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Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks.

Albergante L, Blow JJ, Newman TJ - Elife (2014)

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.

View Article: PubMed Central - PubMed

Affiliation: College of Life Sciences, University of Dundee, Dundee, United Kingdom l.albergante@dundee.ac.uk.

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p-Value estimation for the number of long feedback loops.The theoretical probability density function of the number of feedback loops of a given length is not well characterized. However, calling nloops the number of feedback loops of a given length in a single simulation, the transformation  appears to produce normally distributed data in all the datasets analysed. The normality of the distribution was supported by the Shapiro–Wilk normality test. Using this transformation it is possible to estimate the probability of having no feedback loops of length 14 in a random graph. (A–C). The data for E. coli, yeast and human (black line) support quite well the fitted log-normal distribution (red line), as expected from the very low p-value of the Shapiro–Wilk normality test. Analysing the number of loops of a specific length was preferred to performing an analysis combining the information on the number of loops of different length. This choice was made due to the non-independence of the number of loops of different length.DOI:http://dx.doi.org/10.7554/eLife.02863.006
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fig2s2: p-Value estimation for the number of long feedback loops.The theoretical probability density function of the number of feedback loops of a given length is not well characterized. However, calling nloops the number of feedback loops of a given length in a single simulation, the transformation appears to produce normally distributed data in all the datasets analysed. The normality of the distribution was supported by the Shapiro–Wilk normality test. Using this transformation it is possible to estimate the probability of having no feedback loops of length 14 in a random graph. (A–C). The data for E. coli, yeast and human (black line) support quite well the fitted log-normal distribution (red line), as expected from the very low p-value of the Shapiro–Wilk normality test. Analysing the number of loops of a specific length was preferred to performing an analysis combining the information on the number of loops of different length. This choice was made due to the non-independence of the number of loops of different length.DOI:http://dx.doi.org/10.7554/eLife.02863.006

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.


Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks.

Albergante L, Blow JJ, Newman TJ - Elife (2014)

p-Value estimation for the number of long feedback loops.The theoretical probability density function of the number of feedback loops of a given length is not well characterized. However, calling nloops the number of feedback loops of a given length in a single simulation, the transformation  appears to produce normally distributed data in all the datasets analysed. The normality of the distribution was supported by the Shapiro–Wilk normality test. Using this transformation it is possible to estimate the probability of having no feedback loops of length 14 in a random graph. (A–C). The data for E. coli, yeast and human (black line) support quite well the fitted log-normal distribution (red line), as expected from the very low p-value of the Shapiro–Wilk normality test. Analysing the number of loops of a specific length was preferred to performing an analysis combining the information on the number of loops of different length. This choice was made due to the non-independence of the number of loops of different length.DOI:http://dx.doi.org/10.7554/eLife.02863.006
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4151086&req=5

fig2s2: p-Value estimation for the number of long feedback loops.The theoretical probability density function of the number of feedback loops of a given length is not well characterized. However, calling nloops the number of feedback loops of a given length in a single simulation, the transformation appears to produce normally distributed data in all the datasets analysed. The normality of the distribution was supported by the Shapiro–Wilk normality test. Using this transformation it is possible to estimate the probability of having no feedback loops of length 14 in a random graph. (A–C). The data for E. coli, yeast and human (black line) support quite well the fitted log-normal distribution (red line), as expected from the very low p-value of the Shapiro–Wilk normality test. Analysing the number of loops of a specific length was preferred to performing an analysis combining the information on the number of loops of different length. This choice was made due to the non-independence of the number of loops of different length.DOI:http://dx.doi.org/10.7554/eLife.02863.006
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.

View Article: PubMed Central - PubMed

Affiliation: College of Life Sciences, University of Dundee, Dundee, United Kingdom l.albergante@dundee.ac.uk.

Show MeSH
Related in: MedlinePlus