The effect of polydispersity, shape fluctuations and curvature on small unilamellar vesicle small-angle X-ray scattering curves

Small unilamellar vesicles (20–100 nm diameter) are model systems for strongly curved lipid membranes, in particular for cell organelles. Routinely, small-angle X-ray scattering (SAXS) is employed to study their size and electron-density profile (EDP). Current SAXS analysis of small unilamellar vesicles (SUVs) often employs a factorization into the structure factor (vesicle shape) and the form factor (lipid bilayer electron-density profile) and invokes additional idealizations: (i) an effective polydispersity distribution of vesicle radii, (ii) a spherical vesicle shape and (iii) an approximate account of membrane asymmetry, a feature particularly relevant for strongly curved membranes. These idealizations do not account for thermal shape fluctuations and also break down for strong salt- or protein-induced deformations, as well as vesicle adhesion and fusion, which complicate the analysis of the lipid bilayer structure. Presented here are simulations of SAXS curves of SUVs with experimentally relevant size, shape and EDPs of the curved bilayer, inferred from coarse-grained simulations and elasticity considerations, to quantify the effects of size polydispersity, thermal fluctuations of the SUV shape and membrane asymmetry. It is observed that the factorization approximation of the scattering intensity holds even for small vesicle radii (∼30 nm). However, the simulations show that, for very small vesicles, a curvature-induced asymmetry arises in the EDP, with sizeable effects on the SAXS curve. It is also demonstrated that thermal fluctuations in shape and the size polydispersity have distinguishable signatures in the SAXS intensity. Polydispersity gives rise to low-q features, whereas thermal fluctuations predominantly affect the scattering at larger q, related to membrane bending rigidity. Finally, it is shown that simulation of fluctuating vesicle ensembles can be used for analysis of experimental SAXS curves.