  The adhesion of cells is mediated by membrane receptors that bind to
complementary ligands in apposing cell membranes. It is generally assumed that
the lateral diffusion of mobile receptor-ligand bonds in membrane-membrane
adhesion zones is slower than the diffusion of unbound receptors and ligands.
We find that this slowing down is not only caused by the larger size of the
bound receptor-ligand complexes, but also by thermal fluctuations of the
membrane shape. We model two adhering membranes as elastic sheets pinned
together by receptor-ligand bonds and study the diffusion of the bonds using
Monte Carlo simulations. In our model, the fluctuations reduce the bond
diffusion constant in planar membranes by a factor close to 2 in the
biologically relevant regime of small bond concentrations.
