Abstract
Genetic Network Analyzer (GNA) is a tool for the qualitative modeling and simulation of gene regulatory networks, based on so-called piecewise-linear differential equation models. We describe the use of this tool in the context of the modeling of bacterial regulatory networks, notably the network of global regulators controlling the adaptation of Escherichia coli to carbon starvation conditions. We show how the modeler, by means of GNA, can define a regulatory network, build a model of the network, determine the steady states of the system, perform a qualitative simulation of the network dynamics, and analyze the simulation results using model-checking tools. The example illustrates the interest of qualitative approaches for the analysis of the dynamics of bacterial regulatory networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bolouri H. (2008) Computational Modelling of Gene Regulatory Networks: A Primer. Imperial College Press, London.
Heinrich R, Schuster S. (1996) The Regulation of Cellular Systems. Chapman & Hall, New York.
de Jong H. (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol, 9:67–103.
Fisher J, Henzinger T. (2007) Executable cell biology. Nat Biotechnol, 25(11):1239–1250.
Karlebach G, Shamir R. (2008) Modelling and analysis of gene regulatory networks. Nat Rev Mol Cell Biol, 9(10):770–780.
Thomas R, d’Ari R. (1990) Biological Feedback. CRC Press, Boca Raton, FL.
Chaouiya C. (2007) Petri net modelling of biological networks. Brief Bioinform, 8(4): 210–219.
Palsson B. (2006) Systems Biology: Properties of Reconstructed Networks. Cambridge University Press, New York.
Ciocchetta F, Hillston J. (2008) Process Algebras in Systems Biology. In Proc. 8th International School on Formal Methods for the Design of Computer, Communication, and Software Systems (SFM 2008), Volume 5016 of LNCS. Edited by Bernardo M, Degano P, Zavattaro G, Springer-Verlag, Berlin, 313–365.
Glass L, Kauffman S. (1973) The logical analysis of continuous non-linear biochemical control networks. J Theor Biol, 39:103–129.
Batt G, de Jong H, Page M, Geiselmann J. (2008) Symbolic reachability analysis of genetic regulatory networks using discrete abstractions. Automatica, 44(4):982–989.
Casey R, de Jong H, Gouzé JL. (2006) Piecewise-linear models of genetic regulatory networks: equilibria and their stability. J Math Biol, 52:27–56.
Edwards R. (2006) Analysis of continuous-time switching networks. Physica D, 146(1–4):165–199.
Farcot E, Gouzé JL. (2009) Periodic solutions of piecewise affine gene network models with non uniform decay rates: the case of a negative feedback loop. Acta Biotheor, 57(4):429–455.
Gouzé JL, Sari T. (2002) A class of piecewise linear differential equations arising in biological models. Dyn Syst, 17(4):299–316.
Mestl T, Plahte E, Omholt S. (1995) A mathematical framework for describing and analysing gene regulatory networks. J Theor Biol, 176(2):291–300.
Glass L, Pasternack J. (1978) Stable oscillations in mathematical models of biological control systems. J Math Biol, 6:207–223.
Plahte E, Kjøglum S. (2005) Analysis and generic properties of gene regulatory networks with graded response functions. Physica D, 201:150–176.
de Jong H, Geiselmann J, Hernandez C, Page M. (2003) Genetic Network Analyzer: qualitative simulation of genetic regulatory networks. Bioinformatics, 19(3):336–344.
de Jong H, Page M. (2008) Search for steady states of piecewise-linear differential equation models of genetic regulatory networks. ACM/IEEE Trans Comput Biol Bioinform, 5(2):208–222.
Monteiro P, Ropers D, Mateescu R, Freitas A, de Jong H. (2008) Temporal logic patterns for querying dynamic models of cellular interaction networks. Bioinformatics, 24(16):i227–i233.
Ropers D, de Jong H, Page M, Schneider D, Geiselmann J. (2006) Qualitative simulation of the carbon starvation response in Escherichia coli. Biosystems, 84(2):124–152.
Ropers D, Baldazzi V, de Jong H. (2011) Model reduction using piecewise-linear approximations preserves dynamic properties of the carbon starvation response in Escherichia coli. ACM/IEEE Trans Comput Biol Bioinform, 8(1):166–181.
Novère NL, Hucka M, Mi H, Moodie S, Schreiber F, Sorokin A, Demir E, Wegner K, Aladjem M, Wimalaratne S, Bergman F, Gauges R, Ghazal P, Kawaji H, Li L, Matsuoka Y, Villéger A, Boyd S, Calzone L, Courtot M, Dogrusoz U, Freeman T, Funahashi A, Ghosh S, Jouraku S, Kim S, Kolpakov F, Luna A, Sahle S, Schmidt E, Watterson S, Wu G, Goryanin I, Kell D, Sander C, Sauro H, Snoep J, Kohn K, Kitano H. (2009) The systems biology graphical notation. Nat Biotechnol, 27(8):735–742.
MH Saier J, Ramseier T, Reizer J. (1996) Regulation of Carbon Utilization. In Escherichia coli and Salmonella: Cellular and Molecular Biology, 2nd ed. Edited by Neidhardt et al., ASM Press, Washington, DC, 1325–1343.
Gonzalez-Gil G, Bringmann P, Kahmann R: Fis is a regulator of metabolism in Escherichia coli. Mol. Microbiol. 1996, 22:21–29.
Ishizuka H, Hanamura A, Inada T, Aiba H. (1994) Mechanism of the down-regulation of cAMP receptor protein by glucose in Escherichia coli: role of autoregulation of the crp gene. EMBO J, 13(13):3077–3082.
Azam TA, Iwata A, Nishimura A, Ueda S, Ishihama A. (1999) Growth phase dependent variation in protein composition of the Escherichia coli nucleoid. J Bacteriol, 181(20):6361–6370.
de Jong H, Gouzé JL, Hernandez C, Page M, Sari T, Geiselmann J. (2004) Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull Math Biol, 66(2):301–340.
Kuipers B. (1994) Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge. MIT Press, Cambridge, MA.
Farcot E. (2006) Geometric properties of a class of piecewise affine biological network models. J Math Biol, 52(3):373–418.
Clarke E, Grumberg O, Peled D. (1999) Model Checking. MIT Press, Boston, MA.
Batt G, Ropers D, de Jong H, Geiselmann J, Mateescu R, Page M, Schneider D. (2005) Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in Escherichia coli. Bioinformatics, 21(Suppl 1):i19–i28.
Monteiro P, Dumas E, Besson B, Mateescu R, Page M, Freitas A, de Jong H. (2009) A service-oriented architecture for integrating the modeling and verification of genetic regulatory networks. BMC Bioinform, 10:450.
Cimatti A, Clarke EM, Giunchiglia E, Giunchiglia F, Pistore M, Roveri M, Sebastiani R, Tacchella A. (2002) NuSMV2: An OpenSource Tool for Symbolic Model Checking. In Proc. 14th Intl. Conf. Computer Aided Verification (CAV 2002), Volume 2404 of LNCS. Edited by Brinksma D, Larsen K, Springer-Verlag, Berlin, 359–364.
Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U. (2006) COPASI – a COmplex PAthway SImulator. Bioinformatics, 22(24): 3067–3074.
Chen K, Calzone L, Csikasz-Nagy A, Cross F, Novak B, Tyson J. (2004) Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell, 15(8):3841–3862.
Tyson J. (1991) Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Natl Acad Sci U S A, 88:7328–7332.
Snoussi E. (1989) Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach. Dynam Stab Syst, 4(3–4):189–207.
Plahte E, Mestl T, Omholt S. (1998) A methodological basis for description and analysis of systems with complex switch-like interactions. J Math Biol, 36(4):321–348.
Bernot G, Comet JP, Richard A, Guespin J. (2004) Application of formal methods to biological regulatory networks: extending Thomas’ asynchronous logical approach with temporal logic. J Theor Biol, 229(3): 339–348.
Acknowledgments
This work was partially supported by the FCT program (PhD grant SFRH/BD/32965/2006 to PTM). BB and HdJ were supported by the European commission under project COBIOS (FP6-2005-NEST-PATH-COM/043379). HdJ, JG, and DR were supported by the European commission under project EC-MOAN (FP6-2005-NEST-PATH-COM/043235).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this protocol
Cite this protocol
Batt, G. et al. (2012). Genetic Network Analyzer: A Tool for the Qualitative Modeling and Simulation of Bacterial Regulatory Networks. In: van Helden, J., Toussaint, A., Thieffry, D. (eds) Bacterial Molecular Networks. Methods in Molecular Biology, vol 804. Springer, New York, NY. https://doi.org/10.1007/978-1-61779-361-5_22
Download citation
DOI: https://doi.org/10.1007/978-1-61779-361-5_22
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-61779-360-8
Online ISBN: 978-1-61779-361-5
eBook Packages: Springer Protocols