Elastic interaction of point defects on biological membranes

The interaction between inclusions mediated by biological membranes undulations is analyzed. The interaction law is interpreted in terms of symmetries associated with inclusions. We show, in particular, that for a C3 and C3v symmetries the interaction law falls as 1/r3. We show that for completely isotropic inclusions, the dominant interaction vanishes to all orders, and the first contribution stems from the induced interaction which behaves as 1/r4. The same law holds for any other symmetry which is higher than C4. We introduce a straightforward method to compute these interactions. We point out important differences with results in the literature and explain the discrepancies.