Ab initio electron density determination directly from solution scattering data

Abstract

Using a novel iterative structure factor retrieval algorithm, here I show that electron density can be directly calculated from solution scattering data without modeling. The algorithm was validated with experimental data from 12 different biological macromolecules. This approach avoids many of the assumptions limiting the resolution and accuracy of modeling algorithms by explicitly calculating electron density. This algorithm can be applied to a wide variety of molecular systems.

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Figure 1: Iterative structure factor retrieval algorithm using solution scattering data.
Figure 2: Electron density reconstructions from experimental solution scattering data for samples 1–11 (Supplementary Table 1).
Figure 3: Electron density map reconstruction of sample 12 endophilin–A1 BAR domain interacting with arachidonyl–CoA micelles from experimental solution scattering data.

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Acknowledgements

The author is grateful to W. Bauer, J. Chen, R. Kirian, E. Lattman, E. Snell and J. Spence for discussions and review of the manuscript. Financial support was provided by the BioXFEL NSF Science and Technology Center (NSF 1231306).

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Correspondence to Thomas D Grant.

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Integrated supplementary information

Supplementary Figure 1 Fourier shell correlation curves using experimental SAXS data

Fourier shell correlation (FSC) curves are shown for each of the twelve samples shown in Figures 2 and 3. The solid black curve (—) shows the FSC comparing the averaged maps from the even versus odd halves of the set of ab initio SAXS densities. The dashed curve (---) shows the FSC comparing the averaged SAXS density to the density simulated from the known atomic model. Horizontal dashed lines represent the cutoff used for estimating resolution at 0.5.

Supplementary Figure 2 Electron density maps calculated from models and simulated SAXS data for samples 1 through 11

(a) Electron density maps calculated from atomic coordinates. Electron density was calculated using Chimera to a resolution indicated in parentheses. (b) Electron density maps reconstructed from simulated SAXS data using DENSS. Simulated SAXS profiles were calculated using FoXS to the maximum q value from experiment (Supplementary Table 1). Electron densities are shown as volumes colored according to density (color bar indicates electron density values in e3).

Supplementary Figure 3 Electron density maps calculated from models and simulated SAXS data for sample 12

(a) Electron density maps calculated from atomic coordinates. Electron density was calculated using Chimera to a resolution indicated in parentheses. (b) Electron density maps reconstructed from simulated SAXS data using DENSS. Simulated SAXS profiles were calculated using FoXS to the maximum q value from experiment (Supplementary Table 1). Electron densities are shown as volumes colored according to density (color bar indicates electron density values in e3).

Supplementary Figure 4 Fourier shell correlation curves using simulated SAXS data

Fourier shell correlation (FSC) curves are shown for each of the twelve samples shown in Supplementary Figures 2b and 3b using simulated SAXS data calculated from atomic models with FoXS. The solid black curve (—) shows the FSC comparing the averaged maps from the even versus odd halves of the set of ab initio SAXS densities. The dashed curve (---) shows the FSC comparing the averaged SAXS density to the density simulated from the known atomic model. Horizontal dashed lines represent the cutoff used for estimating resolution at 0.5.

Supplementary Figure 5 Reconstructions from simulations of cylinders of varying aspect ratios

SAXS profiles from three homogenous cylinders of aspect ratio 2:1 (left), 5:1 (middle), and 10:1 (right) were simulated. Each cylinder has a length of 100 Å. The bottom row shows the same objects as in the top row rotated by 90 degrees. For each aspect ratio, the original density is shown on the left, the average of 100 reconstructions generated by DENSS using default parameters is shown in the middle, and the average of ten bead models built by DAMMIF is shown on the right. Densities are shown as volumes colored according to density, and bead models are shown as gray surfaces.

Supplementary Figure 6 Reconstructions using simulated SAXS profiles from a set of protein structures of complex shapes

SAXS profiles from three high-resolution protein structures with complex shapes were calculated from the coordinates deposited in the PDB using FoXS. Each row corresponds to one protein structure using PDB codes 2RCJ (top row), 1A0S (middle row) and 1IC1 (bottom row). The left two columns show averaged density reconstructions from DENSS (rotated 90 degrees relative to one another). The right two columns show the averaged bead models calculated with DAMMIF (rotated 90 degrees relative to one another). Electron density maps are displayed as volumes colored according to density. Bead models are shown as transparent gray surfaces. Reconstructions are shown overlapped by the high-resolution structures in green space-filling (2RCJ) or black cartoon (1A0S, 1IC1) representations.

Supplementary Figure 7 Reconstructions using SAXS data from spheres of various density gradients

Rows correspond to four varieties of electron density gradients from spheres of radius 25 Å. The column labeled “Original” shows the original density used to calculate the SAXS profile. The columns labeled “Single Reconstruction” and “Average” show the results from DENSS for a single reconstruction and average of twenty reconstructions, respectively. The column labeled “Bead Model” shows the average of ten bead models using DAMMIF. Electron densities are shown as volumes colored according to density. Bead models are shown as gray wire mesh to facilitate visualization of internal structure such as cavities.

Supplementary Figure 8 Single reconstructed electron density maps using experimental SAXS data for samples 1 through 11

Electron density maps for a randomly selected single reconstruction from experimental SAXS data for samples 1 through 11 corresponding to Figure 2. Electron densities are shown as volumes colored according to density (color bar indicates electron density values in e3).

Supplementary Figure 9 Ten single reconstructed electron density maps using experimental SAXS data from sample 12

Electron density maps for ten randomly selected single reconstructions from experimental SAXS data for sample 12 corresponding to Figure 3. Electron densities are shown as volumes colored according to density (color bar indicates electron density values in e3).

Supplementary Figure 10 Previously published bead model reconstructions using experimental SAXS data for samples 1 through 12

Figures reprinted with permission. Published ab initio bead models calculated from experimental SAXS data. Note that the sample numbering has been changed to correspond to the current manuscript, and the ordering and image layout is similar to facilitate comparison. The left side corresponds to samples 1 through 11 shown in Fig. 2 and shows high resolution crystal structures (cartoon representation) overlaid onto averaged bead models (transparent gray surface)17. The right side corresponds to sample 12 shown in Fig. 3 and shows the bead model (gray spheres) overlaid on the atomic model (red spheres and blue ribbon)18.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–10, Supplementary Tables 1–3 and Supplementary Notes 1–5 (PDF 2909 kb)

Life Sciences Reporting Summary (PDF 158 kb)

Supplementary Protocol

DENSS installation and usage instructions (PDF 178 kb)

Convergence process of electron density reconstruction from SAXS data

This video shows the convergence process for a single ab initio electron density reconstruction from SAXS data using the software DENSS for sample 11. Electron density is displayed as a volume object colored according to density. The top right graph shows the fit of the calculated scattering profile (red circles) to the smooth (black line) and raw (black circles) experimental data. After convergence is achieved, the known high-resolution atomic coordinates are superimposed to the density, shown in cartoon representation. (MOV 31120 kb)

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Grant, T. Ab initio electron density determination directly from solution scattering data. Nat Methods 15, 191–193 (2018). https://doi.org/10.1038/nmeth.4581

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