Boolean Dynamics of Compound Regulatory circuits

  • Elisabeth RemyEmail author
  • Brigitte Mossé
  • Denis Thieffry


In biological regulatory networks represented in terms of signed, directed graphs, topological motifs such as circuits are known to play key dynamical roles. After reviewing established results on the roles of simple motifs, we present novel results on the dynamical impact of the addition of a short-cut in a regulatory circuit. More precisely, based on a Boolean formalisation of regulatory graphs, we provide complete descriptions of the discrete dynamics of particular motifs, under the synchronous and asynchronous updating schemes. These motifs are made of a circuit of arbitrary length, combining positive and negative interactions in any sequence, and are including a short-cut, and hence a smaller embedded circuit.


Regulatory motifs Boolean dynamics 


  1. 1.
    Alon, U.: Network motifs: theory and experimental approaches. Nat. Rev. Genet. 8 (6), 450–461 (2007)CrossRefGoogle Scholar
  2. 2.
    Aracena, J., Demongeot, J., Goles, E.: Positive and negative circuits in discrete neural networks. IEEE Trans. Neural Netw. 15 (1), 77–83 (2004)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bang-Jensen, J., Gutin, G.: Digraphs, Theory, Algorithms, Applications. Springer, Berlin (2008)zbMATHGoogle Scholar
  4. 4.
    Bérenguier, D., Chaouiya, C., Monteiro, P.T., Naldi, A., Remy, E., Thieffry, D., Tichit, L.: Dynamical modeling and analysis of large cellular regulatory networks. Chaos (Woodbury N.Y.) 23 (2), 025114 (2013)Google Scholar
  5. 5.
    Chaouiya, C., Remy, E., Mossé, B., Thieffry, D.: Qualitative analysis of regulatory graphs: a computational tool based on a discrete formal framework. In: Lecture Notes in Control and Information Science, vol. 294, pp. 119–26. Springer, Berlin (2003)Google Scholar
  6. 6.
    Comet, J.-P., Noual, M., Richard, A., Aracena, J., Calzone, L., Demongeot, J., Kaufman, M., Naldi, A., Snoussi, E.H., Thieffry, D.: On circuit functionality in boolean networks. Bull. Math. Biol. 75 (6), 906–919 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Didier, G., Remy, E.: Relations between gene regulatory networks and cell dynamics in Boolean models. Discret. Appl. Math. 160 (15), 2147–2157 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Garg, A., Dicara, A., Xenarios, I., Mendoza, L., De Micheli, G.: Synchronous vs. Asynchronous Modeling of Gene Regulatory Networks, Bioinformatics (Oxford, England) 24 (17), 1917–1925Google Scholar
  9. 9.
    Khalil, A.S., Collins, J.J.: Synthetic biology: applications come of age. Nat. Rev. Genet. 11 (5), 367–379 (2010)CrossRefGoogle Scholar
  10. 10.
    Naldi, A., Thieffry, D., Chaouiya, C.: Decision diagrams for the representation and analysis of logical models of genetic networks. In: Computational Methods in Systems Biology. Lecture Notes in Computer Science, vol. 4695, pp. 233–47. Springer, Berlin (2007)Google Scholar
  11. 11.
    Naldi, A., Remy, E., Thieffry, D., Chaouiya, C.: Dynamically consistent reduction of logical regulatory graphs. Theor. Comput. Sci. 412 (21), 2207–2218 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Purcell, O., Savery, N.J., Grierson, Claire, S., di Bernardo, M.: A comparative analysis of synthetic genetic oscillators. J. R. Soc. Interface/R. Soc. 7 (52), 1503–1524 (2010)Google Scholar
  13. 13.
    Remy, E., Mossé, B., Chaouiya, C., Thieffry, D.: A description of dynamical graphs associated to elementary regulatory circuits. Bioinformatics (Oxford, England) 19 (Suppl. 2), 172–178 (2003)Google Scholar
  14. 14.
    Remy, E., Ruet, P., Thieffry, D.: Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework. Adv. Appl. Math. 41 (3), 335–350 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Richard, A.: Positive circuits and maximal number of fixed points in discrete dynamical systems. Appl. Math. 157 (15), 3281–3288 (2009)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Richard, A., Comet, J.-P.: Necessary conditions for multistationarity in discrete dynamical systems. Discret. Appl. Math. 155 (18), 2403–2413 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Soulé, C.: Graphic requirements for multistationarity. Complexus 1, 123–133 (2003)CrossRefGoogle Scholar
  18. 18.
    Thomas, R.: On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. In: Numerical Methods in the Study of Critical Phenomena. Springer Series in Synergetics 9, 180–193 (1981)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Thomas, R., D’Ari, R.: Biological Feedback. CRC Press, Boca Raton (1990)zbMATHGoogle Scholar
  20. 20.
    Weber, W., Fussenegger, M.: Synthetic gene networks in mammalian cells. Curr. Opin. Biotechnol. 21 (5), 690–696 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Elisabeth Remy
    • 1
    Email author
  • Brigitte Mossé
    • 1
  • Denis Thieffry
    • 2
  1. 1.Aix Marseille Université, CNRSCentrale MarseilleMarseilleFrance
  2. 2.Computational Systems Biology teamInstitut de Biologie de l’Ecole Normale Supérieure (IBENS), CNRS UMR8197, INSERM U1024, Ecole Normale Supérieure, PSL Research UniversityParisFrance

Personalised recommendations