Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks. fig2s3: General properties and number of feedback loops in the RegulonDB (E. coli) and Harbison et al. (yeast) datasets under different statistical conditions.RegulonDB reports, for each interaction, a list of evidence codes indicating which experimental techniques reported a particular interaction. Some of these codes (called `strong’) are associated with particularly reliable biological techniques (Salgado et al., 2012). The information provided by RegulonDB can be used in different ways to assess the statistical validity of our analysis. A first approach is to use the number of evidence codes as an indicator of the confidence level of an interaction: the larger the number of evidence codes, the greater the confidence. A second approach is to restrict the network only to those interactions supported by strong evidence codes. We decided to study the effect of varying the number of general or strong evidence codes on the results discussed. ‘kEc’ indicates the network constructed using only those interactions supported by at least k evidence codes, while ‘kSEc’ indicates the network constructed using only those interactions supported by at least k strong evidence codes. The number of genes (A), TFs (B), and interactions of the networks (C) vary with the number of evidence codes. However, the edge density (D) is rather stable, suggesting that the global properties of the GRN are mostly preserved in the different types of network. The number of feedback loops is very limited regardless of the number of evidence codes used (E). 2Ec and 2SEc have similar edge density (D) and number of illegal feedback loops (E), thus suggesting that taking two evidence codes gives a network similar to the one obtained by considering only strong biological evidence. In the yeast dataset derived by Harbison et al. (2004) each interaction is associated with a p-value that measures the probability that such an interaction has been detected due to experimental error. Selecting a large threshold p-value increases the probability of false positives, but decreases the probability of false negatives. Lee et al. (2002) reported that a threshold p-value of 10–3 provides a good trade-off for this kind of data. However, a reliable theory would be expected to display a limited sensitivity to a small variation of the threshold. The number of genes (F), TFs (G), and interactions of the network (H) change with different thresholds. Nevertheless, the edge density is quite stable (I). As with the RegulonDB data (A–D), these results suggest that the main characteristics of the network are mostly preserved under different statistical constrains. The number of feedback loops remains low for reasonable variations around the selected threshold (J), and the increase in number is compatible with the expected increase in the rate of false positives. Interestingly, looking at feedback loop number, a ‘phase transition’ becomes apparent for large thresholds. This behaviour suggests the use of great care when performing this type of analysis on very noisy data.DOI:http://dx.doi.org/10.7554/eLife.02863.007
Mentions: On studying feedback loops in the GRNs of these organisms (Figure 2A–C, Figure 2—figure supplement 1A,B, lightly shaded bars), we find that P. aeurginosa, S. cerevisiae and human GRNs have no feedback loops comprising three or more genes. The E. coli GRN has no feedback loops comprising four or more genes, and only two 3-gene feedback loops. M. tuberculosis has two 3-gene feedback loops and one 4-gene feedback loop. Notably, all the 3-gene feedback loops observed in real GRNs share the same peculiar structure, with implications discussed below. In contrast, when networks of the size and connectivity of the biological GRNs are constructed with randomly placed links, they display an exponential increase in feedback loops consisting of three or more genes, which number in the thousands (Figure 2A–C, Figure 2—figure supplement 1A,B, heavily shaded bars, and Figure 2—figure supplement 4B). Each of 1000 randomly simulated E. coli networks had at least one long feedback loop. The vastly different abundances of feedback loops clearly demonstrate the profound difference in topologies between real and random networks. Statistical analyses suggest that there is an extremely small probability (<10−6) that the absence of long feedback loops with >3 genes in E. coli is a chance event (Figure 2—figure supplement 2A). Similar results hold for S. cerevisiae (Figure 2—figure supplement 2B) and human (Figure 2—figure supplement 2C). These results are robust to variations in the confidence levels of the E. coli and S. cerevisiae GRNs (Figure 2—figure supplement 3E,J), despite large variations in other properties of the GRNs (Figure 2—figure supplement 3A–D,F–I), and remain valid when different random models are considered (Figure 2—figure supplement 4B).10.7554/eLife.02863.004Figure 2.Feedback loops in real and simulated GRNs.
Bottom Line: The gene regulatory network (GRN) is the central decision-making module of the cell.BQS explains many of the small- and large-scale properties of GRNs, provides conditions for evolvable robustness, and highlights general features of transcriptional response.BQS is severely compromised in a human cancer cell line, suggesting that loss of BQS might underlie the phenotypic plasticity of cancer cells, and highlighting a possible sequence of GRN alterations concomitant with cancer initiation.
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