  We grafted polyacrylic acid brushes containing cysteine side chains at a
defined surface density on planar lipid membranes. Specular X-ray reflectivity
data indicated that the addition of Cd2+ ions induces the compaction of the
polymer brush layer and modulates the adhesion of lipid vesicles. The critical
threshold level inducing the switch from non-wetting to partial wetting state,
[Cd2+] = 0.25 mM, was determined by microinterferometry. The interactions
between vesicles and brushes were evaluated by height fluctuations of the
membrane in contact with brushes and the shape of vesicles near the surface. To
analyze these experiments, we have studied adhesion of axially symmetric
vesicles for finite-range membrane-substrate interaction and buoyancy through
simulations. We found that the local transversality condition that relates the
maximal curvature at the edge of the adhesion zone to the adhesion strength
remains rather accurate. Thus, although it is not experimentally possible to
prepare vesicles at zero buoyancy, we can use the transversality condition to
estimate the adhesion strength. However, the adhesion diagram is significantly
modified by a finite range of membrane-substrate interaction and buoyancy. For
downward buoyancy, vesicles merely sediment onto the substrate and there is no
mean-field adhesion transition. For upward buoyancy, adhered vesicles are
metastable at best. Thus, a mean-field adhesion transition can only occur at
vanishing buoyancy. Only for zero-range membrane-substrate interaction does a
second-order adhesion transition occur at finite interaction strength. For any
finite-range interaction, the transition occurs when the membrane-substrate
interaction changes from repulsive to attractive. We present a adhesion diagram
as a function of adhesion strength and buoyancy and compare the adhesion
behavior of vesicles to the wetting behavior of droplets of liquids.
