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Co-regulation of metabolic genes is better explained by flux coupling than by network distance.

Notebaart RA, Teusink B, Siezen RJ, Papp B - PLoS Comput. Biol. (2008)

Bottom Line: After validating the computational method with empirical data on flux correlations, we confirm that genes coupled by their enzymatic fluxes not only show similar expression patterns, but also share transcriptional regulators and frequently reside in the same operon.Moreover, the type of flux coupling can explain refined properties of the regulatory network that are ignored by simple graph-theoretical indices.Our results underline the importance of studying functional states of cellular networks to define physiologically relevant associations between genes and should stimulate future developments of novel functional genomic tools.

View Article: PubMed Central - PubMed

Affiliation: Center for Molecular and Biomolecular Informatics (NCMLS), Radboud University Nijmegen Medical Center, Nijmegen, The Netherlands.

ABSTRACT
To what extent can modes of gene regulation be explained by systems-level properties of metabolic networks? Prior studies on co-regulation of metabolic genes have mainly focused on graph-theoretical features of metabolic networks and demonstrated a decreasing level of co-expression with increasing network distance, a naïve, but widely used, topological index. Others have suggested that static graph representations can poorly capture dynamic functional associations, e.g., in the form of dependence of metabolic fluxes across genes in the network. Here, we systematically tested the relative importance of metabolic flux coupling and network position on gene co-regulation, using a genome-scale metabolic model of Escherichia coli. After validating the computational method with empirical data on flux correlations, we confirm that genes coupled by their enzymatic fluxes not only show similar expression patterns, but also share transcriptional regulators and frequently reside in the same operon. In contrast, we demonstrate that network distance per se has relatively minor influence on gene co-regulation. Moreover, the type of flux coupling can explain refined properties of the regulatory network that are ignored by simple graph-theoretical indices. Our results underline the importance of studying functional states of cellular networks to define physiologically relevant associations between genes and should stimulate future developments of novel functional genomic tools.

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The Effect of Flux Coupling and Network Distance on Co-Expression for E. coli (A) and S. cerevisiae (B)(A) The dashed baseline indicates the degree of co-expression between random gene pairs. The confidence interval of directionally coupled pairs at d ≥ 5 is absent, as it contains too few data points (n = 2) for reliable calculation.(B) Relative variance components (i.e., the fraction of total variance in co-expression explained by coupling and distance) were estimated by a general linear model where both flux coupling and distance were treated as random effects in an unbalanced factorial ANOVA design. Expected means squares were used for the estimation (Statistica 6.0, Statsoft). Flux coupling and network distance explain 16.8% and 7.3% of the variance in co-expression, respectively (interaction between the two factors explains 3.7%). A maximum likelihood estimation of variance components gave very similar results (coupling: 14%, distance: 7.1%, and interaction: 3.8%, Statistica 6.0, Statsoft). Note that the average network distance is ∼4.5.
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pcbi-0040026-g005: The Effect of Flux Coupling and Network Distance on Co-Expression for E. coli (A) and S. cerevisiae (B)(A) The dashed baseline indicates the degree of co-expression between random gene pairs. The confidence interval of directionally coupled pairs at d ≥ 5 is absent, as it contains too few data points (n = 2) for reliable calculation.(B) Relative variance components (i.e., the fraction of total variance in co-expression explained by coupling and distance) were estimated by a general linear model where both flux coupling and distance were treated as random effects in an unbalanced factorial ANOVA design. Expected means squares were used for the estimation (Statistica 6.0, Statsoft). Flux coupling and network distance explain 16.8% and 7.3% of the variance in co-expression, respectively (interaction between the two factors explains 3.7%). A maximum likelihood estimation of variance components gave very similar results (coupling: 14%, distance: 7.1%, and interaction: 3.8%, Statistica 6.0, Statsoft). Note that the average network distance is ∼4.5.

Mentions: To unveil which factor (i.e., network distance or flux coupling) is the main determinant of co-expression between metabolic genes, we performed a two-way robust ANOVA [27]. We found that while flux coupling is a significant main effect (p < 0.003), the effect of network distance is not (p = 0.244), and there is an interaction between these two factors (p = 0.003) (Figure 5A). Apparently, the interaction term arises because the degree of co-expression increases with network distance for flux coupled gene pairs (p < 10−4), but decreases for uncoupled pairs (p ≈ 0). Hence, network distance does not explain transcript-level co-expression for inter-operonic flux coupled genes in E. coli, and even for uncoupled genes it predicts only weak co-expression for those located close to each other on the metabolic map: uncoupled neighboring (d = 1) gene pairs have an average co-expression of 0.106, which is only slightly, albeit statistically significantly, higher than the 0.039 observed for random pairs (see baseline in Figure 5A). The idea that considering flux coupling relationships improves the discrimination of gene sets with different levels of co-expression is further exemplified by our observation that although fully and directionally coupled gene pairs do not differ in terms of overall network distance (p = 0.9, Figure S1A), they differ in co-expression (Figure S1B) and TF similarity (Figure 4, p < 10−2). Thus, the type of flux coupling can capture differences in the degree of gene co-regulation that are ignored by network distance.


Co-regulation of metabolic genes is better explained by flux coupling than by network distance.

Notebaart RA, Teusink B, Siezen RJ, Papp B - PLoS Comput. Biol. (2008)

The Effect of Flux Coupling and Network Distance on Co-Expression for E. coli (A) and S. cerevisiae (B)(A) The dashed baseline indicates the degree of co-expression between random gene pairs. The confidence interval of directionally coupled pairs at d ≥ 5 is absent, as it contains too few data points (n = 2) for reliable calculation.(B) Relative variance components (i.e., the fraction of total variance in co-expression explained by coupling and distance) were estimated by a general linear model where both flux coupling and distance were treated as random effects in an unbalanced factorial ANOVA design. Expected means squares were used for the estimation (Statistica 6.0, Statsoft). Flux coupling and network distance explain 16.8% and 7.3% of the variance in co-expression, respectively (interaction between the two factors explains 3.7%). A maximum likelihood estimation of variance components gave very similar results (coupling: 14%, distance: 7.1%, and interaction: 3.8%, Statistica 6.0, Statsoft). Note that the average network distance is ∼4.5.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2211535&req=5

pcbi-0040026-g005: The Effect of Flux Coupling and Network Distance on Co-Expression for E. coli (A) and S. cerevisiae (B)(A) The dashed baseline indicates the degree of co-expression between random gene pairs. The confidence interval of directionally coupled pairs at d ≥ 5 is absent, as it contains too few data points (n = 2) for reliable calculation.(B) Relative variance components (i.e., the fraction of total variance in co-expression explained by coupling and distance) were estimated by a general linear model where both flux coupling and distance were treated as random effects in an unbalanced factorial ANOVA design. Expected means squares were used for the estimation (Statistica 6.0, Statsoft). Flux coupling and network distance explain 16.8% and 7.3% of the variance in co-expression, respectively (interaction between the two factors explains 3.7%). A maximum likelihood estimation of variance components gave very similar results (coupling: 14%, distance: 7.1%, and interaction: 3.8%, Statistica 6.0, Statsoft). Note that the average network distance is ∼4.5.
Mentions: To unveil which factor (i.e., network distance or flux coupling) is the main determinant of co-expression between metabolic genes, we performed a two-way robust ANOVA [27]. We found that while flux coupling is a significant main effect (p < 0.003), the effect of network distance is not (p = 0.244), and there is an interaction between these two factors (p = 0.003) (Figure 5A). Apparently, the interaction term arises because the degree of co-expression increases with network distance for flux coupled gene pairs (p < 10−4), but decreases for uncoupled pairs (p ≈ 0). Hence, network distance does not explain transcript-level co-expression for inter-operonic flux coupled genes in E. coli, and even for uncoupled genes it predicts only weak co-expression for those located close to each other on the metabolic map: uncoupled neighboring (d = 1) gene pairs have an average co-expression of 0.106, which is only slightly, albeit statistically significantly, higher than the 0.039 observed for random pairs (see baseline in Figure 5A). The idea that considering flux coupling relationships improves the discrimination of gene sets with different levels of co-expression is further exemplified by our observation that although fully and directionally coupled gene pairs do not differ in terms of overall network distance (p = 0.9, Figure S1A), they differ in co-expression (Figure S1B) and TF similarity (Figure 4, p < 10−2). Thus, the type of flux coupling can capture differences in the degree of gene co-regulation that are ignored by network distance.

Bottom Line: After validating the computational method with empirical data on flux correlations, we confirm that genes coupled by their enzymatic fluxes not only show similar expression patterns, but also share transcriptional regulators and frequently reside in the same operon.Moreover, the type of flux coupling can explain refined properties of the regulatory network that are ignored by simple graph-theoretical indices.Our results underline the importance of studying functional states of cellular networks to define physiologically relevant associations between genes and should stimulate future developments of novel functional genomic tools.

View Article: PubMed Central - PubMed

Affiliation: Center for Molecular and Biomolecular Informatics (NCMLS), Radboud University Nijmegen Medical Center, Nijmegen, The Netherlands.

ABSTRACT
To what extent can modes of gene regulation be explained by systems-level properties of metabolic networks? Prior studies on co-regulation of metabolic genes have mainly focused on graph-theoretical features of metabolic networks and demonstrated a decreasing level of co-expression with increasing network distance, a naïve, but widely used, topological index. Others have suggested that static graph representations can poorly capture dynamic functional associations, e.g., in the form of dependence of metabolic fluxes across genes in the network. Here, we systematically tested the relative importance of metabolic flux coupling and network position on gene co-regulation, using a genome-scale metabolic model of Escherichia coli. After validating the computational method with empirical data on flux correlations, we confirm that genes coupled by their enzymatic fluxes not only show similar expression patterns, but also share transcriptional regulators and frequently reside in the same operon. In contrast, we demonstrate that network distance per se has relatively minor influence on gene co-regulation. Moreover, the type of flux coupling can explain refined properties of the regulatory network that are ignored by simple graph-theoretical indices. Our results underline the importance of studying functional states of cellular networks to define physiologically relevant associations between genes and should stimulate future developments of novel functional genomic tools.

Show MeSH
Related in: MedlinePlus