Abstract
A well-known discrete approach to modeling biological regulatory networks is the logical framework developed by R. Thomas. The network structure is captured in an interaction graph, which, together with a set of Boolean parameters, gives rise to a state transition graph describing the dynamical behavior. Together with E. H. Snoussi, Thomas later extended the framework by including singular values representing the threshold values of interactions. A systematic approach was taken in [10] to link circuits in the interaction graph with character and number of attractors in the state transition graph by using the information inherent in singular steady states. In this paper, we employ the concept of local interaction graphs to strengthen the results in [10]. Using the local interaction graph of a singular steady state, we are able to construct attractors of the regulatory network from attractors of certain subnetworks. As a comprehensive generalization of the framework introduced in [10], we drop constraints concerning the choice of parameter values to include so-called context sensitive networks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bernot, G., Comet, J.-P., Richard, A., Guespin, J.: Application of formal methods to biological regulatory networks: extending Thomas’ asynchronous logical approach with temporal logic. J. Theor. Biol. 229, 339–347 (2004)
Chaouiya, C., Remy, É., Mossé, B., Thieffry, D.: Qualitative analysis of regulatory graphs: a computational tool based on a discrete formal framework. In: First Multidisciplinary International Symposium on Positive Systems: Theory and Applications, POSTA 2003. LNCIS, vol. 294, pp. 119–126. Springer, Heidelberg (2003)
Naldi, A., Thieffry, D., Chaouiya, C.: Decision diagrams for the representation and analysis of logical models of genetic networks. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 233–247. Springer, Heidelberg (2007)
Remy, É., Mossé, B., Chaouiya, C., Thieffry, D.: A description of dynamical graphs associated to elementary regulatory circuits. Bioinform. 19, 172–178 (2003)
Remy, É., Ruet, P.: On differentiation and homeostatic behaviours of Boolean dynamical systems. In: Priami, C. (ed.) Transactions on Computational Systems Biology VIII. LNCS (LNBI), vol. 4780, pp. 92–101. Springer, Heidelberg (2007)
Remy, É., Ruet, P., Thieffry, D.: Graphic requirements for multistability and attractive cycles in a boolean dynamical framework (prépublication, 2005)
Richard, A., Comet, J.-P.: Necessary conditions for multistationarity in discrete dynamical systems. Rapport de Recherche (2005)
Richard, A., Comet, J.-P., Bernot, G.: R. Thomas’ modeling of biological regulatory networks: introduction of singular states in the qualitative dynamics. Fundamenta Informaticae 65, 373–392 (2005)
Robert, F.: Discrete Iterations: A Metric Study. Springer Series in Computational Mathematics, vol. 6. Springer, Heidelberg (1986)
Siebert, H., Bockmayr, A.: Relating attractors and singular steady states in the logical analysis of bioregulatory networks. In: Anai, H., Horimoto, K., Kutsia, T. (eds.) AB 2007. LNCS, vol. 4545, pp. 36–50. Springer, Heidelberg (2007)
Snoussi, E.H., Thomas, R.: Logical identification of all steady states: the concept of feedback loop characteristic states. Bull. Math. Biol. 55, 973–991 (1993)
Soulé, C.: Graphical requirements for multistationarity. ComPlexUs 1, 123–133 (2003)
Thomas, R., d’Ari, R.: Biological Feedback. CRC Press, Boca Raton (1990)
Thomas, R., Kaufman, M.: Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits. Chaos 11, 180–195 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Siebert, H. (2008). Local Structure and Behavior of Boolean Bioregulatory Networks. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds) Algebraic Biology. AB 2008. Lecture Notes in Computer Science, vol 5147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85101-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-85101-1_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85100-4
Online ISBN: 978-3-540-85101-1
eBook Packages: Computer ScienceComputer Science (R0)