  Several methods now exist to solvate lipid bilayer discoids at the scale of
tens of nanometres. Due to their size, such nanodiscoids have a comparatively
large boundary-to-area ratio, making them unusually well-suited to probing the
effects of Gaussian curvature. Arguing that fluctuations in discoid size and
shape are quenched on formation, we quantify the stability, in terms of size
and shape, of near-solvation discoid-like flaps that are subject to thermal
fluctuations. Using cryo-Electron Microscopy images of Styrene Maleic Acid
stabilised discoids, we deduce that stable, saddle-like discoids (with high
Gaussian curvature) can likely be solvated from bulk lamellar ($L_\alpha$)
phase at moderate-to-high surface tensions ($>10^{-4}$ N/m). We then describe
how such tension-controlled solvation can be used for both measuring, and
fractionating membrane components according-to, the modulus of Gaussian
rigidity $\bar{\kappa}$. Opportunities for investigating the effects of
Gaussian curvature on membrane-embedded proteins, which can be co-solvated
during the formation process, are also discussed.
