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Order or chaos in Boolean gene networks depends on the mean fraction of canalizing functions

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  • Karlsson, Fredrik
  • Hörnquist, Michael

Abstract

We explore the connection between order/chaos in Boolean networks and the naturally occurring fraction of canalizing functions in such systems. This fraction turns out to give a very clear indication of whether the system possesses ordered or chaotic dynamics, as measured by Derrida plots, and also the degree of order when we compare different networks with the same number of vertices and edges. By studying also a wide distribution of indegrees in a network, we show that the mean probability of canalizing functions is a more reliable indicator of the type of dynamics for a finite network than the classical result on stability relating the bias to the mean indegree. Finally, we compare by direct simulations two biologically derived networks with networks of similar sizes but with power-law and Poisson distributions of indegrees, respectively. The biologically motivated networks are not more ordered than the latter, and in one case the biological network is even chaotic while the others are not.

Suggested Citation

  • Karlsson, Fredrik & Hörnquist, Michael, 2007. "Order or chaos in Boolean gene networks depends on the mean fraction of canalizing functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 747-757.
    • Handle: RePEc:eee:phsmap:v:384:y:2007:i:2:p:747-757
    DOI: 10.1016/j.physa.2007.05.050
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    Cited by:

    1. Wang, Huan & Xu, Chuan-Yun & Hu, Jing-Bo & Cao, Ke-Fei, 2014. "A complex network analysis of hypertension-related genes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 166-176.
    2. Xue-Yan Zhang & Tian-Yuan He & Chuan-Yun Xu & Ke-Fei Cao & Xu-Sheng Zhang, 2023. "Theoretical investigation of the pathway-based network of type 2 diabetes mellitus-related genes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-13, June.
    3. Wang, Huan & Hu, Jing-Bo & Xu, Chuan-Yun & Zhang, De-Hai & Yan, Qian & Xu, Ming & Cao, Ke-Fei & Zhang, Xu-Sheng, 2016. "A pathway-based network analysis of hypertension-related genes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 928-939.

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