Links connecting operons in the community that enriches for genes involved in ribosome structure.

<p>CLR links are in light blue, RegulonDB links are in black. Small symbols are genes that are not in the community, but are regulators of genes that are in the community and are therefore candidates for mediating indirect interactions between community genes. Symbol shape and color indicate attributes as follows: red, transcription factors; dark blue, ppGpp regulated promoter by direct assay <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi.1002391-Lemke1" target="_blank">[54]</a>; light blue, ppGpp regulated translation related promoter by microarray <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi.1002391-Traxler1" target="_blank">[55]</a>; pink, other; hexagon, promoter; diamond, promoter; square, promoter; circle, unknown sigma factor. Note that very few interactions observed in the CLR network can be explained by the direct interactions annotated in RegulonDB. The high proportion of ppGpp sensitive promoters among operons contained in the community suggests this molecule as a good candidate for regulating the remaining interactions. The network layout was determined by the circular layout option in Cytoscape 2.8.1, no particular significance should be attached to operons being outside the main circle.</p

Distribution of gene relatedness and network size in the <i>E. coli</i> CLR network.

<p>(A) Probability distribution of relatedness values, , between pairs of genes in <i>E. coli</i> calculated using the CLR algorithm and the full dataset. (B) Size of the largest connected component for relatedness value, . At small values of the network is fully connected but begins to break up into multiple disconnected components at a critical value of approximately .</p

The estimated computational complexity of the algorithm for power-law sequences.

<p>The leading order of the computational complexity of the algorithm as a power of , where is the number of nodes, is plotted as a function of the degree distribution power-law exponent . The black circles correspond to ensembles of sequences without cutoff, while the red squares correspond to ensembles of sequences with structural cutoff in the maximum degree of . The fits that yielded the data points were carried out considering sequences ranging in size from to .</p

Mean and standard deviation of the distributions of the logarithm of the weights vs. number of nodes of samples from an ensemble of power-law sequences with .

<p>The black circles correspond to , the red squares correspond to . The error bars are smaller than the symbols. The solid black line and the dashed red line show the outcomes of fits on the data. The linearity of the data on a logarithmic scale indicates that the and follow power-law scaling relations with : and . The slopes of the fit lines are an estimate of the value of the exponents: and .</p

Change in core community structure as noise is increased from to .

<p>The grey scale value of each element indicates the fraction of times the two genes occurred in the same community over replicate community partitionings. If the element is white (black) the two genes were always (never) found in the same community. At each noise value there are clearly white diagonal blocks indicating sets of genes that are always found in the same community, which we refer to as core communities. Note that, the five core communities at (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi-1002391-g003" target="_blank">Figure 3A</a>) are in the same order in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi-1002391-g003" target="_blank">Figure 3:B, C, D, and E</a>. Within each of the five core communities of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi-1002391-g003" target="_blank">Figure 3A</a>, the node order is allowed to change in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi-1002391-g003" target="_blank">Figure 3:B, C, D, and E</a> in order to display the largest subcommunity first. For each panel, he list of of the order of genes and the core community they belong to is given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi.1002391.s005" target="_blank">Dataset S5</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi.1002391.s006" target="_blank">Dataset S6</a>, respectively. A full size version with each pixel representing a distinct pair of genes is included in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi.1002391.s012" target="_blank">Figure S3</a>.</p

Probability distribution of the logarithm of weights for an ensemble of power-law sequences with and .

<p>The ensemble contained graphical sequences, and for each sequence graph samples were produced. Thus, the total number of samples produced was . The simulation data is given by the solid black line and a Gaussian fit of the data is shown by the dashed red line that nearly obscures the black line.</p

The 25 most relevant relationships found for without noise.

<p>The “P value” or random probability, calculated with a hypergeometric test with Benjamini-Hochberg correction, of the common occurrence, or overlap, of genes in an inferred community and in a GO term for the 25 most statistically relevant relationships are listed. Also listed are the “GO term num” that distinguishes the GO term and its “Description” in the GO database, the number of genes in the GO term “GO size”, the number of genes in the inferred community “Com size”, and the number of genes they have in common “In common.” The complete set of the 239 relevant relationships found for , as well as the relevant relationships found for , are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002391#pcbi.1002391.s007" target="_blank">Dataset S7</a>.</p

The effect of noise on core community structure and GO term enrichment.

<p>(A) Proportion of core community nodes that remain in a core community. (B) The number of significant GO term enrichments as a function of noise level for networks constructed with . If a GO term is enriched by more than one community, each enrichment is counted separately.</p