Abstract
We consider a class of qualitative biological models which describe species (e.g. protein) interactions in terms of promotion or inhibition, from which a piecewise-affine (PWA) hybrid system model can be generated. These models have a special structure under which negative feedback is a necessary condition for the presence of limit cycles, centers, and foci. We describe modifications to reachability algorithms to take advantage of this special structure, and we give conditions on the qualitative model for termination of the algorithm. An example of applying the algorithm to a simple biological system is given.
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Lygeros, J., Tomlin, C., Sastry, S.: Controllers for reachability specifications for hybrid systems. Automatica 35(3), 349–370 (1999)
Gouzé, J.-L., Sari, T.: A class of piecewise linear differential equations arising in biological models. Dynamical Systems 17(4), 299–316 (2002)
de Jong, H., et al.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bulletin of Mathematical Biology 66(2), 301–340 (2004)
Ghosh, R., Tomlin, C.: Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. Systems Biology 1(1), 170–183 (2005)
von Dassow, G., Odell, G.M.: Design and constraints of the Drosophila segment polarity module. Journal of Experimental Zoology 294, 179–215 (2002)
Bouajjani, A., Fernandez, J.-C., Halbwachs, N.: Minimal model generation. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 197–203. Springer, Heidelberg (1991)
Belta, C., et al.: Computational techniques for analysis of genetic network dynamics. International Journal of Robotics Research 24(2-3) (2005)
Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)
Girard, A., Le Guernic, C., Maler, O.: Efficient computation of reachable sets of linear time-invariant systems with inputs. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 257–271. Springer, Heidelberg (2006)
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Aswani, A., Tomlin, C. (2007). Reachability Algorithm for Biological Piecewise-Affine Hybrid Systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds) Hybrid Systems: Computation and Control. HSCC 2007. Lecture Notes in Computer Science, vol 4416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71493-4_49
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DOI: https://doi.org/10.1007/978-3-540-71493-4_49
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