  The disk-to-vesicle transition of a fluid membrane with no spontaneous
curvature is well described by the competition between edge line and curvature
energies. However, the transition of asymmetric membranes with spontaneous
curvatures is not yet understood. In this study, the shape of the fluid
membrane patch with a constant spontaneous curvature and its closing transition
to a vesicle is investigated using theory and meshless membrane simulations. It
is confirmed that the (meta)stable and transient membranes are well
approximated by spherical caps. The membrane Gaussian modulus can be estimated
from the cup shape of membrane patches as well as from the transition
probability, although the latter estimate gives slightly smaller negative
values. Furthermore, the self-assembly dynamics of membranes are presented, in
which smaller vesicles are formed at higher spontaneous curvatures, higher edge
line tension, and lower density.
