  This paper presents a novel framework for the modeling of biological
networks. It makes use of recent tools analyzing the robust satisfaction of
properties of (hybrid) dynamical systems. The main challenge of this approach
as applied to biological systems is to get access to the relevant parameter
sets despite gaps in the available knowledge. An initial estimate of useful
parameters was sought by formalizing the known behavior of the biological
network in the STL logic using the tool Breach. Then, once a set of parameter
values consistent with known biological properties was found, we tried to
locally expand it into the largest possible valid region. We applied this
methodology in an effort to model and better understand the complex network
regulating iron homeostasis in mammalian cells. This system plays an important
role in many biological functions, including erythropoiesis, resistance against
infections, and proliferation of cancer cells.
