Charge fluctuations and membrane attractions

We consider the fluctuations of charges in membranes and their effect on the interactions between two fluid membranes a distance h apart. For the case where the counterions are highly localized in the membrane planes we find that the attraction scales as 1/h(3) at large distances and as 1/h when the membranes are closer than a typical screening length. W-hen the counterions are delocalized between the membranes a simple ideal-gas approximation indicates that a primary contribution to the membrane attraction are the fluctuations of this gas; in some cases, these attractions can exceed the repulsive interactions found for uniform charge distributions (the Poisson-Boltzmann or mean-field repulsions). These results may be relevant to understanding the role of charge fluctuations in membrane attraction and adhesion.