  This paper presents a method for modeling biological systems which combines
formal techniques on intervals, numerical simulations and satisfaction of
Signal Temporal Logic (STL) formulas. The main modeling challenge addressed by
this approach is the large uncertainty in the values of the parameters due to
the experimental difficulties of getting accurate biological data. This method
considers intervals for each parameter and a formal description of the expected
behavior of the model. In a first step, it produces reduced intervals of
possible parameter values. Then by performing a systematic search in these
intervals, it defines sets of parameter values used in the next step. This
procedure aims at finding a sub-space where the model robustly behaves as
expected. We apply this method to the modeling of the cellular iron homeostasis
network in erythroid progenitors. The produced model describes explicitly the
regulation mechanism which acts at the translational level.
