Genetic networks with canalyzing Boolean rules are always stable.

By Stuart A. Kauffman, C. Peterson, B. Samuelsson, C. Troein. Proceedings of the National Academy of Sciences of the United States of America, 2004

352 citations recorded by the source corpus.

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.

Subfields: Genetics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/b082b612bfddafb12178ae508ef922fcc5125955

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Citations in the corpus

Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems (2016, methodology): “For example, Boolean network models were used to study gene evolution [506], attractor number variation with asynchronous stochastic updating [507], gene expression in the state space [499], and organism system growth rate improvement [508].”
Being Critical of Criticality in the Brain (2012, background): “Many other researchers have pointed out, with very general models, that information storage (Socolar and Kauffman, 2003; Kauffman et al., 2004; Haldeman and Beggs, 2005) and computational power (Bertschinger and Natschlager, 2004) are expected to be optimized there as well (Chialvo, 2004, 2010;…”
Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology (2007, result): “It is because our work starts from such a developmental framework that S(0) and S‘ play a central role; this is in contrast with most studies determining the generic properties of random Boolean networks [30,31,37,38,47–50].”