Classification and averaging of random orientation single macromolecular diffraction patterns at atomic resolution

Single molecule imaging experiments at future X-ray free electron laser sources will provide large number of random 3D oriented diffraction patterns with low counting statistics. Grouping of this vast amount of data into classes of similar orientations and averaging must be performed before their orientation and structure reconstruction can take place. Classification algorithms performing all-pair pattern comparisons scale badly with the number of patterns in terms of their computing requirements, which presents a problem in case of improving resolution and decreasing signal to noise ratios. We describe an algorithm performing significantly less pattern comparisons and render classification possible in such cases. The invariance of patterns against rotation of the object about the primary beam axis is also exploited to decrease the number of classes and improve the quality of class averages. This work is the first, which demonstrates that it is possible to classify a dataset with realistic target parameters: 10 keV photon energy, 10(12) photons/pulse, 100 x 100 nm2 focusing, 538 kDa protein, 2.4 A resolution, 10(6) patterns, approximately 3 x 10(4) classes, <1 degree misorientation within classes. The effects of molecular symmetry and its consequences on classification are also analyzed.