Structural variability and the incoherent addition of scattered intensities in single-particle diffraction

X-ray lasers may allow structural studies on single particles and biomolecules without crystalline periodicity in the samples. We examine here the effect of sample dynamics as a source of structural heterogeneity on the resolution of the reconstructed image of a small protein molecule. Structures from molecular-dynamics simulations of lysozyme were sampled and aligned. These structures were then used to calculate diffraction patterns corresponding to different dynamic states. The patterns were incoherently summed and the resulting data set was phased using the oversampling method. Reconstructed images of hydrated and dehydrated lysozyme gave resolutions of 3.7 angstrom and 7.6 angstrom, respectively. These are significantly worse than the root-mean-square deviation of the hydrated (2.7 angstrom for all atoms and 1.45 angstrom for C-alpha positions) or dehydrated (3.7 angstrom for all atoms and 2.5 angstrom for C-alpha positions) structures. The noise introduced by structural dynamics and incoherent addition of dissimilar structures restricts the maximum resolution to be expected from direct image reconstruction of dynamic systems. A way of potentially reducing this effect is by grouping dynamic structures into distinct structural substates and solving them separately.