A resolution criterion for electron tomography based on cross-validation

Despite much progress in electron tomography, quantitative assessment of resolution has remained a problematic issue. The criteria that are used in single particle analysis, based on gauging the consistency between density maps calculated from half data sets, are not directly applicable because of the uniqueness of a tomographic volume. Here, we propose two criteria based on a cross-validation approach. One, called FSCe/o, is based on a Fourier shell correlation comparison between tomograms calculated from the even and odd members of a tilt series. The other, called noise-compensated leave-one-out (NLOO), is based on Fourier ring correlation comparisons between an original projection and the corresponding reprojection of the tomogram calculated from all the other projections, taking into account the differing noise statistics. Plotted as a function of tilt angle, they allow assessment of the angular dependence of resolution and quality control over the series of projections. Integrated over all projections, the results give a global figure for resolution. Tests on simulated tomograms established consistency between these criteria and the FSCref, a correlation coefficient calculated between a known reference structure and the corresponding portion of a tomogram containing that structure. The two criteria-FSCe/o and NLOO-are mutually consistent when residual noise is the major resolution-limiting factor. When the size of the tilt increment becomes a significant factor, NLOO provides a more reliable criterion, as expected, although it is computationally intensive. Applicable to entire tomograms or selected structures, NLOO has also been tested on experimental tomographic data.