Small angle x-ray scattering (SAXS)

Lipid bilayer thicknesses were measured at 20°C by small angle x-ray scattering (SAXS) using the F-2 beamline at MacCHESS synchrotron facilities (Cornell University, Ithaca, NY) at 9.881 keV. Liposomes of 70 mol% diCnPC (14:1–22:1) and 30 mol % POPG in buffer A pH 7.5 were generated by 49 passes through a 50nm PC membrane using a lipid extruder (Avanti Polar Lipids). A quantity of 200 µL samples were exposed 10 times for 30 s each and scattering data were collected using a Dual Pilatus 100K-S SAXS/WAXS detector. To avoid radiation damage, the samples were oscillated continuously throughout measurements. Intensity as a function of momentum transfer:

where λ is the wavelength of the beam, and θ is the angle of diffraction [⁴¹], was plotted and analyzed online using Bioxtas RAW v0.99.12b software [⁴²]. Scattering from buffer A alone was subtracted from liposome samples to determine lipid dependent scattering. Electron density of the bilayer and parameters of the bilayer, including hydrophobic thickness (or interleaflet distance between the first carbon atoms of the lipid acyl tail following the glycerol backbone), were determined by a 3-Gaussian model derived from Lorentzian fits of the I-q relationship [⁴³,⁴⁴].

The Form Factor (Fh) is determined from the square root of the area under the Lorentzian curve fitting the I-q relationship determined by SAXS, and used to determine the electron density ρ*(z) of the lipid bilayer according to the relationship:

where z is the distance of the system (d-spacing) in Å units. This expression is then converted to a tri-gaussian curve according to the following equation:

where z_H is the distance between the center of the bilayer and the lipid head-group, σ_H is the width of the gaussian describing the headgroups, ρ_r is the ratio between the electron density of acyl tails and the headgroup, and σ_C is the width of the Gaussian curve describing the hydrophobic core.