Abstract
When studying a biological regulatory network, it is usual to use boolean network models. In these models, boolean variables represent the behavior of each component of the biological system. Taking in account that the size of these state transition models grows exponentially along with the number of components considered, it becomes important to have tools to minimize such models. In this paper, we relate bisimulations, which are relations used in the study of automata (general state transition models) with attractors, which are an important feature of biological boolean models. Hence, we support the idea that bisimulations can be important tools in the study some main features of boolean network models. We also discuss the differences between using this approach and other well-known methodologies to study this kind of systems and we illustrate it with some examples.
This work was supported in part by the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013. The author also acknowledges the support of FCT via the Ph.D. scholarship PD/BD/114186/2016.
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References
Blackburn, P., De Rijke, M., Venema, Y.: Modal Logic: Graph. Darst, vol. 53. Cambridge University Press, Cambridge (2002)
Chaves, M.: Predictive analysis of dynamical systems: combining discrete and continuous formalisms. Ph.D. thesis, Gipsa-lab (2013)
Chaves, M., Preto, M.: Hierarchy of models: from qualitative to quantitative analysis of circadian rhythms in cyanobacteria. Chaos Interdisc. J. Nonlinear Sci. 23(2), 025113 (2013)
Chaves, M., Tournier, L.: Predicting the asymptotic dynamics of large biological networks by interconnections of boolean modules. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 3026–3031. IEEE (2011)
De Jong, H.: Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9(1), 67–103 (2002)
Figueiredo, D.: Differential dynamic logic and applications. Master’s thesis, University of Aveiro (2015)
Naldi, A., Remy, E., Thieffry, D., Chaouiya, C.: A reduction of logical regulatory graphs preserving essential dynamical properties. In: Degano, P., Gorrieri, R. (eds.) CMSB 2009. LNCS, vol. 5688, pp. 266–280. Springer, Heidelberg (2009)
Platzer, A.: Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics. Springer, Heidelberg (2010)
Thomas, R., Kaufman, M.: Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits. Chaos Interdisc. J. Nonlinear Sci. 11(1), 180–195 (2001)
Tournier, L., Chaves, M.: Interconnection of asynchronous boolean networks, asymptotic and transient dynamics. Automatica 49(4), 884–893 (2013)
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Figueiredo, D. (2016). Relating Bisimulations with Attractors in Boolean Network Models. In: Botón-Fernández, M., MartÃn-Vide, C., Santander-Jiménez, S., Vega-RodrÃguez, M.A. (eds) Algorithms for Computational Biology. AlCoB 2016. Lecture Notes in Computer Science(), vol 9702. Springer, Cham. https://doi.org/10.1007/978-3-319-38827-4_2
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DOI: https://doi.org/10.1007/978-3-319-38827-4_2
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