Abstract
Recent advances of experimental techniques in biology have led to the production of enormous amounts of data on the dynamics of genetic regulatory networks. In this paper, we present an approach for the identification of PieceWise-Affine (PWA) models of genetic regulatory networks from experimental data, focusing on the reconstruction of switching thresholds associated with regulatory interactions. In particular, our method takes into account geometric constraints specific to models of genetic regulatory networks. We show the feasibility of our approach by the reconstruction of switching thresholds in a PWA model of the carbon starvation response in the bacterium Escherichia coli.
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References
D’haeseleer, P., Liang, S., Somogyi, R.: Genetic network inference: From co-expression clustering to reverse engineering. Bioinformatics 16, 707–726 (2000)
Gardner, T., di Bernardo, D., Lorenz, D., Collins, J.: Inferring genetic networks and identifying compound mode of action via expression profiling. Science 301, 102–105 (2003)
van Someren, E., Wessels, L., Reinders, M.: Linear modeling of genetic networks from experimental data. In: Altman, R., et al. (eds.) Proc. Eight Int. Conf. Intell. Syst. Mol. Biol., ISMB 2000, pp. 355–366. AAAI Press, Menlo Park (2000)
Lemeille, S., Latifi, A., Geiselmann, J.: Inferring the connectivity of a regulatory network from mRNA quantification in Synechocystis PCC6803. Nucleic Acids Res. 33, 3381–3389 (2005)
Jaeger, J., Surkova, S., Blagov, M., Janssens, H., Kosman, D., Kozlov, K., Manu, M.E., Vanario-Alonso, C., Samsonova, M., Sharp, D., Reinitz, J.: Dynamic control of positional information in the early Drosophila embryo. Nature 430, 368–371 (2004)
Ronen, M., Rosenberg, R., Shraiman, B., Alon, U.: Assigning numbers to the arrows: Parameterizing a gene regulation network by using accurate expression kinetics. Proc. Natl. Acad. Sci. USA 99, 10555–10560 (2002)
Glass, L., Kauffman, S.: The logical analysis of continuous non-linear biochemical control networks. J. Theor. Biol. 39, 103–129 (1973)
Batt, G., Ropers, D., de Jong, H., Geiselmann, J., Page, M., Schneider, D.: Qualitative analysis and verification of hybrid models of genetic regulatory networks: Nutritional stress response in Escherichia coli. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 134–150. Springer, Heidelberg (2005)
Belta, C., Finin, P., Habets, L., Halász, A., Imiliǹski, M., Kumar, R., Rubin, H.: Understanding the bacterial stringent response using reachability analysis of hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 111–125. Springer, Heidelberg (2004)
de Jong, H., Gouzé, J.L., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull. Math. Biol. 66, 301–340 (2004)
Edwards, R., Siegelmann, H., Aziza, K., Glass, L.: Symbolic dynamics and computation in model gene networks. Chaos 11, 160–169 (2001)
Ghosh, R., Tomlin, C.: Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. Syst. Biol. 1, 170–183 (2004)
Mestl, T., Plahte, E., Omholt, S.: A mathematical framework for describing and analysing gene regulatory networks. J. Theor. Biol. 176, 291–300 (1995)
Ropers, D., de Jong, H., Page, M., Schneider, D., Geiselmann, J.: Qualitative simulation of the carbon starvation response in Escherichia coli. BioSystems (in press, 2006)
Juloski, A.L., Heemels, W.P.M.H., Ferrari-Trecate, G., Vidal, R., Paoletti, S., Niessen, J.H.G.: Comparison of four procedures for the identification of hybrid systems. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 354–369. Springer, Heidelberg (2005)
Perkins, T., Hallett, M., Glass, L.: Inferring models of gene expression dynamics. J. Theor. Biol. 230, 289–299 (2004)
de Jong, H.: Modeling and simulation of genetic regulatory systems: A literature review. J. Comput. Biol. 9, 67–103 (2002)
Ferrari-Trecate, G., Muselli, M., Liberati, D., Morari, M.: A clustering technique for the identification of piecewise affine and hybrid systems. Automatica 39, 205–217 (2003)
Bennett, K., Mangasarian, O.: Multicategory discrimination via linear programming. Optimization Methods and Software 3, 27–39 (1993)
Vapnik, V.: Statistical Learning Theory. John Wiley, NY (1998)
Drulhe, S., Ferrari-Trecate, G., de Jong, H., Viari, A.: Reconstruction of switching thresholds in piecewise-affine models of genetic regulatory networks. Technical report, INRIA (2005), http://www.inria.fr/rrrt/index.en.html
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Drulhe, S., Ferrari-Trecate, G., de Jong, H., Viari, A. (2006). Reconstruction of Switching Thresholds in Piecewise-Affine Models of Genetic Regulatory Networks. In: Hespanha, J.P., Tiwari, A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11730637_16
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DOI: https://doi.org/10.1007/11730637_16
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