Abstract
We address the identification of genetic networks under stationary conditions. A stochastic hybrid description of the genetic interactions is considered and an approximation of it in stationary conditions is derived. Contrary to traditional structure identification methods based on fitting deterministic models to several perturbed equilibria of the system, we set up an identification strategy which exploits randomness as an inherent perturbation of the system. Estimation of the dynamics of the system from sampled data under stability constraints is then formulated as a convex optimization problem. Numerical results are shown on an artificial genetic network model. While our methods are conceived for the identification of interaction networks, they can as well be applied in the study of general piecewise deterministic systems with randomly switching inputs.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
de Jong, H.: Modeling and simulation of genetic regulatory systems: A literature review. Journal of Computational Biology 9(1), 69–105 (2002)
Alur, R., Belta, C., Ivancic, F., Kumar, V., Mintz, M., Pappas, G., Rubin, H., Schug, J.: Hybrid modeling and simulation of biological systems. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 19–32. Springer, Heidelberg (2001)
de Jong, H., Gouze, J.L., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Hybrid modeling and simulation of genetic regulatory networks: A qualitative approach. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 267–282. Springer, Heidelberg (2003)
Drulhe, S., Ferrari-Trecate, G., de Jong, H., Viari, A.: Reconstruction of switching thresholds in piecewise-affine models of genetic regulatory networks. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 184–199. Springer, Heidelberg (2006)
Batt, G., Ropers, D., de Jong, H., Geiselmann, J., Mateescu, R., Page, M., Schneider, D.: Validation of qualitative models of genetic regulatory networks by model checking: Analysis of the nutritional stress response in escherichia coli. Bioinformatics 21(1), i19–i28 (2005)
Ghosh, R., Tomlin, C.: Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modeling: Delta-notch protein signaling. IET Systems Biology 1(1), 170–183 (2004)
Longo, D., Hasty, J.: Dynamics of single-cell gene expression. Molecular Systems Biology 2 (2006)
Elowitz, M.B., Levine, A.J., Siggia, E.D., Swain, P.S.: Stochastic gene expression in a single cell. Science 297(5584), 1183–1186 (2002)
McAdams, H.H., Arkin, A.: It’s a noisy business! genetic regulation at the nanomolar scale. Trends in Genetics 15(2), 65–69 (2002)
Paulsson, J.: Models of stochastic gene expression. Physics of Life Reviews 2(2), 157–175 (2005)
Samad, H.E., Khammash, M., Petzold, L., Gillespie, D.: Stochastic modeling of gene regulatory networks. International Journal of Robust Nonlinear Control 15, 691–711 (2005)
Cinquemani, E., Milias-Argeitis, A., Summers, S., Lygeros, J.: Stochastic dynamics of genetic networks: modelling and parameter identification. Bioinformatics 24(23), 2748–2754 (2008)
Zeiser, S., Franz, U., Wittich, O., Liebscher, V.: Simulation of genetic networks modelled by piecewise deterministic markov processes. IET Systems Biology 2, 113–135 (2008)
Perkins, T., Hallett, M., Glass, L.: Inferring models of gene expression dynamics. Journal of Theoretical Biology 230(3), 289–299 (2004)
Fujarewicz, K., Kimmel, M., Swierniak, A.: On fitting of mathematical models of cell signaling pathways using adjoint systems. Mathematical Biosciences and Engineering 2(3), 527–534 (2005)
Dunlop, M., Franco, E., Murray, R.M.: A multi-model approach to identification of biosynthetic pathways. In: Proceedings of the 26th American Control Conference (2007)
Cinquemani, E., Porreca, R., Ferrari-Trecate, G., Lygeros, J.: Subtilin production by bacillus subtilis: Stochastic hybrid models and parameter identification. IEEE Transactions on Automatic Control, Special Issue on Systems Biology 53, 38–50 (2008)
Reinker, S., Altman, R., Timmer, J.: Parameter estimation in stochastic biochemical reactions. IET Systems Biology 153, 168–178 (2006)
Tian, T., Xu, S., Gao, J., Burrage, K.: Simulated maximum likelihood method for estimating kinetic rates in gene expression. Bioinformatics 23(1), 84–91 (2007)
Golightly, A., Wilkinson, D.: Bayesian inference for stochastic kinetic models using a diffusion approximation. Biometrics (61), 781–788 (2005)
Zavlanos, M.M., Julius, A., Boyd, S.P., Pappas, G.J.: Identification of stable genetic networks using convex programming. In: Proceedings of the American Control Conference, Seattle, WA (June 2008)
Bansal, M., Belcastro, V., Ambesi-Impiombato, A., di Bernardo, D.: How to infer gene networks from expression profiles. Molecular Systems Biology 3(78)
Gardner, T.S., di Bernardo, D., Lorenz, D., Collins, J.J.: Inferring Genetic Networks and Identifying Compound Mode of Action via Expression Profiling. Science 301(5629), 102–105 (2003)
van Overschee, P., De Moor, B.L.: Subspace Identification for Linear Systems: Theory - Implementation - Applications. Springer, Heidelberg (1996)
Golding, I., Paulsson, J., Zawilski, S.M., Cox, E.C.: Real-time kinetics of gene activity in individual bacteria. Cell 123(6), 1025–1036 (2005)
Cai, L., Friedman, N., Xie, X.S.: Stochastic protein expression in individual cells at the single molecule level. Nature 440, 358–362 (2006)
Davis, M.: Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models. Journal of the Royal Statistical Society B 46(3), 353–388 (1984)
Boyd, S.P., Vandenberghe, L.: Convex optimization. Cambridge University Press, Cambridge (2004)
Lacy, S.L., Bernstein, D.S.: Subspace identification with guaranteed stability using constrained optimization. IEEE Transactions on Automatic Control 48(7) (2003)
Smith, M.I.: A Schur algorithm for computing matrix pth roots. SIAM Journal on Matrix Analysis and Applications 24(4), 971–989 (2003)
Bini, D.A., Higham, N.J., Meini, B.: Algorithms for the matrix pth root. Numerical Algorithms 39, 349–378 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cinquemani, E., Milias-Argeitis, A., Summers, S., Lygeros, J. (2009). Local Identification of Piecewise Deterministic Models of Genetic Networks. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-00602-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00601-2
Online ISBN: 978-3-642-00602-9
eBook Packages: Computer ScienceComputer Science (R0)