Abstract
We propose a new method to explore the characteristics of genetic networks whose dynamics are described by a linear discrete dynamical model x t + 1 = Ax t . The gene expression data x t is given for various time points and the matrix A of interactions among the genes is unknown. First we formulate and solve a parameter estimation problem by linear programming in order to obtain the entries of the matrix A. We then use ideas from Vester’s Sensitivity Model, more precisely, the Impact Matrix, and the determination of the Systemic Roles, to understand the interactions among the genes and their role in the system. The method identifies prominent outliers, that is, the most active, reactive, buffering and critical genes in the network. Numerical examples for different datasets containing mRNA transcript levels during the cell cycle of budding yeast are presented.
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References
Ay, A., Arnosti, D.N., Steegenga, W.T., Sijbers, A.M., Dechering, K.J., Reinders, M.J.T.: Mathematical Modeling of Gene Expression: A Guide for the Perplexed Biologist. Crit. Rev. Biochem. Mol. Biol. 46(2), 137–151 (2011)
Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering Gene Expression Patterns. Computational Biology 6(3-4) (1999)
Cole, A.: The Influence Matrix Methodology: A Technical Report. LC0506/175, Foundation for Research, Science and Technology, FRST (2006)
Temocçin, B.Z., Weber, G.W.: Optimal Control of Stochastic Hybrid System with Jumps: A Numerical Approximation. Computational and Applied Mathematics 259, 443–451 (2014)
Wolf, C., Person, F., Jelse, K.: A Logistic Analysis with the Sensitivity Model Prof. Vester. Tech. Rep. B2048, IVL Swedish Environmental Research Institute Ltd (2012)
van Someren, E.P., Vaes, B.L.T., Steegenga, W.T., Sijbers, A.M., Dechering, K.J., Reinders, M.J.T.: Least Absolute Regression Network Analysis of the Murine Osteoblast Differentiation Network. Bioinformatics 22(4), 477–484 (2006)
van Someren, E.P., Wessels, L.F.A., Reinders, M.J.T.: Linear Modeling of Genetic Networks from Experimental Data. In: Proc. Int. Conf. Intell. Syst. Mol. Biol., vol. 8, pp. 355–366 (2000)
Vester, F.: Die Kunst vernetzt zu denken. Ideen und Werkzeuge fuer einen neuen Umgang mit Komplexitaet. Deutsche Verlags-Anstalt GmbH Stuttgart (1999)
Vester, F., von Hesler, A.: Sensitivitaetsmodell. Bundesminister d. Innern, Bonn (1980)
Neumann, G., Düring, D.: Methodology to Understand the Role of Knowledge Management in Logistic Companies. LogForum 4(5) (2008)
Weber, G.W., Kropat, E., Akteke-Öztürk, B., Görgülü, Z.K., Guo, D.: A Survey on OR and Mathematical Methods Applied on Gene-Environment Networks. CEJOR 17, 315–341 (2009)
Weber, G.W., Defterli, O., Kropat, E.: Qualitative Simulation of Genetic Regulatory Networks Using Piecewise-Linear Models. European Journal of Operational Research 211(1), 1–14 (2011)
Bossel, H.: System, Dynamik, Simulation. Modellbildung, Analyse und Simulation komplexer Systeme. Books on Demand GmbH Norderstedt/Germany (2004)
de Jong, H.: Modeling and Simulation of Genetic Regulatory Systems: A Literature Review. Computational Biology 9(1), 67–107 (2002)
de Jong, H., Gouzé, L.J., Page, C., Sari, T., Geiselmann, J.: Qualitative Simulation of Genetic Regulatory Networks Using Piecewise-Linear Models. Bulletin of Mathematical Biology 66, 301–340 (2004)
Yeung, K.Y., Ruzzo, W.L.: An Empirical Study on Principal Component Analysis for Clustering Gene Expression Data. Tech. Rep. UWCSE20001103, Department of Computer Science & Engineering University of Washington (2000)
Bansal, M., Belcastro, V., Ambesi-Impiombato, A., di Bernardo, D.: How to Infer Gene Networks from Expression Profiles. Molecular Systems Biology 3(78) (2007)
Defterli, O.: Modern Mathematical Methods in Modeling and Dynamics of Regulatory Systems of Gene-Environment Networks. Ph.D. thesis, Graduate School of Natural Sciences, Department of Mathematics, Middle East Technical University (August 2011)
Defterli, O., Fügenschuh, A., Weber, G.W.: New Discretization and Optimization Techniques with Results in the Dynamics of Gene-Environment Networks. In: 3rd Global Conference on Power Control & Optimization (February 2010)
Defterli, O., Fügenschuh, A., Weber, G.W.: Modern Tools for the Time-Discrete Dynamics and Optimization of Gene-Environment Networks. Commun. Nonlinear Sci. Numer. Simulat. 16, 4768–4779 (2011)
Cho, R.J., Campell, M.J., Winzeler, E.A., Steinmetz, L., Conway, A., Wolfsberg, T.G., Gabrielian, L.A.E., Landsman, D., Lockhart, D.J., Davis, R.W.: A Genome-Wide Transcriptional Analysis of the Mitotic Cell Cycles. Molecular Cell 2, 65–73 (1998)
Zhang, S.Q., Ching, W.K., Tsing, N.K., Leung, H.Y., Guo, D.: A New Multiple Regression Approach for the Construction of Genetic Regulatory Networks. Artificial Intelligence in Medicine 48(2-3), 153–160 (2010)
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Amaya Moreno, L., Defterli, O., Fügenschuh, A., Weber, GW. (2014). Vester’s Sensitivity Model for Genetic Networks with Time-Discrete Dynamics. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Algorithms for Computational Biology. AlCoB 2014. Lecture Notes in Computer Science(), vol 8542. Springer, Cham. https://doi.org/10.1007/978-3-319-07953-0_3
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DOI: https://doi.org/10.1007/978-3-319-07953-0_3
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