We present a new entropic interaction between foreign inclusions (e.g.
proteins) confined to fluid membranes in a layered phase. This intera
ction arises from the coupling of thermal shape fluctuations to the va
riation in rigidity associated with the presence of inclusions. The fo
rce between inclusions exhibits interesting nonmonotonic behaviour as
a function of the separation distance. At large separation, we find a
weak power law attraction between inclusions of similar composition.