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On Circuit Functionality in Boolean Networks

Bulletin of Mathematical Biology volume 75, pages 906–919 (2013)Cite this article

Abstract

It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it “generates” several stable states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of “generates.” Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.

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Acknowledgements

This paper results from a collective discussion that took place during the workshop Logical formalism, gains, and challenges for the modeling of regulatory networks, held at Rabat, Morocco, from 12th to 15th of April 2011. We are grateful to Mohamed Hedi Ben Amor, Claudine Chaouiya, Madalena Chaves, Eric Fanchon, Pedro Monteiro, Elisabeth Remy, Paul Ruet, Sylvain Sené, Christophe Soulé, Laurent Tournier, and Laurent Trilling for taking part to this discussion. This work is partially supported by FONDECYT project 1090549 and BASAL project CMM, Universidad de Chile, and also by the French National Agency for Research (ANR-10-BLANC-0218 BioTempo project).

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Authors and Affiliations

  1. Lab. I3S UMR CNRS 7271, Université Nice-Sophia Antipolis, 2000 Route des Lucioles, 06903, Sophia Antipolis, France

    Jean-Paul Comet, Mathilde Noual & Adrien Richard

  2. CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Concepción, Chile

    Julio Aracena

  3. U900 INSERM, Mines ParisTech, Institut Curie, Paris, France

    Laurence Calzone

  4. AGIM CNRS FRE 3405, Université Joseph Fourier-Grenoble 1, 38706, La Tronche, France

    Jacques Demongeot

  5. IXXI, Institut Rhône-Alpin des Systèmes Complexes, 69007, Lyon, France

    Jacques Demongeot

  6. Unit of Theoretical and Computational Biology, Université Libre de Bruxelles, C.P. 231, 1050, Brussels, Belgium

    Marcelle Kaufman

  7. Centre Intégratif de Génomique, UNIL-Université de Lausanne, 1015, Lausanne, Switzerland

    Aurélien Naldi

  8. Université Mohammed V, Rabat, Morocco

    El Houssine Snoussi

  9. Institut de Biology de l’ENS (IBENS) INSERM U1024 & CNRS UMR 8197, École Normale Supérieure, Paris, France

    Denis Thieffry

Authors
  1. Jean-Paul Comet
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  2. Mathilde Noual
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  3. Adrien Richard
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  4. Julio Aracena
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  5. Laurence Calzone
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  6. Jacques Demongeot
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  7. Marcelle Kaufman
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  8. Aurélien Naldi
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  9. El Houssine Snoussi
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  10. Denis Thieffry
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Correspondence to Jean-Paul Comet.

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Comet, JP., Noual, M., Richard, A. et al. On Circuit Functionality in Boolean Networks. Bull Math Biol 75, 906–919 (2013). https://doi.org/10.1007/s11538-013-9829-2

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  • DOI: https://doi.org/10.1007/s11538-013-9829-2

Keywords

  • Boolean network
  • Interaction graph
  • Feedback circuit
  • Fixed point
  • Multistability
  • Cyclic attractor