  We investigate a model of brane cosmology to find a unified description of
the radiation-matter-dark energy universe. It is of the interacting holographic
dark energy with a bulk-holographic matter $\chi$. This is a five-dimensional
cold dark matter, which plays a role of radiation on the brane. Using the
effective equations of state $\omega^{\rm eff}_{\rm \Lambda}$ instead of the
native equations of state $\omega_{\rm \Lambda}$, we show that this model
cannot accommodate any transition from the dark energy with $\omega^{\rm
eff}_{\rm \Lambda}\ge-1$ to the phantom regime $\omega^{\rm eff}_{\rm
\Lambda}<-1$. Furthermore, the case of interaction between cold dark matter and
five dimensional cold dark matter is considered for completeness. Here we find
that the redshift of matter-radiation equality $z_{\rm eq}$ is the same order
as $z^{\rm ob}_{\rm eq}=2.4\times10^{4} \Omega_{\rm m}h^2$. Finally, we obtain
a general decay rate $\Gamma$ which is suitable for describing all interactions
including the interaction between holographic dark energy and cold dark matter.
