Figure 3.
(a) The geometric model used and definitions of the relevant parameters. (b), (c) A breakdown of the scattering intensity and the P(r) function for a lipid nanodisc, based on the model shown in panel (a). The scattering intensity of panel (b) is first represented as a two-dimensional function I(q r, q z) (upper panel) and subsequently converted into an isotropic average (blue symbols in the lower panel), as described in the text. The geometric parameters are based on the WillItFit results for the 55 min fraction data presented in Fig. 1 ▸. For comparison, the isotropic average of the contributions from the lipid bilayer alone (green line) and the protein belt alone (red line) are also shown. Note that a small constant has been added to the calculated intensity to match the experimental data. The two-dimensional scattering amplitude maps for the individual components and the corresponding one-dimensional scattering profiles are presented in the supporting information (Figs. S1 and S2). The breakdown of the distance distribution function P(r) (thick black line) is shown in panel (c), as calculated from the same geometric model. The contributions from the individual components are also shown: lipid heads (cyan dots), lipid chains (magenta dots), the cross-correlation between the lipid heads and lipid tails (yellow dots), the lipid bilayer as a whole (blue line), the protein belt (green line), and the cross correlation between the lipid bilayer and the protein belt (red line). Note that these curves have been smoothed using a low-pass filter to eliminate artefacts due to the discrete grid used to represent the continuous electron-density distribution of the nanodisc. For reference, the vertical red dashed lines indicate the head-to-head distance of the bilayer [(L 1 + L 2)/2] and a characteristic length {[(2a)2 + (L BT)2]1/2} to represent the protein belt.