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Projection to latent pathways (PLP): a constrained projection to latent variables (PLS) method for elementary flux modes discrimination.

Ferreira AR, Dias JM, Teixeira AP, Carinhas N, Portela RM, Isidro IA, von Stosch M, Oliveira R - BMC Syst Biol (2011)

Bottom Line: PLP has two concomitant goals: (1) maximisation of correlation between EFM weighting factors and measured envirome data and (2) minimisation of redundancy by eliminating EFM with low correlation with the envirome.Overall, our results demonstrate that PLP slightly outperforms PLS in terms of predictive power.This offers a significant advantage over PLS since its abstract structure cannot be associated with the underlying biological structure.

View Article: PubMed Central - HTML - PubMed

Affiliation: REQUIMTE, Systems Biology & Engineering Group, DQ/FCT, Universidade Nova de Lisboa, Campus Caparica, Portugal.

ABSTRACT

Background: Elementary flux modes (EFM) are unique and non-decomposable sets of metabolic reactions able to operate coherently in steady-state. A metabolic network has in general a very high number of EFM reflecting the typical functional redundancy of biological systems. However, most of these EFM are either thermodynamically unfeasible or inactive at pre-set environmental conditions.

Results: Here we present a new algorithm that discriminates the "active" set of EFM on the basis of dynamic envirome data. The algorithm merges together two well-known methods: projection to latent structures (PLS) and EFM analysis, and is therefore termed projection to latent pathways (PLP). PLP has two concomitant goals: (1) maximisation of correlation between EFM weighting factors and measured envirome data and (2) minimisation of redundancy by eliminating EFM with low correlation with the envirome.

Conclusions: Overall, our results demonstrate that PLP slightly outperforms PLS in terms of predictive power. But more importantly, PLP is able to discriminate the subset of EFM with highest correlation with the envirome, thus providing in-depth knowledge of how the environment controls core cellular functions. This offers a significant advantage over PLS since its abstract structure cannot be associated with the underlying biological structure.

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PLP regression coefficients. Regression coefficients of selected EFM quantify the contribution of each environmental factor in X to the respective EFM weighting factor.
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Figure 5: PLP regression coefficients. Regression coefficients of selected EFM quantify the contribution of each environmental factor in X to the respective EFM weighting factor.

Mentions: While PLS regression coefficients are associated with latent variables lacking physical meaning, PLP regression coefficients are directly associated to the discriminated EFM (see Figure 5). Thus they provide information of how the envirome up- or down-regulates each EFM. This interpretation should however be done with care as regression coefficients cannot disclose between a cause and an effect. An EFM is per definition a non-decomposable sub-network. Most of them start and end in extracellular compounds. Each EFM produces a characteristic dynamic footprint in the environment in terms of consumed or produced metabolites, which is more an effect rather than a cause. Moreover, it is an important feature of PLS and per inheritance of PLP that the X-loadings are computed in a way to maximise predictive power of Y in detriment of interpretability of the individual contribution of X variables. Although many papers have attempted to develop interpretation of PLS regression coefficients (e.g. [26,27]), other techniques are in principle better suited for this purpose. Even so, main causal-effects can be extracted from the analysis of regression coefficients. For this analysis it is however important to calculate the confidence intervals of the regression coefficients, which can be obtained from the previously described bootstrapping technique [28]. From the z = 200 PLP runs with randomly selected calibration and validation data sets, z = 200 vectors of regression coefficients are calculated (see Additional File 3). The respective mean and standard deviation can be estimated as follows:


Projection to latent pathways (PLP): a constrained projection to latent variables (PLS) method for elementary flux modes discrimination.

Ferreira AR, Dias JM, Teixeira AP, Carinhas N, Portela RM, Isidro IA, von Stosch M, Oliveira R - BMC Syst Biol (2011)

PLP regression coefficients. Regression coefficients of selected EFM quantify the contribution of each environmental factor in X to the respective EFM weighting factor.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750108&req=5

Figure 5: PLP regression coefficients. Regression coefficients of selected EFM quantify the contribution of each environmental factor in X to the respective EFM weighting factor.
Mentions: While PLS regression coefficients are associated with latent variables lacking physical meaning, PLP regression coefficients are directly associated to the discriminated EFM (see Figure 5). Thus they provide information of how the envirome up- or down-regulates each EFM. This interpretation should however be done with care as regression coefficients cannot disclose between a cause and an effect. An EFM is per definition a non-decomposable sub-network. Most of them start and end in extracellular compounds. Each EFM produces a characteristic dynamic footprint in the environment in terms of consumed or produced metabolites, which is more an effect rather than a cause. Moreover, it is an important feature of PLS and per inheritance of PLP that the X-loadings are computed in a way to maximise predictive power of Y in detriment of interpretability of the individual contribution of X variables. Although many papers have attempted to develop interpretation of PLS regression coefficients (e.g. [26,27]), other techniques are in principle better suited for this purpose. Even so, main causal-effects can be extracted from the analysis of regression coefficients. For this analysis it is however important to calculate the confidence intervals of the regression coefficients, which can be obtained from the previously described bootstrapping technique [28]. From the z = 200 PLP runs with randomly selected calibration and validation data sets, z = 200 vectors of regression coefficients are calculated (see Additional File 3). The respective mean and standard deviation can be estimated as follows:

Bottom Line: PLP has two concomitant goals: (1) maximisation of correlation between EFM weighting factors and measured envirome data and (2) minimisation of redundancy by eliminating EFM with low correlation with the envirome.Overall, our results demonstrate that PLP slightly outperforms PLS in terms of predictive power.This offers a significant advantage over PLS since its abstract structure cannot be associated with the underlying biological structure.

View Article: PubMed Central - HTML - PubMed

Affiliation: REQUIMTE, Systems Biology & Engineering Group, DQ/FCT, Universidade Nova de Lisboa, Campus Caparica, Portugal.

ABSTRACT

Background: Elementary flux modes (EFM) are unique and non-decomposable sets of metabolic reactions able to operate coherently in steady-state. A metabolic network has in general a very high number of EFM reflecting the typical functional redundancy of biological systems. However, most of these EFM are either thermodynamically unfeasible or inactive at pre-set environmental conditions.

Results: Here we present a new algorithm that discriminates the "active" set of EFM on the basis of dynamic envirome data. The algorithm merges together two well-known methods: projection to latent structures (PLS) and EFM analysis, and is therefore termed projection to latent pathways (PLP). PLP has two concomitant goals: (1) maximisation of correlation between EFM weighting factors and measured envirome data and (2) minimisation of redundancy by eliminating EFM with low correlation with the envirome.

Conclusions: Overall, our results demonstrate that PLP slightly outperforms PLS in terms of predictive power. But more importantly, PLP is able to discriminate the subset of EFM with highest correlation with the envirome, thus providing in-depth knowledge of how the environment controls core cellular functions. This offers a significant advantage over PLS since its abstract structure cannot be associated with the underlying biological structure.

Show MeSH
Related in: MedlinePlus