We irst studied the case in which the area impacted by the Ca 2+ ions was localized to a small patch (1% of the total surface area) of the vesicle near the north pole. For a vesicle of 100 nm in diameter, as the spontaneous curvature c 0 was gradually increased from 0 to 0.3 nm -1 , which matched the maximum spontaneous curvature estimated from Eq. ( ) in Fig. , the impacted membrane patch protruded further outward and developed into a hemispherical cap (Fig. ). The positive spontaneous curvature could be induced by a local accumulation of Ca 2+ in the inner part of the membrane. Similar trends were also observed for negative c 0 , in which the impacted membrane patch bent inward and developed into a small spherical vesicle with a diameter of ∼ 20 nm (Fig. ), as indicated by the relative height, which is the difference of the pole-to-pole distance between the deformed vesicle and the undeformed spherical vesicle (Fig. ). If the diameter of the undeformed spherical vesicle was increased to 200 nm, the impacted membrane patch (1% of the total surface area) would form a pearl-shaped structure in which multi-spherical vesicles are interconnected via narrow necks (Fig. ).