Fourier shell correlation criteria for local resolution estimation

The resolution of three-dimensional (3D) maps obtained by electron microscopy and reconstruction is rarely constant, owing to the flexibility or compositional variability of the macromolecules of interest. Accurately estimating the local resolution within 3D reconstruction volumes is desirable for analytical purposes, and may help improve the reconstruction process itself. One approach to estimating the local resolution is to compute Fourier shell correlations (FSC) between equivalent local regions of maps computed from half datasets: the estimated local resolution is that of the Fourier shell where the FSC drops below a pre-established threshold value. Existing thresholds can lead to significant over-estimates of the local resolution because they do not take into account the low number of independent voxels in low-resolution Fourier shells typically encountered when dealing with small sub-volumes. We derive a modified FSC threshold criterion, and a simple statistical test of whether the FSC significantly exceeds it, which aims to remedy this by taking into account the bias and variance of the FSC as an estimator of signal-to-noise ratio.