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.
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Notes
- 1.
Two sigmoids are on IRP, and one on Fe.
- 2.
This situation corresponds to the phase 3 described in Sect. 4.
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Acknowledgement
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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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. https://doi.org/10.1007/978-3-319-47151-8_5
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