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Vester’s Sensitivity Model for Genetic Networks with Time-Discrete Dynamics

  • Liana Amaya Moreno
  • Ozlem Defterli
  • Armin Fügenschuh
  • Gerhard-Wilhelm Weber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8542)

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.

Keywords

Linear Programming Parameter Estimation Discrete Dynamical System Sensitivity Analysis Genetic Networks Operational Research Systems Biology 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Liana Amaya Moreno
    • 1
  • Ozlem Defterli
    • 2
  • Armin Fügenschuh
    • 1
  • Gerhard-Wilhelm Weber
    • 3
  1. 1.Department of Mechanical EngineeringUniversity of the Federal Armed Forces HamburgHamburgGermany
  2. 2.Department of Mathematics and Computer Science, Faculty of Art and SciencesÇankaya UniversityAnkaraTurkey
  3. 3.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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