Crystallography without crystals I: the common-line method for assembling a 3D intensity volume from single-particle scattering

TL;DR

This paper introduces a common-line method to reconstruct 3D diffraction intensities from 2D patterns in single-particle X-ray imaging, addressing ambiguities and practical limitations for high-resolution structure determination.

Contribution

The paper presents a novel common-line approach for assembling 3D diffraction data from single-particle scattering experiments, overcoming Friedel's Law ambiguities.

Findings

Effective for photon counts above 10 per pixel

Requires approximately 10^9 diffraction patterns for high-resolution structure

High data acquisition time (~10^7 seconds) needed for practical application

Abstract

We demonstrate that a common-line method can assemble a 3D oversampled diffracted intensity distribution suitable for high-resolution structure solution from a set of measured 2D diffraction patterns, as proposed in experiments with an X-ray free electron laser (XFEL) (Neutze {\it et al.}, 2000). Even for a flat Ewald sphere, we show how the ambiguities due to Friedel's Law may be overcome. The method breaks down for photon counts below about 10 per detector pixel, almost 3 orders of magnitude higher than expected for scattering by a 500 kDa protein with an XFEL beam focused to a 0.1 micron diameter spot. Even if 10**3 orientationally similar diffraction patterns could be identified and added to reach the requisite photon count per pixel, the need for about 10**6 orientational classes for high-resolution structure determination suggests that about ~ 10**9 diffraction patterns must be recorded. Assuming pulse and read-out rates of 100 Hz, such measurements would require ~ 10**7 seconds, i.e. several months of continuous beam time.