Multivariate analysis of single unit cells in electron crystallography

High-resolution electron cryomicroscopy of two-dimensional protein crystals is associated with extremely noisy raw data in which even the crystal lattice often cannot be discerned. Correlation averaging procedures, aimed at calculating the total average of all unit cells of crystals in order to reduce noise, are now used routinely in electron crystallography. Multivariate statistical analysis (MSA) may be used for finding not only the average structure but also for quantifying the systematic departures from that average within the population of individual unit cells. We show that the MSA approach is applicable to single unit-cell images in the low-dose (< 10 electrons/A2), high-resolution (< 5 A) realm using 400 keV electron spot-scan images of ice-embedded gp32*I protein crystals. Our feasibility study opens a pathway toward exploiting these naturally occurring variations on the unit-cell theme in order to achieve higher-resolution three-dimensional reconstruction results, or to better understand the dynamic behaviour of molecules within two-dimensional crystals. We explain how single unit-cell images can be processed and classified into homogeneous groups, and we review how the results of such discriminate averaging may subsequently be exploited within the context of conventional "h, k"-space electron crystallographic approaches. Variations among the individual unit cells may thus be one of the most significant resolution-limiting factors currently experienced in electron crystallography. The quantitative assessment and exploitation of such variations may lead to an increased performance of electron crystallographic procedures.