How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review
Abstract
:1. Introduction
- Dealing with the underdeterminacy—this strategy is adopted in several methods where minimal and maximal bounds on the admissible fluxes are determined. This category of methods includes Flux Pathway Analysis (FPA), where convex analysis is used to decompose the admissible flux distributions into Elementary Flux Modes (EFMs) or Extreme Pathways [3,4], Flux Variability Analysis (FVA), which is a Linear-Programming (LP)-based method determining the range of admissible fluxes [5], Flux Spectrum Approach (FSA), which is another LP-based method taking insufficient and uncertain measurements into account [6]. Random sampling of the admissible solution set allows determining the marginal probability density functions of the fluxes [7,8,9,10], and statistical methods based on the maximum entropy principle can be used to infer intracellular flux distributions [11,12].
- Reducing or eliminating the underdeterminacy—this strategy consists in adding constraints in various ways, e.g., including more measurements of the extracellular fluxes or, possibly, measurements of the intracellular fluxes using specific techniques such as tracing [13,14] and parallel labeling [15], leading to the sophisticated procedures of MFA. Alternatively, additional constraints can be introduced by formulating biological assumptions either based on prior knowledge and/or experimental observations [16,17] or systematic procedures to determine active constraints [18]. The use of thermodynamic constraints can be important in relation with reaction reversibility and the limitation of the solution space [19]. Moreover, thermodynamical constraints can prevent infeasible loops in a metabolic network as demonstrated in [20]. Underdeterminacy can also 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. Recently, the increasing availability of metabolite profiling data obtained through gas and liquid chromatography combined with mass spectroscopy has also allowed the integration of time-course absolute quantitative metabolomics in unsteady-state (or dynamic) FBA [23,24]. In the usual situation where FBA still leads to an underdetermined system with an infinite number of flux distributions that optimize the cost function, variants of FBA have been proposed in order to define a unique solution, e.g., the geometric approach developed in [25] that searches for the minimal flux distribution satisfying the given objective. Assuming that fluxes correlate with enzyme levels, this specific flux distribution would correspond to the minimization of the amount of enzymes required to satisfy the objective defined in FBA. Ultimately, the concept of Most Accurate Fluxes [26] allows computing a unique flux distribution, hence eliminating the system underdeterminacy, with a very low computational load and without any assumption regarding an optimal biological behavior.
2. A Toy Example
3. Dealing with the Underdeterminacy
4. Reducing or Eliminating the Underdeterminacy
5. An Overview of Important Topics
5.1. How to Select the Size/Detail of the Metabolic Network?
5.2. Dynamic Metabolic Flux Interval Analysis
5.3. How to Represent the Accumulation of Internal Metabolites?
5.4. Model Reduction to Macroscopic Scale
5.5. How to Handle the Measurement Errors?
5.6. Some Further Perspectives on Sampling Algorithms
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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Bogaerts, P.; Vande Wouwer, A. How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review. Processes 2021, 9, 1577. https://doi.org/10.3390/pr9091577
Bogaerts P, Vande Wouwer A. How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review. Processes. 2021; 9(9):1577. https://doi.org/10.3390/pr9091577
Chicago/Turabian StyleBogaerts, Philippe, and Alain Vande Wouwer. 2021. "How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review" Processes 9, no. 9: 1577. https://doi.org/10.3390/pr9091577