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. 2011 Feb;20(2):457-64.
doi: 10.1002/pro.572. Epub 2011 Jan 18.

A new approach for structure analysis of two-dimensional membrane protein crystals using X-ray powder diffraction data

R A Dilanian  1 , C Darmanin, J N Varghese, S W Wilkins, T Oka, N Yagi, H M Quiney, K A Nugent
Affiliations

A new approach for structure analysis of two-dimensional membrane protein crystals using X-ray powder diffraction data

R A Dilanian et al. Protein Sci. 2011 Feb.

Abstract

The application of powder diffraction methods to problems in structural biology is generally regarded as intractable because of the large number of unresolved, overlapping X-ray reflections. Here, we use information about unit cell lattice parameters, space group transformations, and chemical composition as a priori information in a bootstrap process that resolves the ambiguities associated with overlapping reflections. The measured ratios of reflections that can be resolved experimentally are used to refine the position, the shape, and the orientation of low-resolution molecular structures within the unit cell, in leading to the resolution of the overlapping reflections. The molecular model is then made progressively more sophisticated as additional diffraction information is included in the analysis. We apply our method to the recovery of the structure of the bacteriorhodopsin molecule (bR) to a resolution of 7 Å using experimental data obtained from two-dimensional purple membrane crystals. The approach can be used to determine the structure factors directly or to provide reliable low-resolution phase information that can be refined further by the conventional methods of protein crystallography.

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Figures

Figure. 1
Figure. 1
(a) The model of the molecular envelope located in the asymmetric unit of the p3 symmetry unit cell. The low-resolution shape and size of the envelope is matched with the form and size of the asymmetric unit. The parameters R, α, and β define the origin and orientation of the molecule in the unit cell. (b,c) The normalized MFF calculated for 7-Å resolution using discrete and continuous representation of bR, respectively. (d) The variation of the MFF of bR along the [1,0] direction calculated for different resolutions: 7 Å (dotted curve) and 5 Å (dashed curve). The solid curve represents the case of the continuous representation of bR. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
Figure. 2
Figure. 2
(a) The geometrical interpretation of Eq. (4). (b) The variation of the γ parameter as a function of the intensity ratio of two diffraction peaks, P, calculated for three selected orientations of the molecular envelope: (black asterisks) as shown in Figure 2(a), (blue asterisks) rotated by 120°, and (red asterisks) rotated by −120°. The vertical lines correspond to the intensity ratios P = 1/2 and P = 2/1. A, B, C, and D indicate four possible solutions for γ, corresponding to P = 0.5. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
Figure. 3
Figure. 3
Intensity ratios of three pairs of reflections are represented as functions of (a) Δα = α − αTrue and (b) Δβ = β − βTrue. ΔP = P − PTrue represents difference between the calculated values of intensity ratios and the exact values. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
Figure. 4
Figure. 4
The normalized molecular form factor of PM (a) simulated using discrete representation of the BR molecule, and (b) reconstructed using continuous representation of the BR molecule. The complex molecular form factor, formula image, where Aφ(S) is the magnitude and ϕφ(S) is the phase of φ(S). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
Figure. 5
Figure. 5
(a) Results of the Le Bail analysis of the powder diffraction pattern obtained from PM crystals. The upper solid line (red) represents the calculated intensities and small asterisks (black) superimposed on it are the observed intensities. The lower solid line (blue) is the difference between the observed and calculated intensities. The short vertical lines (green) below the profiles indicate peak positions of possible reflections. (b) The resulting low-resolution 2D electron density map of PM reconstructed from experimental data. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
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