Abstract
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.
Highlights
The shape of fluctuating membranes has received abiding attention in the context of measuring bending rigidity (Gompper & Kroll, 1997) and explaining frequent, but surprising, membrane shapes such as the discoid shape of red blood cells (Canham, 1970; Helfrich, 1973; Seifert et al, 1991; Discher et al, 1994; Safran, 1994; Lim et al, 2002; Li et al, 2005)
Thereby, we address the limitations of current small unilamellar vesicles (SUVs) small-angle X-ray scattering (SAXS) analysis paradigms, namely idealization of one or more of the following effects: (i) polydispersity distribution of vesicle radii, (ii) thermal vesicle shape fluctuations and (iii) curvature dependence of the electron-density profile (EDP)
To understand qualitatively the features of the scattering intensity I(q), we factorize I(q) into a structure factor, which describes the shape of the vesicle and its fluctuations, and a form factor of the membrane, which contains information about the EDP of the bilayer membrane (Kiselev et al, 2002)
Summary
The shape of fluctuating membranes has received abiding attention in the context of measuring bending rigidity (Gompper & Kroll, 1997) and explaining frequent, but surprising, membrane shapes such as the discoid shape of red blood cells (Canham, 1970; Helfrich, 1973; Seifert et al, 1991; Discher et al, 1994; Safran, 1994; Lim et al, 2002; Li et al, 2005). One of the most widely used experimental techniques to study the structure and shape of lipid bilayers and vesicles is small-angle X-ray scattering (SAXS) (Zubay, 1999; Pabst et al, 2000; Kiselev et al, 2002; Brzustowicz & Brunger, 2005; Pencer et al, 2006; Kucerka et al, 2008; Szekely et al, 2010; Heberle et al, 2012). It allows information to be obtained starting from the molecular level, such as the location of a particular chemical entity (e.g. carbon double bonds), up to the overall vesicle shape.
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