Novel column generation-based optimization approach for poly-pathway kinetic model applied to CHO cell culture.

Mathematical modelling can provide precious tools for bioprocess simulation, prediction, control and optimization of mammalian cell-based cultures. In this paper we present a novel method to generate kinetic models of such cultures, rendering complex metabolic networks in a poly-pathway kinetic model. The model is based on subsets of elementary flux modes (EFMs) to generate macro-reactions. Thanks to our column generation-based optimization algorithm, the experimental data are used to identify the EFMs, which are relevant to the data. Here the systematic enumeration of all the EFMs is eliminated and a network including a large number of reactions can be considered. In particular, the poly-pathway model can simulate multiple metabolic behaviors in response to changes in the culture conditions. We apply the method to a network of 126 metabolic reactions describing cultures of antibody-producing Chinese hamster ovary cells, and generate a poly-pathway model that simulates multiple experimental conditions obtained in response to variations in amino acid availability. A good fit between simulated and experimental data is obtained, rendering the variations in the growth, product, and metabolite uptake/secretion rates. The intracellular reaction fluxes simulated by the model are explored, linking variations in metabolic behavior to adaptations of the intracellular metabolism.

Poly-pathway model, a novel approach to simulate multiple metabolic states by reaction network-based model - Application to amino acid depletion in CHO cell culture.

Mammalian cell lines are characterized by a complex and flexible metabolism. A single model that could describe the variations in metabolic behavior triggered by variations in the culture conditions would be a precious tool in bioprocess development. In this paper, we introduce an approach to generate a poly-pathway model and use it to simulate diverse metabolic states triggered in response to removal, reduction or doubling of amino acids in the culture medium of an antibody-producing CHO cell line. Macro-reactions were obtained from a metabolic network via elementary flux mode enumeration and the fluxes were modeled by kinetic equations with saturation and inhibition effects from external medium components. Importantly, one set of kinetic parameters was estimated using experimental data of the multiple metabolic states. A good fit between the model and the data was obtained for the majority of the metabolites and the experimentally observed flux variations. We find that the poly-pathway modeling approach is promising for the simulation of multiple metabolic states.

RETRACTED: Poly-pathway model, a novel approach to simulate multiple metabolic states by reaction network-based model - Application to amino acid depletion in CHO cell culture.

This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/our-business/policies/article-withdrawal). The authors of the paper wish to retract the paper due to the discovery of a calculation error in the processing of the raw data. The discovered error concerns the calculation of the specific uptake/secretion rates for several metabolites in one of the experimental conditions, i.e. glutamine omission (called Q0). In other words, in Figure 2, the variations of the metabolic fluxes for the condition Q0 are not correct. When this error is corrected, the resulting mathematical model changes (in particular for the results associated with Q0 conditions), several figures and tables are modified, and the interpretation of the fluxes in Q0 has to be slightly modified. Therefore the authors wish to retract the article. However, the error does not affect the modelling approach or the methodology presented in the article. Therefore, a revised version with the correct data has since been published: http://www.sciencedirect.com/science/article/pii/S0168165617302663. We apologize to the scientific community for the need to retract the article and the inconvenience caused.

Robustness analysis of elementary flux modes generated by column generation.

Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux measurements through least-squares data fitting. The measurements used in the data fitting are subject to errors. A robust optimization problem includes information on errors and gives a way to examine the sensitivity of the solution of the EFMs-based MFA to these errors. In general, formulating a robust optimization problem may make the problem significantly harder. We show that in the case of the EFMs-based MFA, when the errors are only in measurements and bounded by an interval, the robust problem can be stated as a convex quadratic programming (QP) problem. We have previously shown how the data fitting problem may be solved in a column-generation framework. In this paper, we show how column generation may be applied also to the robust problem, thereby avoiding explicit enumeration of EFMs. Furthermore, the option to indicate intervals on metabolites that are not measured is introduced in this column generation framework. The robustness of the data is evaluated in a case-study, which indicates that the solutions of our non-robust problems are in fact near-optimal also when robustness is considered, implying that the errors in measurement do not have a large impact on the optimal solution. Furthermore, we showed that the addition of intervals on unmeasured metabolites resulted in a change in the optimal solution.

On dynamically generating relevant elementary flux modes in a metabolic network using optimization.

Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal metabolites have been eliminated and only external metabolites remain. In EFMs-based metabolic flux analysis (MFA) experimentally determined external fluxes are used to estimate the flux of each EFM. It is in general prohibitive to enumerate all EFMs for complex networks, since the number of EFMs increases rapidly with network complexity. In this work we present an optimization-based method that dynamically generates a subset of EFMs and solves the EFMs-based MFA problem simultaneously. The obtained subset contains EFMs that contribute to the optimal solution of the EFMs-based MFA problem. The usefulness of our method was examined in a case-study using data from a Chinese hamster ovary cell culture and two networks of varied complexity. It was demonstrated that the EFMs-based MFA problem could be solved at a low computational cost, even for the more complex network. Additionally, only a fraction of the total number of EFMs was needed to compute the optimal solution.