  Sakuma and Imai [Phys. Rev. Lett. 107, 198101 (2011)] established a
temperature-controlled cyclic process for a model system of self-reproducing
vesicles without feeding. The vesicle generates a smaller inclusion vesicle
called "daughter vesicle" inside the original vesicle (we call this "mother
vesicle") and then the daughter vesicle is expelled through a small pore on the
mother vesicle. This self-reproducing process is called birthing. In the
present study we present theoretical model on the birthing process of a single,
rigid daughter vesicle through a pore. By using a simple geometric picture, we
derive the free energy constituting the material properties of the bending,
stretching and line tension moduli of the mother vesicle, as a function of the
distance between the centers of the daughter and mother vesicles, and the size
of the daughter vesicle. We see clearly the disappearance of the energy barrier
by selecting appropriate moduli. The dynamics of the system is studied by
employing the Onsager principle. The results indicate that translocation time
decreases as the friction parameter decreases, or the initial size of the
daughter vesicle decreases.
