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Proc Natl Acad Sci U S A. 2004 Dec 7;101(49):17102-7. Epub 2004 Nov 30.

Genetic networks with canalyzing Boolean rules are always stable.

Author information

1
Department of Cell Biology and Physiology, Health Sciences Center, University of New Mexico, Albuquerque, NM 87131, USA.

Abstract

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.

PMID:
15572453
PMCID:
PMC534611
DOI:
10.1073/pnas.0407783101
[Indexed for MEDLINE]
Free PMC Article

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