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Boolean networks with biologically relevant rules show ordered behavior.

S Nikolajewa1, M Friedel, T Wilhelm

  • 1Theoretical Systems Biology, Leibniz Institute for Age Research, Fritz Lipmann Institute, Beutenbergstr. 11, Jena D-07745, Germany.

Bio Systems
|December 26, 2006
PubMed
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Hierarchically canalyzing functions (HCFs) govern natural gene regulatory systems. Biologically relevant functions belong to simple HCF subclasses, leading to ordered behavior in Boolean networks.

Area of Science:

  • Computational Biology
  • Systems Biology
  • Boolean Networks

Background:

  • Natural gene regulatory systems are increasingly understood through Boolean networks (BNs).
  • Hierarchically canalyzing functions (HCFs) have been identified as a key subclass of Boolean functions governing these systems.

Purpose of the Study:

  • To conduct a detailed study of the HCF class of Boolean functions.
  • To derive a minimal logical expression for HCFs and calculate the cardinality of the HCF class and its subclasses.
  • To analyze the order-chaos transitions in BNs regulated by HCF subclasses and their biological relevance.

Main Methods:

  • Derivation of a minimal logical expression for all HCFs.
  • Calculation of the cardinality for the HCF class and defined subclasses.

Related Experiment Videos

  • Analysis of Boolean networks using the critical connectivity condition (2K(c)p(1-p)=1).
  • Examination of real gene regulatory rules.

    • Main Results:

    • A new minimal logical expression for HCFs was established.
    • The cardinality of the HCF class and its subclasses was calculated.
    • Nearly all biologically relevant gene regulatory functions were found to belong to the simplest HCF subclasses.
    • Boolean networks utilizing biologically relevant HCF subclasses exhibit ordered behavior.

    Conclusions:

    • The study provides a comprehensive mathematical framework for understanding HCFs.
    • The restriction of biological regulatory functions to simple HCF subclasses simplifies reverse engineering and ensemble studies in systems biology.
    • Ordered behavior in BNs is linked to biologically relevant HCF subclasses.