Natural Computing

, Volume 16, Issue 2, pp 353–363 | Cite as

Dynamical regimes in non-ergodic random Boolean networks

  • Marco Villani
  • Davide Campioli
  • Chiara Damiani
  • Andrea Roli
  • Alessandro Filisetti
  • Roberto Serra


Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. Random boolean networks not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a theoretical viewpoint, since it is possible to tune their asymptotic behaviour from order to disorder. The usual approach characterizes network families as a whole, either by means of static or dynamic measures. We show here that a more detailed study, based on the properties of system’s attractors, can provide information that makes it possible to predict with higher precision important properties, such as system’s response to gene knock-out. A new set of principled measures is introduced, that explains some puzzling behaviours of these networks. These results are not limited to random Boolean network models, but they are general and hold for any discrete model exhibiting similar dynamical characteristics.


Random Boolean networks Dynamical regimes Attractors Dynamical measures Gene knock-out 



We are deeply indebted to Stuart Kauffman for his inspiring ideas and for several discussions on various aspects of random Boolean networks. We also gratefully acknowledge useful discussions with David Lane and Alex Graudenzi.

Authors’ contributions

MV and RS conceived and designed the experiments and provided a first analysis of the results. DC developed the code and performed the experiments. CD performed further experiments. MV, RS, CD, AR and AF analysed and discussed the results. AR, MV, CD, and AF wrote the paper. All authors gave final approval for publication.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Marco Villani
    • 1
    • 2
  • Davide Campioli
    • 1
  • Chiara Damiani
    • 3
  • Andrea Roli
    • 4
  • Alessandro Filisetti
    • 2
    • 5
  • Roberto Serra
    • 1
    • 2
  1. 1.Department of Physics, Informatics and MathematicsUniversity of Modena and Reggio EmiliaModenaItaly
  2. 2.European Centre for Living Technology, Ca’ MinichVenetiaItaly
  3. 3.Department of Informatics, Systems and CommunicationUniversity Milano-BicoccaMilanItaly
  4. 4.Department of Computer Science and Engineering (DISI)Università di BolognaCesenaItaly
  5. 5.Explora Srl.RomeItaly

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