Abstract
Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not define a unique solution for the distribution of intracellular fluxes, but instead a set of solutions belonging to a convex polytope. Various methods have been proposed to tackle this underdeterminacy, including flux pathway analysis, flux balance analysis, flux variability analysis and sampling. These approaches are reviewed in this article and a toy example supports the discussion with illustrative numerical results.
Highlights
Computational approaches for studying the flux distribution inside metabolic networks of microbial strains or mammalian cell lines have gained a tremendous importance in biotechnology
Different approaches have been developed to compute this flux distribution, which are based on a common assumption that the intracellular metabolites do not accumulate, or in other words, that the cell is in a metabolic pseudo-steady state [1]
This paper reviews and applies to a toy example some methods that can be used with underdetermined problems in metabolic flux analysis
Summary
Computational approaches for studying the flux distribution inside metabolic networks of microbial strains or mammalian cell lines have gained a tremendous importance in biotechnology. N is assumed full-row rank, defining ns independent mass balance equations This system of equations expresses the zero balance in each internal node of the metabolic network, and imposes a set of linear equality constraints, which are not sufficient to determine a unique solution for the flux vector v. Underdeterminacy can be reduced (or even eliminated) through the formulation of an optimization problem originating from the assumption of an optimal metabolic behavior of the cells This approach corresponds to Flux Balance Analysis (FBA) [21,22], which uses an objective function expressed as a linear combination of selected fluxes. The Matlab code of this example is provided in the Supplementary Materials associated to this article
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