Acta Biotheoretica

, Volume 61, Issue 1, pp 21–39 | Cite as

Formal Methods for Hopfield-Like Networks

  • Hedi Ben Amor
  • Fabien Corblin
  • Eric Fanchon
  • Adrien Elena
  • Laurent Trilling
  • Jacques Demongeot
  • Nicolas Glade
Regular Article

Abstract

Building a meaningful model of biological regulatory network is usually done by specifying the components (e.g. the genes) and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge (about structure and behavior). The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors.

Keywords

Regulatory networks Hopfield-like networks Biological model building Constraint-based programming Arabidopsis thaliana 

References

  1. Alon U (2003) Biological networks: the tinkerer as an engineer. Science 301:1866–1867CrossRefGoogle Scholar
  2. Apt K (2003) Principles of constraint programming. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  3. Aracena J, Demongeot J (2004) Mathematical methods for inferring regulatory networks interactions: application to genetic regulation. Acta Biotheoretica 52:391–400CrossRefGoogle Scholar
  4. Aracena J, Lamine SB, Mermet M, Cohen O, Demongeot J (2003) Mathematical modelling in genetic networks: relationships between the genetic expression and both chromosomic breakage and positive circuits. IEEE Trans Syst Man Cyber 33:825–834CrossRefGoogle Scholar
  5. Ben-Amor H, Demongeot J, Sené S (2008) Structural sensitivity of neural and genetic networks. In: Springer (ed) LNCS 5317 Proceedings of 7th mexican international conference on artificial intelligence, 2008 (MICAI’08), pp 973–986Google Scholar
  6. Ben-Amor H, Cadau S, Elena A, Dhouailly D, Demongeot J (2009) Regulatory networks analysis: robustness in biological regulatory networks. In: IEEE (ed) IEEE Proceedings of international conference on advanced information networking and applications workshops, 2009 (AINA’09), pp 924–929Google Scholar
  7. Carlsson M, Ottosson G, Carlson B (1997) An open-ended finite domain constraint solver. In: Proceedings of programming languages: implementations, logics, and programsGoogle Scholar
  8. Coen ES, Meyerowitz EM (1991) The war of the whorls: genetic interactions controlling flower development. Nature pp 31–37Google Scholar
  9. Corblin F, Tripodi S, Fanchon E, Ropers D, Trilling L (2009) A declarative constraint-based method for analysing discrete genetic regulatory networks. Biosystems 98:91–104CrossRefGoogle Scholar
  10. Corblin F, Fanchon E, Trilling L (2010) Applications of a formal approach to decipher discrete genetic networks. BMC Bioinformatics 11:385CrossRefGoogle Scholar
  11. Corblin F, Bordeaux F, Fanchon E, Hamadi Y, Trilling L (2011) Connections and integration with sat solvers: a survey and a case study in computational biology. In: Springer (ed) Hybrid Optimization: optimization and its applications, vol 45, pp 425–461Google Scholar
  12. Demongeot J, Aracena J, Thuderoz F, Baum TP, Cohen O (2003) Genetic regulation networks: circuits, regulons and attractors. C R Biol 326:171–188CrossRefGoogle Scholar
  13. Demongeot J, Elena A, Sené S (2008) Robustness in neural and genetic networks. Acta Biotheor 56:27–49CrossRefGoogle Scholar
  14. Dubrova E, Teslenko M (2011) A sat-based algorithm for finding attractors in synchronous boolean networks. IEEE/ACM Trans Comput Biol Bioinfo 8:1393–1399CrossRefGoogle Scholar
  15. Eén N, Biere A (2005) Effective preprocessing in SAT through variable and clause elimination. In: SAT’2005—theory and applications of satisfiability testing, LNCS 3569Google Scholar
  16. Eén N, Sörensson N (2004) An extensible SAT-solver. In: SAT’2003—theory and applications of satisfiability testing, LNCS 2919Google Scholar
  17. Elena A (2009) Robustesse des réseaux d’automates booléens à seuil aux modes d’itération. application à la modélisation des réseaux de régulation génétique. PhD thesis, Université Joseph Fourier, GrenobleGoogle Scholar
  18. Giacomantonio EC, Goodhill GJ (2010) A boolean model of the gene regulatory network underlying mammalian cortical area development. PLoS Comput Biol 6:e1000,936. doi:10.1371/journal.pcbi.1000936
  19. Glade N, Elena A, Corblin F, Fanchon E, Demongeot J, Ben-Amor H (2011) Determination, optimization and taxonomy of regulatory networks. the example of Arabidopsis thaliana flower morphogenesis. In: IEEE (ed) IEEE proceedings of international conference on advanced information networking and applications workshops, AINA’ 11 and BLSMC’ 11, Singapore, IEEE Proceedings, PsicatawayGoogle Scholar
  20. Gowda T, Vrudhula S, Seungchan K (2009) Prediction of pairwise gene interaction using threshold logic. The challenges of systems biology. Ann N Y Acad Sci 1158(1):276–286CrossRefGoogle Scholar
  21. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79:2554–2558CrossRefGoogle Scholar
  22. Kauffman S (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 22:437–467CrossRefGoogle Scholar
  23. Mendoza L, Alvarez-Buylla E (1998) Dynamics of the genetic regulatory network: Arabidopsis thaliana flower morphogenesis. J Theor Biol 193(2):307–319CrossRefGoogle Scholar
  24. Remy E, Ruet P, Thieffry D (2008) Graphic requirements for multistability and attractive cycles in a boolean dynamical framework. Adv Appl Math 41:335–350CrossRefGoogle Scholar
  25. Richard A (2010) Negative circuits and sustained oscillations in asynchronous automata networks. Adv Appl Math 44:378–392CrossRefGoogle Scholar
  26. Thomas R (1980) On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. Springer Ser Synerg 9:180–193CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Hedi Ben Amor
    • 1
  • Fabien Corblin
    • 2
  • Eric Fanchon
    • 2
  • Adrien Elena
    • 1
  • Laurent Trilling
    • 2
  • Jacques Demongeot
    • 1
  • Nicolas Glade
    • 1
  1. 1.UJF—University of Grenoble 1—CNRSAGIM Laboratory, Laboratory of Ageing Imaging and Modeling, FRE 3405La TroncheFrance
  2. 2.UJF—University of Grenoble 1—CNRSTIMC-IMAG Laboratory, Laboratory of Techniques for biomedical engineering and complexity management—Informatics, Mathematics and Applications, UMR 5525La TroncheFrance

Personalised recommendations