Abstract
The method of angular correlations recovers quantities from diffraction patterns of randomly oriented particles, as expected to be measured with an X-ray free electron laser (XFEL), proportional to quadratic functions of the spherical harmonic expansion coefficients of the diffraction volume of a single particle. We have previously shown that it is possible to reconstruct a randomly oriented icosahedral or helical virus from the average over all measured diffraction patterns of such correlations. We point out in this paper that a structure of even simpler particles of 50 Å or so in diameter and consisting of heavier atomic elements (to enhance scattering) that has been used as a test case for reconstructions from XFEL diffraction patterns can also be solved by this technique. Even though there has been earlier work on similar objects (prolate spheroids), one advantage of the present technique is its potential to also work with diffraction patterns not only due to single particles as has been suggested on the basis on nonoverlapping delta functions of angular scattering. Accordingly, we calculated from the diffraction patterns the angular momentum expansions of the pair correlations and triple correlations for general particle images and reconstructed those images in the standard way. Although the images looked pretty much the same, it is not totally clear to us that the angular correlations are exactly the same as different numbers of particles due to the possibility of constructive or destructive interference between the scattered waves from different particles. It is of course known that, for a large number of particles contributing to a diffraction parttern, the correlations converge to that of a single particle. It could be that the lack of perfect agreement between the images reconstructed with one and two particles is due to uncancelling constructive and destructive conditions that are not found in the case of solution scattering.
Highlights
An X-ray free electron laser (XFEL) produces X-rays of unprecedented brilliance of about 10 billion times what was previously possible
If the experiment we propose is possible, it may be possible to avoid crystallization in structural studies and still avoid the very low scattered intensities that are inevitable in single particle studies even with an X-ray free electron laser (XFEL)
It should be noted that the images computed from the diffraction patterns of single particles do not agree perfectly with those from two particles
Summary
An X-ray free electron laser (XFEL) produces X-rays of unprecedented brilliance of about 10 billion times what was previously possible. The ultimate aim is to determine the structures of biomolecules, it would be helpful to demonstrate the feasibility of the approach to simpler objects initially. In this vein, there has been some work already on reconstructing prolate spheroids [2] of metallic particles. There has been some work already on reconstructing prolate spheroids [2] of metallic particles What such experiments demonstrate is the feasibility of reconstructing the structure of particles of random unknown orientations. The aim of the present paper is to show that reconstruction of the structure of such particles is possible even with two particles in independent random orientations contributing to a single diffraction pattern.
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