Graph-Based Modeling of Biological Regulatory Networks: Introduction of Singular States
In the field of biological regulation, models extracted from experimental works are usually complex networks comprising intertwined feedback circuits. R. Thomas and coworkers introduced a qualitative description of the dynamics of such regulatory networks, called the generalized logical analysis, and used the concept of circuit-characteristic states to identify all steady states and functional circuits. These characteristic states play an essential role on the dynamics of the system, but they are not represented in the state graph. In this paper we present an extension of this formalism in which all singular states including characteristic ones are represented. Consequently, the state graph contains all steady states. Model checking is then able to verify temporal properties concerning singular states. Finally, we prove that this new modeling is coherent with R. Thomas’ modeling since all paths of R. Thomas’ dynamics are represented in the new state graph, which in addition shows the influence of singular states on the dynamics.
KeywordsModel Check State Graph Feedback Circuit Regular State Computation Tree Logic
Unable to display preview. Download preview PDF.
- 13.Bernot, G., Comet, J.P., Richard, A., Guespin, J.: A Fruitful Application of Formal Methods to Biological Regulatory Networks, extending Thomas’ asynchronous logical approach with temporal logic. J. Theor. Biol. (in press, 2004)Google Scholar
- 14.Guespin, J., Bernot, G., Comet, J.P., Mriau, A., Richard, A., Hulen, C., Polack, B.: Epigenesis and dynamic similarity in two regulatory networks in pseudomonas aeruginosa. Acta Biotheoretica (in press, 2004)Google Scholar
- 16.Richard, A., Comet, J.P., Bernot, G.: SMBioNet: Selection of Models of Biological Networks, http://smbionet.lami.univ-evry.fr
- 21.Soulé, C.: Graphic requirements for multistationarity. ComPlexUs 1 (2003)Google Scholar
- 24.Heidtke, K.R., Schulze-Kremer, S.: BioSim: A New Qualitative Simulation Environment for Molecular Biology. In: Proceedings of the 6th International Conference in Intelligent Systems for Molecular Biology, pp. 85–94. AAAI Press, Menlo Park (1998)Google Scholar
- 26.Chaouiya, C., Remy, E., Mossé, B., Thieffry, D.: Qualitative analysis of regulatory graphs: a computation tools based an a discrete formal framwork. Lecture Notes on Control and Information Sciences (accepted, 2003)Google Scholar
- 27.Chabrier-Rivier, N., Chiaverini, M., Danos, V., Fages, F., Schächter, V.: Modeling and querying biochemical networks. Theoretical Computer Science (to appear, 2004)Google Scholar
- 33.Bassano, V., Bernot, G.: Marked regulatory graphs: A formal framework to simulate biological regulatory networks with simple automata. In: Proc. of the 14th IEEE International Workshop on Rapid System Prototyping, RSP 2003, San Diego, California, USA (2003)Google Scholar
- 34.Bernot, G., Cassez, F., Comet, J.P., Delaplace, F., Müller, C., Roux, O., Roux, O.H.: Semantics of Biological Regulatory Networks. In: BioConcur, Workshop on Concurrent Models in Molecular Biology. ENTCS series (2003)Google Scholar