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. 2018 Jun 18;12(1):71.
doi: 10.1186/s12918-018-0589-3.

Dynamic Elementary Mode Modelling of Non-Steady State Flux Data

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Free PMC article

Dynamic Elementary Mode Modelling of Non-Steady State Flux Data

Abel Folch-Fortuny et al. BMC Syst Biol. .
Free PMC article

Abstract

Background: A novel framework is proposed to analyse metabolic fluxes in non-steady state conditions, based on the new concept of dynamic elementary mode (dynEM): an elementary mode activated partially depending on the time point of the experiment.

Results: Two methods are introduced here: dynamic elementary mode analysis (dynEMA) and dynamic elementary mode regression discriminant analysis (dynEMR-DA). The former is an extension of the recently proposed principal elementary mode analysis (PEMA) method from steady state to non-steady state scenarios. The latter is a discriminant model that permits to identify which dynEMs behave strongly different depending on the experimental conditions. Two case studies of Saccharomyces cerevisiae, with fluxes derived from simulated and real concentration data sets, are presented to highlight the benefits of this dynamic modelling.

Conclusions: This methodology permits to analyse metabolic fluxes at early stages with the aim of i) creating reduced dynamic models of flux data, ii) combining many experiments in a single biologically meaningful model, and iii) identifying the metabolic pathways that drive the organism from one state to another when changing the environmental conditions.

Keywords: Cross validation; Dynamic modelling; Elementary mode; Metabolic network; N-way; Partial least squares regression discriminant analysis; Principal component analysis; Principal elementary mode analysis.

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Competing interests

The authors declare that they have no competing interests.

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Figures

Fig. 1
Fig. 1
S. cerevisiae metabolic models. Model a), from [19], is used for the simulated study, and b), from [13], for the real case study
Fig. 2
Fig. 2
a Small metabolic network. b Steady state flux distribution. In b), the flux carried by each reaction is shown. Reactions 7-8 have no flux
Fig. 3
Fig. 3
Schematic representation of data matrices in the PEMA model
Fig. 4
Fig. 4
Small metabolic network with non-steady state fluxes from time point 1 to 4 (a) to d), respectively). Graphics show the flux carried by each reaction, which changes depending on the time point. The first subindex of the weighting factor αej,k indicates the EM E=1. The other two subindices indicate time point j=1,..,4 and reaction k=1,..,8
Fig. 5
Fig. 5
Schematic representation of data matrices in the dynEMA model
Fig. 6
Fig. 6
dynEMR-DA procedure. XH and XL denote the flux data matrices of two different experimental conditions
Fig. 7
Fig. 7
3CV procedure. 75% of the samples from both classes (red and blue) are used in the calibration, projection and test sets (25% in each). The remaining 25% of samples are used in validation set
Fig. 8
Fig. 8
Simulated study. a dynEM8 depicted on the metabolic model. b-e dynEM8 coefficients at 3, 6, 9 and 36 s (first 3 times points and when the fluxes reach the steady state). Blue (red) lines show the mean of the coefficients for the high (low) glucose experiments
Fig. 9
Fig. 9
Real case study. a dynEM9 depicted on the metabolic model. b-e dynEM9 coefficients at 3, 6, 9 and 24 s (when system is close to steady state). Blue (red) lines show the coefficients for the high (low) glucose experiments
Fig. 10
Fig. 10
Real case study. a dynEM8 depicted on the metabolic model. b-e dynEM8 coefficients at 3, 6, 9 and 24 s (when reaching steady state). Blue (red) lines show the coefficients for aerobic (anaerobic) experiments
Fig. 11
Fig. 11
NPLS-DA loading plots for the fluxes (high versus low intial glucose data)
Fig. 12
Fig. 12
NPLS-DA loading plots for the fluxes (aerobic versus anaerobic data)

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