  We present a general formalism to study the growth of dark matter
perturbations when dark energy perturbations and interactions between dark
sectors are present. We show that dynamical stability of the growth of
structure depends on the type of coupling between dark sectors. By taking the
appropriate coupling to ensure the stable growth of structure, we observe that
the effect of the dark sectors' interaction overwhelms that of dark energy
perturbation on the growth function of dark matter perturbation. Due to the
influence of the interaction, the growth index can differ from the value
without interaction by an amount within the observational sensibility, which
provides a possibility to disclose the interaction between dark sectors through
future observations on the growth of large structure.
