  We present the results of a survey of the brightest UV-selected galaxies in
protoclusters. These proto-brightest cluster galaxy (proto-BCG) candidates are
drawn from 179 overdense regions of $g$-dropout galaxies at $z\sim4$ from the
Hyper Suprime-Cam Subaru Strategic Program identified previously as good
protocluster candidates. This study is the first to extend the systematic study
of the progenitors of BCGs from $z\sim2$ to $z\sim4$. We carefully remove
possible contaminants from foreground galaxies and, for each structure, we
select the brightest galaxy that is at least 1 mag brighter than the fifth
brightest galaxy. We select 63 proto-BCG candidates and compare their
properties with those of galaxies in the field and those of other galaxies in
overdense structures. The proto-BCG candidates and their surrounding galaxies
have different rest-UV color $(i - z)$ distributions to field galaxies and
other galaxies in protoclusters that do not host proto-BCGs. In addition,
galaxies surrounding proto-BCGs are brighter than those in protoclusters
without proto-BCGs. The image stacking analysis reveals that the average
effective radius of proto-BCGs is $\sim28\%$ larger than that of field
galaxies. The $i-z$ color differences suggest that proto-BCGs and their
surrounding galaxies are dustier than other galaxies at $z\sim4$. These results
suggest that specific environmental effects or assembly biasses have already
emerged in some protoclusters as early as $z \sim 4$, and we suggest that
proto-BCGs have different star formation histories than other galaxies in the
same epoch.
