Application of the Reachability Analysis for the Iron Homeostasis Study
Our work is motivated by a model of the mammalian cellular Iron Homeostasis, which was analysed using simulations in . 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  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 , with an exhaustive analysis over uncertain parameters and initial conditions.
KeywordsParametric ODE Reachability analysis Non-linear systems Biological systems
This work is partially supported by the ANR CADMIDIA project (ANR-13-CESA-0008-03) and the ANR MALTHY project (ANR-12-INSE-003).
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