  We investigate the galaxy population in simulated proto-cluster regions using
a semi-analytic model of galaxy formation, coupled to merger trees extracted
from N-body simulations. We select the most massive clusters at redshift $z=0$
from our set of simulations, and follow their main progenitors back in time.
The analysis shows that proto-cluster regions are dominated by central galaxies
and their number decreases with time as many become satellites, clustering
around the central object. In agreement with observations, we find an
increasing velocity dispersion with cosmic time, the increase being faster for
satellites. The analysis shows that proto-clusters are very extended regions,
$\gtrsim 20 \, Mpc$ at $z \gtrsim 1$. The fraction of galaxies in proto-cluster
regions that are not progenitor of cluster galaxies varies with redshift,
stellar mass and area considered. It is about 20-30 per cent for galaxies with
stellar mass $\sim 10^9\,{\rm M}_{\sun}$, while negligible for the most massive
galaxies considered. Nevertheless, these objects have properties similar to
those of progenitors. We investigate the building-up of the passive-sequence in
clusters, and find that their progenitors are on average always active at any
redshift of interest of proto-clusters. The main mechanism which quenches their
star formation is the removal of the hot gas reservoir at the time of
accretion. The later galaxies are accreted (become satellite), and the more the
cold gas available, the longer the time spent as active. Central galaxies are
active over all redshift range considered, although a non-negligible fraction
of them become passive at redshift $z<1$, due to strong feedback from Active
Galactic Nuclei.
