Application of the Reachability Analysis for the Iron Homeostasis Study
Résumé
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.