  Using field theoretic approach, we study equilibrium shape deformation of a
vesicle induced by the presence of enclosed flexible polymers, which is a
simple model of drug delivery system or endocytosis. To evaluate the total free
energy of this system, it is necessary to calculate the bending elastic energy
of the membrane, the conformation entropy of the polymers and their
interactions. For this purpose, we combine phase field theory for the membrane
and self-consistent field theory for the polymers. Simulations on this coupled
model system for axiosymmetric shapes show a shape deformation of the vesicle
induced by introducing polymers into it. We examined the dependence of the
stability of the vesicle shape on the chain length of the polymers and the
packing ratio of the vesicle. We present a simple model calculation that shows
the relative stability of the prolate shape compared to the oblate shape.
