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

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.

Prediction of Metabolic Flux Distribution by Flux Sampling: As a Case Study, Acetate Production from Glucose in Escherichia coli

“…Since it was difficult to measure many intracellular fluxes experimentally, we used the results of 13 C-based metabolic flux analysis (MFA) for validation. 13 C-MFA was the method of choice for detailed inference of intracellular metabolic fluxes in cells or organisms under quasi-steadystate conditions [25].…”

“…Since it was difficult to measure many intracellular fluxes experimentally, we used the results of 13 C-based metabolic flux analysis (MFA) for validation. 13 C-MFA was the method of choice for detailed inference of intracellular metabolic fluxes in cells or organisms under quasi-steadystate conditions [25]. The carbon source was selected as glucose, and the Zhao and Shimizu [5] literature was used for validation as one of the references from which the acetic acid production flux and the flux values predicted to be important in the previous section could be obtained.…”

“…One such previous study was a patent that uses L-lysin production as an example [ 11 ]. In this method, the fluxes important for L-lysin production were predicted by (1) elementary mode analysis [ 12 ], which was very computationally demanding, and (2) selection of independent metabolic fluxes (called free fluxes) equal to the number of degrees of freedom in the stoichiometric matrix [ 13 ], generation of their combinations, and application to metabolic models. However, the GS, a commonly used metabolic model for metabolic simulation, was a very large model in terms of both the number of constituent metabolites and metabolic reactions.…”

“…In addition, the mass isotope 13 C labeling data [5][6][7][8][9][10], metabolome data [1] by LC-MS, and other methods were also used to predict and estimate intracellular metabolic states in previous studies. However, it was still a time-consuming and labor-intensive process to reacquire, simulate, and analyze omics data every time the culture medium composition, culture conditions, or target organisms or strains changed.…”

Special Issue: Mathematical Modeling and Control of Bioprocesses

“…One of the major issues with models based on metabolic networks is their underdetermination, in the sense that the number of unknown intracellular fluxes to be determined is usually higher than the number of available equations corresponding to the mass balances and the available measurements. Bogaerts and Vande Wouwer [1] review various methods to tackle this underdetermination, among which are flux pathway analysis, flux balance analysis, flux variability analysis and sampling of the flux solution space. One of these methods, namely Dynamic Flux Balance Analysis, is used by Shen and Budman [2] to infer metabolite concentrations for which hardware measurements are not available.…”