title: Robustness analysis of elementary flux modes generated by column generation.
abstract: 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.
authors.affiliation: Department of Mathematics, Optimization and Systems Theory, KTH Royal Institute of Technology, Stockholm SE-100 44, Sweden. Electronic address: haodd@kth.se.
authors.forename: Hildur Æsa
authors.initials: HÆ
authors.lastname: Oddsdóttir
authors.affiliation: Division of Industrial Biotechnology/Bioprocess Design, KTH Royal Institute of Technology, Albanova Center, Stockholm SE-106 91, Sweden.
authors.forename: Erika
authors.initials: E
authors.lastname: Hagrot
authors.affiliation: Division of Industrial Biotechnology/Bioprocess Design, KTH Royal Institute of Technology, Albanova Center, Stockholm SE-106 91, Sweden.
authors.forename: Véronique
authors.initials: V
authors.lastname: Chotteau
authors.affiliation: Department of Mathematics, Optimization and Systems Theory, KTH Royal Institute of Technology, Stockholm SE-100 44, Sweden.
authors.forename: Anders
authors.initials: A
authors.lastname: Forsgren
mesh_terms: D000818:Animals; D016466:CHO Cells; D003198:Computer Simulation; D003412:Cricetulus; D016018:Least-Squares Analysis; D055641:Mathematical Concepts; D064688:Metabolic Flux Analysis / Q000706:statistics & numerical data*; D053858:Metabolic Networks and Pathways; D008954:Models, Biological
keywords: Chinese hamster ovary cell; Elementary flux mode; Least-squares; Metabolic network; Robust optimization