  We calculate the induced elastic-interaction between pointwise membrane
inclusions that locally interact up to quadratic order with the membrane
curvature tensor. For isotropic inclusions, we recover the usual interaction
proportional to the inverse fourth power of the separation, however with a
prefactor showing a non-trivial dependence on the rigidity $\Gamma$ of the
quadratic potential. In the large $\Gamma$ limit, corresponding to ``hard''
inclusions, we recover the standard prefactor first obtained by Goulian et al.
[Europhys. Lett. \textbf{22}, 145 (1993)]. In the small $\Gamma$ limit,
corresponding to "soft" inclusions, we recover the recent result of Marchenko
and Misbah [Eur. Phys. J. E \textbf{8}, 477 (2002)]. This shows that the latter
result bears no fundamental discrepancy with previous works, but simply
corresponds to the limit of soft inclusions. We discuss how the same inclusion
can be depicted as hard or soft according to the degree of coarse-graining of
the pointwise description. Finally, we argue that conical transmembrane
proteins should be fundamentally considered as hard inclusions.
