  We characterize vesicle adhesion onto homogeneous substrates by means of a
perturbative expansion around the infinite adhesion limit, where curvature
elasticity effects are absent. At first order in curvature elasticity, we
determine analytically various global physical quantities associated with
adhering vesicles: height, adhesion radius, etc. Our results are valid for
adhesion energies above a certain threshold, that we determine numerically. We
discuss the haptotactic force acting on a vesicle in the limit of weak adhesion
gradients. We also propose novel methods for measuring adhesion energies and we
suggest a possible way of determining the size of suboptical vesicles using
controlled adhesion gradients.
