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

Solvated Membrane Nanodiscoids: A Probe For The Effects Of Gaussian Curvature