Biology – Quantitative Biology – Molecular Networks
Scientific paper
2004-12-02
Proc. Natl. Acad. Sci. USA 101 (2004), 17102-17107
Biology
Quantitative Biology
Molecular Networks
Final version available through PNAS open access at http://www.pnas.org/cgi/content/abstract/0407783101v1
Scientific paper
10.1073/pnas.0407783101
We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are dynamically stable. Furthermore, for architectures with few inputs per node, the dynamics of the networks is close to critical. In addition, the fraction of genes that are active decreases with the number of inputs per node. These results are based upon investigating ensembles of networks using analytical methods. Also, for different in-degree distributions, the numbers of fixed points and cycles are calculated, with results intuitively consistent with stability analysis; fewer inputs per node implies more cycles, and vice versa. There are hints that genetic networks acquire broader degree distributions with evolution, and hence our results indicate that for single cells, the dynamics should become more stable with evolution. However, such an effect is very likely compensated for by multicellular dynamics, because one expects less stability when interactions among cells are included. We verify this by simulations of a simple model for interactions among cells.
Kauffman Stuart
Peterson Carsten
Samuelsson Björn
Troein Carl
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