Abstract
Constraint-based models use steady-state mass balances to define a solution space of flux configurations, which can be narrowed down by measuring as many fluxes as possible. Due to loops and redundant pathways, this process typically yields multiple alternative solutions. To address this ambiguity, flux sampling can estimate the probability distribution of each flux, or a flux configuration can be singled out by further minimizing the sum of fluxes according to the assumption that cellular metabolism favors states where enzyme-related costs are economized. However, flux sampling is susceptible to artifacts introduced by thermodynamically infeasible cycles and is it not clear if the economy of fluxes assumption (EFA) is universally valid. Here, we formulated a constraint-based approach, MaxEnt, based on the principle of maximum entropy, which in this context states that if more than one flux configuration is consistent with a set of experimentally measured fluxes, then the one with the minimum amount of unwarranted assumptions corresponds to the best estimation of the non-observed fluxes. We compared MaxEnt predictions to Escherichia coli and Saccharomyces cerevisiae publicly available flux data. We found that the mean square error (MSE) between experimental and predicted fluxes by MaxEnt and EFA-based methods are three orders of magnitude lower than the median of 1,350,000 MSE values obtained using flux sampling. However, only MaxEnt and flux sampling correctly predicted flux through E. coli’s glyoxylate cycle, whereas EFA-based methods, in general, predict no flux cycles. We also tested MaxEnt predictions at increasing levels of overflow metabolism. We found that MaxEnt accuracy is not affected by overflow metabolism levels, whereas the EFA-based methods show a decreasing performance. These results suggest that MaxEnt is less sensitive than flux sampling to artifacts introduced by thermodynamically infeasible cycles and that its predictions are less susceptible to overfitting than EFA-based methods.
Highlights
Genome-scale metabolic networks provide the basis for reconstructing the set of metabolic reactions occurring within a living organism
We found that MaxEnt predictions (Fig 4A and 4C) have a significantly larger information entropy (p-values < 10−5, one-tailed test of a normal distribution) than the mean information entropy obtained by flux sampling, with MinFlux and Geometric having information entropy values in between these two methods
We found that MaxEnt, MinFlux, and Geometric outperforms the average solution of flux sampling (Fig 4), producing mean square error (MSE) values that are more than 3 orders of magnitude lower than the median MSE of flux sampling (Fig 4B and 4D)
Summary
Genome-scale metabolic networks provide the basis for reconstructing the set of metabolic reactions occurring within a living organism. The mass balance principle can be applied to obtain a mathematical model describing the variation of all concentrations for the metabolic system This model can be further simplified by assuming a steady-state condition, resulting in a linear mathematical model which provides a solution space for all possible flux configuration that comply with the constraints set by the stoichiometry of the reaction network. As FBA is formulated as a linear programming problem, it does not necessarily yield a single solution [8, 9] This is typically the case for metabolic networks as they contain loops and alternative pathways [10] that accept various flux configurations to be compatible with a given set of know uptake rates and maximized objective function values [11]. Using alternative metrics of cellular fitness, e.g. ATP production, or measuring extra uptake rates is typically insufficient to reduce the solution space to a single flux configuration
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
