  Cosmic acceleration may be the result of unknown physical processes involving
either new fields in high energy physics or modifications of gravitation
theory. In the latter case, such modifications are usually related to the
existence of extra dimensions (which is also required by unification theories),
giving rise to the so-called brane cosmology. In this paper we investigate the
phenomenon of the acceleration of the Universe in a particular class of brane
scenarios in which a large scale modification of gravity arises due to a
gravitational \emph{leakage} into extra dimensions. By using the most recent
supernova observations we study the transition (deceleration/acceleration)
epoch as well as the constraints imposed on the parameters characterizing the
model. We show that these models provide a good description for the current
supernova data, which may be indicating that the existence of extra dimensions
play an important role not only in fundamental physics but also in cosmology.
