Advertisement

Qualitative Analysis of Genetic Regulatory Networks in Bacteria

  • Valentina Baldazzi
  • Pedro T. Monteiro
  • Michel Page
  • Delphine Ropers
  • Johannes Geiselmann
  • Hidde de Jong
Chapter

Abstract

The adaptation of the bacterium Escherichia coli to carbon starvation is controlled by a large network of biochemical reactions involving genes, mRNAs, proteins, and signalling molecules. The dynamics of this network is difficult to analyze, notably due to a lack of quantitative information on parameter values. To overcome these limitations, the application of model reduction approaches based on QSS and PL approximations may result in models that are easier to handle mathematically and computationally. In particular, PL models allow the analysis of the qualitative dynamics of the network using only weak information on the ordering of parameters rather than their exact numerical values.We illustrate the use of these techniques, implemented in the computer tool Genetic Network Analyzer (GNA), in the case of the E. coli network.

Keywords

Inequality Constraint Global Regulator Boolean Network Stable RNAs Genetic Regulatory Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgment

VB, DR, JG, HdJ were supported by the European commission under project EC-MOAN (FP6-2005-NEST-PATH-COM/043235). PM was partially supported by FCT program (PhD grant SFRH/BD/32965/2006 to PTM) and PDTC program (project PTDC/EIA/71587/2006).

References

  1. T. Ali Azam, A. Iwata, A. Nishimura, S. Ueda, and A. Ishihama. Growth phase-dependent variation in protein composition of the Escherichia coli nucleoid. J. Bacteriol., 181 (20): 6361–6370, 1999.PubMedGoogle Scholar
  2. M. Antoniotti, A. Policriti, N. Ugel, and B. Mishra. Model building and model checking for biochemical processes. Cell Biochem. Biophys., 38 (3): 271–286, 2003.PubMedCrossRefGoogle Scholar
  3. C. A. Ball, R. Osuna, K. C. Ferguson, and R. C. Johnson. Dramatic changes in Fis levels upon nutrient upshift in Escherichia coli. J. Bacteriol., 174 (24): 8043–8056, 1992.PubMedGoogle Scholar
  4. G. Batt, D. Ropers, H. de Jong, J. Geiselmann, R. Mateescu, M. Page, and D. Schneider. 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, 2005.PubMedCrossRefGoogle Scholar
  5. G. Batt, B. Yordanov, R. Weiss, and C. Belta. Robustness analysis and tuning of synthetic gene networks. Bioinformatics, 23 (18): 2415–2422, 2007.PubMedCrossRefGoogle Scholar
  6. G. Batt, H. de Jong, M. Page, and J. Geiselmann. Symbolic reachability analysis of genetic regulatory networks using discrete abstractions. Automatica, 44 (4): 982–989, 2008.CrossRefGoogle Scholar
  7. C. Belta and L. C. G. J. M. Habets. Controlling a class of nonlinear systems on rectangles. IEEE Trans. Autom. Control, 51 (11): 1749–1759, 2006.Google Scholar
  8. G. Bernot, J.-P. Comet, A. Richard, and J. Guespin. Application of formal methods to biological regulatory networks: Extending Thomas’ asynchronous logical approach with temporal logic. J. Theor. Biol., 229 (3): 339–348, 2004.PubMedCrossRefGoogle Scholar
  9. K. Bettenbrock, S. Fischer, A. Kremling, K. Jahreis, T. Sauter, and E. D. Gilles. A quantitative approach to catabolite repression in Escherichia coli. J. Biol. Chem., 281 (5): 2578–2584, 2005.PubMedCrossRefGoogle Scholar
  10. K. Bettenbrock, S. Fischer, A. Kremling, K. Jahreis, T. Sauter, and E. D. Gilles. A quantitative approach to catabolite repression in Escherichia coli. J. Biol. Chem., 281 (5): 2578–2584, 2006.PubMedCrossRefGoogle Scholar
  11. M. Calder, V. Vyshemirsky, D. Gilbert, and R. Orton. Analysis of signalling pathways using the PRISM model checker. In G. Plotkin, editor, Proc. of CMSB, pages 179–190, Edinburgh, Scotland, 2005.Google Scholar
  12. R. Casey, H. de Jong, and J.-L. Gouzé. Piecewise-linear models of genetic regulatory networks: Equilibria and their stability. J. Math. Biol., 52 (1): 27–56, 2006.PubMedCrossRefGoogle Scholar
  13. N. Chabrier-Rivier, M. Chiaverini, V. Danos, F. Fages, and V. Schächter. Modeling and querying biomolecular interaction networks. Theor. Comput. Sci., 325 (1): 25–44, 2004.CrossRefGoogle Scholar
  14. C. Chassagnole, N. Noisommit-Rizzi, J. W. Schmid, K. Mauch, and M. Reuss. Dynamic modeling of the central carbon metabolism of Escherichia coli. Biotechnol. Bioeng., 79 (1): 53–73, 2002.PubMedCrossRefGoogle Scholar
  15. M. Chaves, E. D. Sontag, and R. Albert. Methods of robustness analysis for Boolean models of gene control networks. IET Syst. Biol., 153 (4): 154–167, 2006.CrossRefGoogle Scholar
  16. K. C. Chen, L. Calzone, A. Csikasz-Nagy, F. R. Cross, B. Novak, and J. J. Tyson. Integrative analysis of cell cycle control in budding yeast. Mol. Biol. Cell, 15 (8): 3841–3862, 2004.PubMedCrossRefGoogle Scholar
  17. A. Cimatti, E. Clarke, E. Giunchiglia, F. Giunchiglia, M. Pistore, M. Roveri, R. Sebastiani, and A. Tacchella. NuSMV2: An OpenSource tool for symbolic model checking. In D. Brinksma and K. G. Larsen, editors, 14th International Conference on Computer Aided Verification (CAV 2002), volume 2404 of LNCS, pages 359–364. Springer, Berlin, 2002.CrossRefGoogle Scholar
  18. E. M. Clarke, O. Grumberg, and D. A. Peled. Model Checking. MIT, Boston, MA, 1999.Google Scholar
  19. A. Cornish-Bowden. Fundamentals of Enzyme Kinetics. Portland Press, London, revised edition, 1995.Google Scholar
  20. M. Davidich and S. Bornholdt. The transition from differential equations to Boolean networks: A case study in simplifying a regulatory network model. J. Theor. Biol., 255: 269–277, 2008.PubMedCrossRefGoogle Scholar
  21. H. de Jong and M. Page. Search for steady states of piecewise-linear differential equation models of genetic regulatory networks. ACM/IEEE Trans. Comput. Biol. Bioinform., 5 (2): 208–222, 2008.CrossRefGoogle Scholar
  22. H. de Jong and D. Ropers. Strategies for dealing with incomplete information in the modeling of molecular interaction networks. Brief. Bioinform., 7 (4): 354–363, 2006.PubMedCrossRefGoogle Scholar
  23. H. de Jong, J. Geiselmann, C. Hernandez, and M. Page. Genetic Network Analyzer: Qualitative simulation of genetic regulatory networks. Bioinformatics, 19: 336–344, 2003.PubMedCrossRefGoogle Scholar
  24. H. de Jong, J. Geiselmann, G. Batt, C. Hernandez, and M. Page. Qualitative simulation of the initiation of sporulation in B. subtilis. B. Math. Biol., 66 (2): 261–299, 2004a.Google Scholar
  25. H. de Jong, J.-L. Gouzé, C. Hernandez, M. Page, T. Sari, and J. Geiselmann. Qualitative simulation of genetic regulatory networks using piecewise-linear models. B. Math. Biol., 66 (2): 301–340, 2004b.CrossRefGoogle Scholar
  26. R. Edwards. Analysis of continuous-time switching networks. Phys. D, 146 (1–4): 165–199, 2000.CrossRefGoogle Scholar
  27. J. Fisher, N. Piterman, A. Hajnal, and T. A. Henzinger. Predictive modeling of signaling crosstalk during C. elegans vulval development. PLoS Comput. Biol., 3 (5): e92, 2007.Google Scholar
  28. T. S. Gardner, C. R. Cantor, and J. J. Collins. Construction of a genetic toggle switch in escherichia coli. Nature, 403 (6767): 339–342, 2000.PubMedCrossRefGoogle Scholar
  29. T. S. Gardner, D. di Bernardo, D. Lorenz, and J. J. Collins. Inferring genetic networks and identifying compound mode of action via expression profiling. Science, 301 (5629): 102–105, 2003.PubMedCrossRefGoogle Scholar
  30. R. Ghosh and C. J. Tomlin. Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. IET Syst. Biol., 1 (1): 170–183, 2004.CrossRefGoogle Scholar
  31. L. Glass and S. A. Kauffman. The logical analysis of continuous non-linear biochemical control networks. J. Theor. Biol., 39 (1): 103–129, 1973.PubMedCrossRefGoogle Scholar
  32. A. Gonzalez Gonzalez, A. Naldi, L. Sánchez, D. Thieffry, and C. Chaouiya. GINsim: a software suit for the qualitative modelling, simulation and analysis of regulatory networks. Biosystems, 84 (2): 91–100, 2006.PubMedCrossRefGoogle Scholar
  33. J.-L. Gouzé and T. Sari. A class of piecewise linear differential equations arising in biological models. Dyn. Syst., 17 (4): 299–316, 2002.CrossRefGoogle Scholar
  34. R. M. Gutierrez-Ríos, J. A. Freyre-Gonzalez, O. Resendis, J. Collado-Vides, M. Saier, and G. Gosset. Identification of regulatory network topological units coordinating the genome-wide transcriptional response to glucose in Escherichia coli. BMC Microbiol., 7: 53–53, 2007.PubMedCrossRefGoogle Scholar
  35. A. Halász, V. Kumar, M. Imielinski, C. Belta, O. Sokolsky, S. Pathak, and H. Rubin. Analysis of lactose metabolism in E. coli using reachability analysis of hybrid systems. IET Syst. Biol., 1 (2): 130–48, 2007.Google Scholar
  36. T. Hardiman, K. Lemuth, M. A. Keller, M. Reuss, and M. Siemann-Herzberg. Topology of the global regulatory network of carbon limitation in Escherichia coli. J. Biotechnol., 132: 359–374, 2007.PubMedCrossRefGoogle Scholar
  37. J. J. Heijnen. Approximative kinetic formats used in metabolic network modeling. Biotechnol. Bioeng., 91 (5): 534–545, 2005.PubMedCrossRefGoogle Scholar
  38. R. Heinrich and S. Schuster. The regulation of cellular systems. Chapman & Hall, New York, 1996.CrossRefGoogle Scholar
  39. G. W. Huisman, M. M. Siegele D. A., Zambrano, and Kolter R. Morphological and physiological changes during stationary phase. In F. C. Neidhardt, R. Curtiss III, J. L. Ingraham, E. C. C. Lin, K. B. Low, B. Magasanik, W. S. Reznikoff, M. Riley, M. Schaechter, and H. E. Umbarger, editors, Escherichia coli and Salmonella: Cellular and Molecular Biology, pages 1672–1682. ASM, Washington D.C., 1996.Google Scholar
  40. H. Ishizuka, A. Hanamura, T. Inada, and H. Aiba. 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, 1994.PubMedGoogle Scholar
  41. S. A. Kauffman. The origins of order: Self-organization and selection in evolution. Oxford University Press, New York, 1993.Google Scholar
  42. S. A. Kauffman. Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol., 22 (3): 437–467, 1969.PubMedCrossRefGoogle Scholar
  43. E. Klipp, B. Nordlander, R. Krüger, P. Gennemark, and S. Hohmann. Integrative model of the response of yeast to osmotic shock. Nat. Biotechnol., 23 (8): 975–982, 2005.PubMedCrossRefGoogle Scholar
  44. K. W. Kohn. Molecular interaction maps as information organizers and simulation guides. Chaos, 11 (1): 84–97, 2001.PubMedCrossRefGoogle Scholar
  45. A. Kremling, S. Kremling, and K. Bettenbrock. Catabolite repression in Escherichia coli- a comparison of modelling approaches. FEBS J., 276: 594–602, 2009.PubMedCrossRefGoogle Scholar
  46. L. Kuepfer, M. Peter, U. Sauer, and J. Stelling. Ensemble modeling for analysis of cell signaling dynamics. Nat. Biotechnol., 25 (9): 1001–1006, 2007.PubMedCrossRefGoogle Scholar
  47. J.-C. Leloup and A. Goldbeter. Toward a detailed computational model for the mammalian circadian clock. Proc. Nat. Acad. Sci. USA, 100 (12): 7051–7056, 2003.PubMedCrossRefGoogle Scholar
  48. L. Mendoza, D. Thieffry, and E. R. Alvarez-Buylla. Genetic control of flower morphogenesis in Arabidopsisthaliana: A logical analysis. Bioinformatics, 15 (7–8): 593–606, 1999.PubMedCrossRefGoogle Scholar
  49. T. Mestl, E. Plahte, and S. W. Omholt. A mathematical framework for describing and analysing gene regulatory networks. J. Theor. Biol., 176 (2): 291–300, 1995.PubMedCrossRefGoogle Scholar
  50. T. Millat, E. Bullinger, J. Rohwer, and O. Wolkenhauer. Approximations and their consequences for dynamic modelling of signal transduction pathways. Math. Biosci., 207 (1): 40–57, 2007.PubMedCrossRefGoogle Scholar
  51. C. G. Moles, P. Mendes, and J. R. Banga. Parameter estimation in biochemical pathways: A comparison of global optimization methods. Genome Res., 13 (11): 2467–2474, 2003.PubMedCrossRefGoogle Scholar
  52. P. T. Monteiro, D Ropers, R Mateescu, A. T. Freitas, and H. de Jong. Temporal logic patterns for querying dynamic models of cellular interaction networks. Bioinformatics, 24: i227–i233, 2008.Google Scholar
  53. M. S. Okino and M. L. Mavrovouniotis. Simplification of mathematical models of chemical reaction systems. Chem. Rev., 98 (2): 391–408, 1998.PubMedCrossRefGoogle Scholar
  54. J. A. Papin, J. Stelling, N. D. Price, S. Klamt, S. Schuster, and B. O. Palsson. Comparison of network-based pathway analysis methods. Trends Biotechnol., 22 (8): 400–405, 2004.PubMedCrossRefGoogle Scholar
  55. E. Pecou. Splitting the dynamics of large biochemical interaction networks. J. Theor. Biol., 232 (3): 375–384, 2005.PubMedCrossRefGoogle Scholar
  56. E. Plahte and S. Kjóglum. Analysis and generic properties of gene regulatory networks with graded response functions. Phys. D, 201 (1): 150–176, 2005.CrossRefGoogle Scholar
  57. R. Porreca, S. Drulhe, H. de Jong, and G. Ferrari-Trecate. Structural identification of piecewise-linear models of genetic regulatory networks. J. Comput. Biol., 15 (10): 1365–1380, 2008.PubMedCrossRefGoogle Scholar
  58. T. S. Pratt, T. Steiner, L. S. Feldman, K. A. Walker, and R. Osuna. Deletion analysis of the fis promoter region in Escherichia coli: antagonistic effects of integration host factor and Fis. J. Bacteriol., 179 (20): 6367–6377, 1997.PubMedGoogle Scholar
  59. M. Quach, N. Brunel, and F. d’Alché Buc. Estimating parameters and hidden variables in non-linear state-space models based on ODEs for biological networks inference. Bioinformatics, 23 (23): 3209–3216, 2007.Google Scholar
  60. Y. Reyes-Dominguez, G. Contreras-Ferrat, J. Ramirez-Santos, J. Membrillo-Hernandez, and M. C. Gomez-Eichelmann. Plasmid DNA supercoiling and gyrase activity in Escherichia coli wild-type and rpoS stationary-phase cells. J. Bacteriol., 185 (3): 1097–1100, 2003.PubMedCrossRefGoogle Scholar
  61. J. M. Rohwer, N. D. Meadow, S. Roseman, H. V. Westerhoff, and P. W. Postma. Understanding glucose transport by the bacterial phosphoenolpyruvate:glycose phosphotransferase system on the basis of kinetic measurements in vitro. J. Biol. Chem., 275 (45): 34909–34921, 2000.PubMedCrossRefGoogle Scholar
  62. M. Ronen, R. Rosenberg, B. I. Shraiman, and U. Alon. Assigning numbers to the arrows: Parameterizing a gene regulation network by using accurate expression kinetics. Proc. Natl. Acad. Sci. USA, 99 (16): 10555–10560, 2002.PubMedCrossRefGoogle Scholar
  63. D. Ropers, H. de Jong, M. Page, D. Schneider, and J. Geiselmann. Qualitative simulation of the carbon starvation response in Escherichia coli. Biosystems, 84 (2): 124–152, 2006.PubMedCrossRefGoogle Scholar
  64. D. Ropers, V. Baldazzi, and H. de Jong. Model reduction using piecewise-linear approximations preserves dynamic properties of the carbon starvation response in Escherichia coli. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 8 (1): 166–181, 2011.PubMedCrossRefGoogle Scholar
  65. M. R. Roussel and S. J. Fraser. Invariant manifold methods for metabolic model reduction. Chaos, 11 (1): 196–206, 2001.PubMedCrossRefGoogle Scholar
  66. L. Sánchez and D. Thieffry. Segmenting the fly embryo: A logical analysis of the pair-rule cross-regulatory module. J. Theor. Biol., 224 (4): 517–537, 2003.PubMedCrossRefGoogle Scholar
  67. M. A. Savageau. Design principles for elementary gene circuits: Elements, methods, and examples. Chaos, 11 (1): 142–159, 2001.PubMedCrossRefGoogle Scholar
  68. B. Schoeberl, C. Eichler-Jonsson, E.-D. Gilles, and G. Mller. Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat. Biotechnol., 20 (4): 370–375, 2002.PubMedCrossRefGoogle Scholar
  69. J.-A. Sepulchre, S. Reverchon, and W. Nasser. Modeling the onset of virulence in a pectinolytic bacterium. J. Theor. Biol., 44 (2): 239–257, 2007.CrossRefGoogle Scholar
  70. M. Sugita. Functional analysis of chemical systems in vivo using a logical circuit equivalent: II. The idea of a molecular automaton. J. Theor. Biol., 4: 179–192, 1963.Google Scholar
  71. R. Thomas. Boolean formalization of genetic control circuits. J. Theor. Biol., 42 (3): 563–585, 1973.PubMedCrossRefGoogle Scholar
  72. R. Thomas and R. d’Ari. Biological feedback. CRC, Boca Raton, FL, 1990.Google Scholar
  73. R. Thomas and M. Kaufman. Multistationarity, the basis of cell differentiation and memory: II. Logical analysis of regulatory networks in terms of feedback circuits. Chaos, 11 (1): 180–195, 2001.Google Scholar
  74. A. Usseglio Viretta and M. Fussenegger. Modeling the quorum sensing regulatory network of human-pathogenic Pseudomonas aeruginosa. Biotechnol. Prog., 20 (3): 670–678, 2004.CrossRefGoogle Scholar
  75. N. A. W. van Riel and E. D. Sontag. Parameter estimation in models combining signal transduction and metabolic pathways: The dependent input approach. IET Syst. Biol., 153 (4): 263–274, 2006.CrossRefGoogle Scholar
  76. M. Vilela, I. Chou, S. Vinga, A. Vasconcelos, E. Voit, and J. Almeida. Parameter optimization in S-system models. BMC Syst. Biol., 2: 35, 2008.PubMedCrossRefGoogle Scholar
  77. R. L. Westra, G. Hollanders, G. J. Bex, M. Gyssens, and K. Tuyls. The identification of dynamic gene-protein networks. In K. Tuyls, R. Westra, Y. Saeys, and A. Nowé, editors, Proc. KDECB 2006, volume 4366 of LNCS, pages 157–170. Springer, Berlin, 2007.Google Scholar
  78. C.-H. Yuh, H. Bolouri, and E. H. Davidson. Genomic cis-regulatory logic: Experimental and computational analysis of a sea urchin gene. Science, 279: 1896–1902, 1998.PubMedCrossRefGoogle Scholar
  79. J. W. Zwolak, J. J. Tyson, and L. T. Watson. Parameter estimation for a mathematical model of the cell cycle in frog eggs. J. Comput. Biol., 12 (1): 48–63, 2005.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Valentina Baldazzi
    • 1
  • Pedro T. Monteiro
  • Michel Page
  • Delphine Ropers
  • Johannes Geiselmann
  • Hidde de Jong
  1. 1.INRIA Grenoble – Rhône-AlpesGrenobleFrance

Personalised recommendations