  Models with interacting dark energy can alleviate the cosmic coincidence
problem by allowing dark matter and dark energy to evolve in a similar fashion.
At a fundamental level, these models are specified by choosing a functional
form for the scalar potential and for the interaction term. However, in order
to compare to observational data it is usually more convenient to use
parameterizations of the dark energy equation of state and the evolution of the
dark matter energy density. Once the relevant parameters are fitted it is
important to obtain the shape of the fundamental functions. In this paper I
show how to reconstruct the scalar potential and the scalar interaction with
dark matter from general parameterizations. I give a few examples and show that
it is possible for the effective equation of state for the scalar field to
cross the phantom barrier when interactions are allowed. I analyze the
uncertainties in the reconstructed potential arising from foreseen errors in
the estimation of fit parameters and point out that a Yukawa-like linear
interaction results from a simple parameterization of the coupling.
