Application of the Reachability Analysis for the Iron Homeostasis Study

  • Alexandre Rocca
  • Thao Dang
  • Eric Fanchon
  • Jean-Marc Moulis
Conference paper

DOI: 10.1007/978-3-319-47151-8_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9957)
Cite this paper as:
Rocca A., Dang T., Fanchon E., Moulis JM. (2016) Application of the Reachability Analysis for the Iron Homeostasis Study. In: Cinquemani E., Donzé A. (eds) Hybrid Systems Biology. HSB 2016. Lecture Notes in Computer Science, vol 9957. Springer, Cham

Abstract

Our work is motivated by a model of the mammalian cellular Iron Homeostasis, which was analysed using simulations in [9]. The result of this analysis is a characterization of the parameters space such that the model satisfies a set of constraints, proposed by biologists or coming from experimental results. We now propose an approach to hypothesis validation which can be seen as a complement to the approach based on simulation. It uses reachability analysis (that is set-based simulation) to formally validate a hypothesis. For polynomials systems, reachability analysis using the Bernstein expansion is an appropriate technique. Moreover, the Bernstein technique allows us to tackle uncertain parameters at a small cost. In this work, we extend the reachability analysis method presented in [7] to handle polynomial fractions. Furthermore, to tackle the complexity of the Iron Homeostasis model, we use a piecewise approximation of the dynamics and propose a reachability method to deal with the resulting hybrid dynamics. These approximations and adaptations allowed us to validate a hypothesis stated in [9], with an exhaustive analysis over uncertain parameters and initial conditions.

Keywords

Parametric ODE Reachability analysis Non-linear systems Biological systems 

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Alexandre Rocca
    • 1
    • 2
  • Thao Dang
    • 1
  • Eric Fanchon
    • 2
  • Jean-Marc Moulis
    • 3
  1. 1.VERIMAG/CNRSSaint Martin D’HèresFrance
  2. 2.Université Grenoble-Alpes - Grenoble 1/CNRS, TIMC-IMAG, UMR 5525GrenobleFrance
  3. 3.Université Grenoble-Alpes - Grenoble 1, Laboratoire de Bioénergétique Fondamentale et Appliquée (LBFA) - Inserm U1055GrenobleFrance

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