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Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks

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Modeling, Dynamics, Optimization and Bioeconomics I

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 73))

Abstract

In this study, some methodologies and a review of the recently obtained new results are presented for the problem of modeling, anticipation and forecasting of genetic regulatory systems, as complex systems. In this respect, such kind of complex systems are modeled in the dynamical sense into the two different ways, namely, by a system of ordinary differential equations (ODEs) and Gaussian graphical methods (GGM). An artificial time-course microarray dataset of a gene-network is modeled as an example by using both ODE method and GGM. In this analysis, since the actual interactions of the nodes, i.e., genes, are assumed to be unknown, the discrete time measurements are initially used for the inference of the system’s interactions, i.e., the edges between nodes, by the underlying two methods. Then, the results of inference from ordinary differential equation based model are applied to a class of previously developed new numerical schemes for the generation of further states of the system. In this simulation, we present the recent results of a set of explicit Runge-Kutta methods that are implemented.

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Acknowledgements

This study is a part of Ph.D. thesis of Özlem Defterli at the Department of Mathematics in Middle East Technical University (METU). Her work is partially supported by the Scientific and Technical Research Council of Turkey. Moreover, Vilda Purutçuoğlu and Gerhard-Wilhelm Weber thank to the EU 7th Framework Programme Project PATHOSYS (No: 260429) for their financial support in the computational equipment.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Çankaya University, 06810, Ankara, Turkey

    Özlem Defterli

  2. Department of Statistics, Middle East Technical University, 06531, Ankara, Turkey

    Vilda Purutçuoğlu

  3. Institute of Applied Mathematics, Middle East Technical University, 06531, Ankara, Turkey

    Gerhard-Wilhelm Weber

Authors
  1. Özlem Defterli
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  2. Vilda Purutçuoğlu
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  3. Gerhard-Wilhelm Weber
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Correspondence to Özlem Defterli .

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Editors and Affiliations

  1. University of Porto, Department of Mathematics, Porto, Portugal

    Alberto Adrego Pinto

  2. Univ. of California, Dept. of Agricultural and Resource Economics, Berkeley, California, USA

    David Zilberman

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Defterli, Ö., Purutçuoğlu, V., Weber, GW. (2014). Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics I. Springer Proceedings in Mathematics & Statistics, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-04849-9_14

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