  Piezo ion channels underlie many forms of mechanosensation in vertebrates,
and have been found to bend the membrane into strongly curved dome shapes. We
develop here a methodology describing the self-assembly of lipids and Piezo
into polyhedral bilayer vesicles. We validate this methodology for bilayer
vesicles formed from bacterial mechanosensitive channels of small conductance,
for which experiments found a polyhedral arrangement of proteins with snub cube
symmetry and a well-defined characteristic vesicle size. On this basis, we
calculate the self-assembly diagram for polyhedral bilayer vesicles formed from
Piezo. We find that the radius of curvature of the Piezo dome provides a
critical control parameter for the self-assembly of Piezo vesicles, with high
abundances of Piezo vesicles with octahedral, icosahedral, and snub cube
symmetry with increasing Piezo dome radius of curvature.
