Abstract
We discuss different ways of applying logic to analyze the structure and dynamics of regulatory networks in molecular biology. First, the structure of a bioregulatory network may be described naturally using propositional or multi-valued logic. Second, the resulting non-deterministic dynamics may be analyzed using temporal logic and model checking. Third, information on time delays may be incorporated using a refined modeling approach based on timed automata.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alur, R.: Timed Automata. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 8–22. Springer, Heidelberg (1999)
Alur, R., Henzinger, T., Lafferriere, G., Pappas, G.: Discrete abstractions of hybrid systems. Proceedings of the IEEE 88, 971–984 (2000)
Batt, G., Ropers, D., de Jong, H., Geiselmann, J., Mateescu, R., Page, M., Schneider, D.: Analysis and verification of qualitative models of genetic regulatory networks: A model-checking approach. In: 19th International Joint Conference on Artificial Intelligence, IJCAI 2005, Edinburgh, pp. 370–375 (2005)
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)
Chabrier-Rivier, N., Chiaverini, M., Danos, V., Fages, F., Schächter, V.: Modeling and querying biomolecular interaction networks. Theoret. Comput. Sci. 325(1), 25–44 (2004)
Chaouiya, C., Remy, E., Mossé, B., Thieffry, D.: Qualitative Analysis of Regulatory Graphs: A Computational Tool Based on a Discrete Formal Framework. In: Bru, R., Romero-Vivó, S. (eds.) POSTA 2009. Lecture Notes in Control and Information Sciences, vol. 389, pp. 830–832. Springer, Heidelberg (2009)
Fauré, A., Naldi, A., Chaouiya, C., Thieffry, D.: Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinform. 22, 124–131 (2006)
Fauré, A., Thieffry, D.: Logical modelling of cell cycle control in eukaryotes: a comparative study. Mol. BioSyst. 5, 1569–1581 (2009)
Glass, L., Kauffman, S.A.: The logical analysis of continuous, non-linear biochemical control networks. J. Theor. Biol. 39, 103–129 (1973)
Kauffman, S.: The Origins of Order. Oxford University Press (1993)
Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22, 437–467 (1969)
Kaufman, M., Andris, F., Leo, O.: A logical analysis of T cell activation and anergy. PNAS 96(7), 3894–3899 (1999)
Kitano, H.: Systems biology: A brief overview. Science 295, 1662–1664 (2002)
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, E., Ruet, P.: Incorporating Time Delays into the Logical Analysis of Gene Regulatory Networks. Bioinform. 24, 220–226 (2008)
Richard, A.: Modèle formel pour les réseaux de régulation génétique et influence des circuits de rétroaction. PhD thesis, Univ. d’Evry, France (2006)
Richard, A.: Negative circuits and sustained oscillations in asynchronous automata networks. Advances in Applied Mathematics 44(4), 378–392 (2010)
Richard, A., Comet, J.-P.: Necessary conditions for multistationarity in discrete dynamical systems. Discrete Appl. Math. 155(18), 2403–2413 (2007)
Siebert, H.: Analysis of discrete bioregulatory networks using symbolic steady states. Bull. Math. Biol. 73, 873–898 (2011)
Siebert, H., Bockmayr, A.: Incorporating time delays into the logical analysis of gene regulatory networks. In: Priami, C. (ed.) CMSB 2006. LNCS (LNBI), vol. 4210, pp. 169–183. Springer, Heidelberg (2006)
Siebert, H., Bockmayr, A.: Context Sensitivity in Logical Modeling with Time Delays. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 64–79. Springer, Heidelberg (2007)
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)
Siebert, H., Bockmayr, A.: Temporal constraints in the logical analysis of regulatory networks. Theor. Comput. Sci. 391(3), 258–275 (2008)
Soulé, C.: Mathematical approaches to gene regulation and differentiation. C.R. Paris Biolgies 329, 13–20 (2006)
Sugita, M.: Functional analysis of chemical systems in vivo using a logical circuit equivalent. J. Theor. Biol. 1, 415–430 (1961)
Szallasi, Z., Stelling, J., Periwal, V.: System modeling in cellular biology. MIT Press (2006)
Thomas, R.: Boolean formalisation of genetic control circuits. J. Theor. Biol. 42, 565–583 (1973)
Thomas, R.: Kinetic logic: a boolean approach to the analysis of complex regulatory systems. Lecture Notes in Biomathematics, vol. 29. Springer (1979)
Thomas, R.: On the relation between the logical structure of systems and their abilities to generate multiple steady states and sustained oscillations. In: Series in Synergetics, vol. 9, pp. 180–193. Springer (1981)
Thomas, R., d’Ari, R.: Biological Feedback. CRC Press (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
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bockmayr, A., Siebert, H. (2013). Bio-Logics: Logical Analysis of Bioregulatory Networks. In: Voronkov, A., Weidenbach, C. (eds) Programming Logics. Lecture Notes in Computer Science, vol 7797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37651-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-37651-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37650-4
Online ISBN: 978-3-642-37651-1
eBook Packages: Computer ScienceComputer Science (R0)