Genetic networks with canalyzing Boolean rules are always stable.

@article{citeulike:3060, 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.}, address = {Department of Cell Biology and Physiology, Health Sciences Center, University of New Mexico, Albuquerque, NM 87131.}, author = {Kauffman, Stuart and Peterson, Carsten and Samuelsson, Bj\"{o}rn and Troein, Carl }, citeulike-article-id = {3060}, doi = {http://dx.doi.org/10.1073/pnas.0407783101}, issn = {0027-8424}, journal = {Proc Natl Acad Sci U S A}, keywords = {boolean}, month = {November}, posted-at = {2007-06-19 22:41:44}, priority = {2}, title = {Genetic networks with canalyzing Boolean rules are always stable.}, url = {http://dx.doi.org/10.1073/pnas.0407783101}, year = {2004} }

TY - JOUR ID - citeulike:3060 L3 - citeulike-article-id:3060 TI - Genetic networks with canalyzing Boolean rules are always stable. JF - Proc Natl Acad Sci U S A AD - Department of Cell Biology and Physiology, Health Sciences Center, University of New Mexico, Albuquerque, NM 87131. SN - 0027-8424 N2 - 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. KW - boolean AU - Kauffman, Stuart AU - Peterson, Carsten AU - Samuelsson, Björn AU - Troein, Carl PY - 2004/11/30/ UR - http://dx.doi.org/10.1073/pnas.0407783101 ER -