We establish a model of cell-tissue interaction consisting of vesicles
carrying lipopolymers (to mimic the glycocalix) and mobile specific ligands
of the blood platelet integrin \alpha _\ab{IIb}\beta _{3} covering the
substrate. We find the phase diagram with a first-order transition between
a gravity-controlled weak state of the vesicle-substrate adhesion and a
strong-adhesion state governed by receptor-ligand interaction. Adhesion
energy \varepsilon _\ab{adh} is measured as a function of ligand and
repeller concentration by interferometric contour analysis on the basis of a
new refined model of soft shell adhesion (accounting for the membrane bending
and stretching at the adhesion rim of the ellipsoidal vesicle). At ligand
densities comparable to integrin density, \varepsilon _\ab{adh}
decreases sharply. Increasing the repeller content weakens the adhesion
strength
