …”

“…More recently, the combination of information about the metabolic network with a kinetic gray-box model was proposed by Hebing et al based upon the elementary modes (EM) of the metabolic network [8,9]. The evolution of the EM was first parameterized over time along the batch and then kinetic expressions were fitted to this evolution.…”

How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review

“…Based on extensions of Dynamic Metabolic Flux Analysis introduced in [76], that only uses concentration measurements and avoids any numerical differentiation, refs. [77,78] select reduced sets of EFMs via a geometrical reduction (excluding EFMs with a cosine-similarity algorithm) followed by a multi-objective genetic algorithm that minimizes the prediction error and the size of the EFMs subset. A linear optimization problem has been formulated in [79] for selecting the best subset of EFMs based on a relaxation criterion.…”