Formal Methods for Hopfield-Like Networks
- 147 Downloads
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.
KeywordsRegulatory networks Hopfield-like networks Biological model building Constraint-based programming Arabidopsis thaliana
The authors are very grateful to O. Bastien (PCV, CEA Grenoble, France) and J. Cohen (Brandeis University, USA) for their help and stimulating discussions. This work was supported by the European Network of Excellence ‘Virtual Physiological Human’ (VPH-NoE) through its PhD scholarship program, and by the Rhône-Alpes Complex System Insitute IXXI.
- 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
- 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
- Carlsson M, Ottosson G, Carlson B (1997) An open-ended finite domain constraint solver. In: Proceedings of programming languages: implementations, logics, and programsGoogle Scholar
- Coen ES, Meyerowitz EM (1991) The war of the whorls: genetic interactions controlling flower development. Nature pp 31–37Google Scholar
- 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
- 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
- Eén N, Sörensson N (2004) An extensible SAT-solver. In: SAT’2003—theory and applications of satisfiability testing, LNCS 2919Google Scholar
- 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
- 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
- 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