  The adhesion bonds connecting a lipid bilayer to an underlying surface may
undergo a condensation transition resulting from an interplay between a short
range attractive potential between them, and a long range fluctuation-induced
potential of mean force. Here, we use computer simulations of a coarse-grained
molecular model of supported lipid bilayers to study this transition in
confined membranes, and in membranes subjected to a non-vanishing surface
tension. Our results show that confinement may alter significantly the
condensation transition of the adhesion bonds, whereas the application of
surface tension has a very minor effect on it. We also investigate domain
formation in membranes under negative tension which, in free membranes, causes
enhancement of the amplitude of the membrane thermal undulations. Our results
indicate that in supported membranes, this effect of a negative surface tension
on the fluctuation spectrum is largely eliminated by the pressure resulting
from the mixing entropy of the adhesion bonds.
