Figure 1.
A Hypothetical Network with Metabolites (Nodes), Reactions (Arrows), and Exchange Reactions (Ex) with the Environment
Indicated are three types of flux coupling between reactions that are located at distance 1 (directly connected by one node): i) A-B: directionally coupled, ii) B-C: fully coupled, and iii) C-D: uncoupled.
Figure 2.
The Average Level of Empirically Determined Flux Correlations for Different Flux Coupling Types (A) and at Different Network Distances (B)
Figure 3.
The Effect of Flux Coupling and Network Distance on Operonic Organization in E. coli
(A) The fraction of intra-operonic gene pairs correlates with the type of flux coupling. The dashed baseline indicates the fraction of intra-operonic gene pairs expected by chance.
(B) The effect of flux coupling on the fraction of intra-operonic gene pairs in different network distance groups: χ2d=1 = 715.3, χ2d=2,3,4 = 5347.3, χ2d≥5 = 5022.3, d.f. = 2, and p < 10−155.
Figure 4.
Transcription Factor (TF) Similarity Correlates with the Type of Flux Coupling
Figure 5.
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.