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

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.