Spherical vesicles distorted by a grafted latex bead: an exact solution.

We present an exact solution to the problem of the global shape description of a spherical vesicle distorted by a grafted latex bead. This solution is derived by treating the nonlinearity in bending elasticity through the (topological) Bogomol'nyi decomposition technique and elastic compatibility. We recover the "hat-model" approximation in the limit of a small latex bead and find that the region antipodal to the grafted latex bead flattens. We also derive the appropriate shape equation using the variational principle and relevant constraints.