  (abridged) We combined several N-body methods in order to investigate the
interaction scenario between NGC 4449 and DDO 125, a close companion in
projected space. In a first step fast restricted N-body models are used to
confine a region in parameter space reproducing the main observational
features. In a second step a genetic algorithm is applied for a uniqueness test
of our preferred parameter set. We show that our genetic algorithm reliably
recovers orbital parameters, provided that the data are sufficiently accurate,
i.e. all the key features are included.
  In the third step the results of the restricted N-body models are compared
with self-consistent N-body simulations. In the case of NGC 4449, the
applicability of the simple restricted N-body calculations is demonstrated.
Additionally, it is shown that the HI gas can be modeled here by a purely
stellar dynamical approach.
  In a series of simulations, we demonstrate that the observed features of the
extended HI disc can be explained by a gravitational interaction between NGC
4449 and DDO 125. According to these calculations the closest approach between
both galaxies happened $\sim 4-6 \cdot 10^8$ yr ago at a minimum distance of
$\sim 25$ kpc on a parabolic or slightly elliptic orbit. In the case of an
encounter scenario, the dynamical mass of DDO 125 should not be smaller than
10% of NGC 4449's mass. Before the encounter, the observed HI gas was arranged
in a disc with a radius of 35-40 kpc around the center of NGC 4449. It had the
same orientation as the central ellipsoidal HI structure. The origin of this
disc is still unclear, but it might have been caused by a previous interaction.
