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Stability depends on positive autoregulation in Boolean gene regulatory networks.

Pinho R, Garcia V, Irimia M, Feldman MW - PLoS Comput. Biol. (2014)

Bottom Line: The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood.We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation.Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops.

View Article: PubMed Central - PubMed

Affiliation: Department of Biology, Stanford University, Stanford, California, United States of America; PhD Program in Computational Biology, Instituto Gulbenkian de Ciência, Oeiras, Portugal.

ABSTRACT
Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs). The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of GRN models, Boolean networks, to investigate the relationship between autoregulation and network stability and robustness under various conditions. We ran evolutionary simulation experiments for different models of selection, including mutation and recombination. Each generation simulated the development of a population of organisms modeled by GRNs. We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation. Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops. This seems to be the case for most studied eukaryotic transcription factor networks, including those in yeast, flies and mammals.

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Positive autoregulation favors stability.A. Boxplots of the sign of autoregulation (p in Equation (6)) for two network classes: stable (fixed points) and unstable (cycles). Whiskers are 1.5 times the inter-quartile range (the difference between the first and third quartiles). All outliers are represented. B. Histogram of the values of p for stable matrices, i.e., stability (Equation (3)) as a function of p. The dotted line is an exponential function of p. Networks are random and non-evolved. Panels A and B represent the same data in different form. Equation (1) is solved n = 105 times for each p = 0, 0.1,…, 1 (11 bins).
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pcbi-1003916-g001: Positive autoregulation favors stability.A. Boxplots of the sign of autoregulation (p in Equation (6)) for two network classes: stable (fixed points) and unstable (cycles). Whiskers are 1.5 times the inter-quartile range (the difference between the first and third quartiles). All outliers are represented. B. Histogram of the values of p for stable matrices, i.e., stability (Equation (3)) as a function of p. The dotted line is an exponential function of p. Networks are random and non-evolved. Panels A and B represent the same data in different form. Equation (1) is solved n = 105 times for each p = 0, 0.1,…, 1 (11 bins).

Mentions: Figure 1A shows that individual-level stability is strongly associated with p. Stable networks have significantly higher values of p than unstable networks (median of 0.9 compared to 0.4 for unstable networks; Mann-Whitney U p-value ∼0, Figure 1A).


Stability depends on positive autoregulation in Boolean gene regulatory networks.

Pinho R, Garcia V, Irimia M, Feldman MW - PLoS Comput. Biol. (2014)

Positive autoregulation favors stability.A. Boxplots of the sign of autoregulation (p in Equation (6)) for two network classes: stable (fixed points) and unstable (cycles). Whiskers are 1.5 times the inter-quartile range (the difference between the first and third quartiles). All outliers are represented. B. Histogram of the values of p for stable matrices, i.e., stability (Equation (3)) as a function of p. The dotted line is an exponential function of p. Networks are random and non-evolved. Panels A and B represent the same data in different form. Equation (1) is solved n = 105 times for each p = 0, 0.1,…, 1 (11 bins).
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4222607&req=5

pcbi-1003916-g001: Positive autoregulation favors stability.A. Boxplots of the sign of autoregulation (p in Equation (6)) for two network classes: stable (fixed points) and unstable (cycles). Whiskers are 1.5 times the inter-quartile range (the difference between the first and third quartiles). All outliers are represented. B. Histogram of the values of p for stable matrices, i.e., stability (Equation (3)) as a function of p. The dotted line is an exponential function of p. Networks are random and non-evolved. Panels A and B represent the same data in different form. Equation (1) is solved n = 105 times for each p = 0, 0.1,…, 1 (11 bins).
Mentions: Figure 1A shows that individual-level stability is strongly associated with p. Stable networks have significantly higher values of p than unstable networks (median of 0.9 compared to 0.4 for unstable networks; Mann-Whitney U p-value ∼0, Figure 1A).

Bottom Line: The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood.We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation.Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops.

View Article: PubMed Central - PubMed

Affiliation: Department of Biology, Stanford University, Stanford, California, United States of America; PhD Program in Computational Biology, Instituto Gulbenkian de Ciência, Oeiras, Portugal.

ABSTRACT
Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs). The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of GRN models, Boolean networks, to investigate the relationship between autoregulation and network stability and robustness under various conditions. We ran evolutionary simulation experiments for different models of selection, including mutation and recombination. Each generation simulated the development of a population of organisms modeled by GRNs. We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation. Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops. This seems to be the case for most studied eukaryotic transcription factor networks, including those in yeast, flies and mammals.

Show MeSH