H

V:i where v,; is the mass carried by reaction j which produces (consumes) metabolite i. If all reactions producing (consuming) metabolite i have comparable v/( values, Y{k,í) scales as Ilk. If, however, a single reactions activity dominates Eq. (6), we expect Y(k,i) - 1, i.e. Y[k,t), is independent of k. For the E. coli metabolism optimized for succinate and glutamate uptake (Fig. 5) we find that both the in and out degrees follow the power law Y[k,i) - k"0'27, representing an intermediate behavior between the two extreme cases.4 This indicates that the large-scale inhomogeneity observed in the overall flux distribution is increasingly valid at the level of the individual metabolites as well: the more reactions consume (produce) a given metabolite, the more likely it is that a single reaction carries the majority of the flux. This implies that the majority of the metabolic flux is carried along linear pathways—the metabolic high flux backbone (HFB).4

A power law pattern is also observed when one investigates the strength of the various genetic regulatory interactions provided by microarray datasets. Assigning each pair of genes a correlation coefficient which captures the degree to which they are coexpressed, one finds that the distribution of these pair-wise correlation coefficients follows a power law.24'45 That is, while the majority of gene pairs have only weak correlations, a few gene pairs display a significant correlation coefficient. These highly correlated pairs likely correspond to direct regulatory and protein interactions. This hypothesis is supported by the finding that the correlations are

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