  The free energy of inserting a protein into a membrane is determined by
considering the variation in the spectrum of thermal fluctuations in response
to the presence of a rigid inclusion. Both numerically and through a simple
analytical approximation, we find that the primary effect of fluctuations is to
reduce the effective surface tension, hampering the insertion at low surface
tension. Our results, which should also be relevant for membrane pores, suggest
(in contrast to classical nucleation theory) that a finite surface tension is
necessary to facilitate the opening of a pore.
