Bulletin of Mathematical Biology

, Volume 75, Issue 6, pp 906–919 | Cite as

On Circuit Functionality in Boolean Networks

  • Jean-Paul Comet
  • Mathilde Noual
  • Adrien Richard
  • Julio Aracena
  • Laurence Calzone
  • Jacques Demongeot
  • Marcelle Kaufman
  • Aurélien Naldi
  • El Houssine Snoussi
  • Denis Thieffry
Original Article


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.


Boolean network Interaction graph Feedback circuit Fixed point Multistability Cyclic attractor 



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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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Jean-Paul Comet
    • 1
  • Mathilde Noual
    • 1
  • Adrien Richard
    • 1
  • Julio Aracena
    • 2
  • Laurence Calzone
    • 3
  • Jacques Demongeot
    • 4
    • 5
  • Marcelle Kaufman
    • 6
  • Aurélien Naldi
    • 7
  • El Houssine Snoussi
    • 8
  • Denis Thieffry
    • 9
  1. 1.Lab. I3S UMR CNRS 7271Université Nice-Sophia AntipolisSophia AntipolisFrance
  2. 2.CI2MA and Departamento de Ingeniería MatemáticaUniversidad de ConcepciónConcepciónChile
  3. 3.U900 INSERM, Mines ParisTechInstitut CurieParisFrance
  4. 4.AGIM CNRS FRE 3405Université Joseph Fourier-Grenoble 1La TroncheFrance
  5. 5.IXXI, Institut Rhône-Alpin des Systèmes ComplexesLyonFrance
  6. 6.Unit of Theoretical and Computational BiologyUniversité Libre de BruxellesBrusselsBelgium
  7. 7.Centre Intégratif de GénomiqueUNIL-Université de LausanneLausanneSwitzerland
  8. 8.Université Mohammed VRabatMorocco
  9. 9.Institut de Biology de l’ENS (IBENS) INSERM U1024 & CNRS UMR 8197École Normale SupérieureParisFrance

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