Birthing of a daughter vesicle in a model system for self-reproduction vesicles

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.