Assessment of resolution in biological electron crystallography

The resolution of images or density maps produced by electron microscopy and electron crystallography can be objectively defined in terms of the spatial frequency of the highest resolution diffraction spot, or Fourier coefficient, included in the data processing. In practice, this objective definition of resolution is expected to be too optimistic if the amplitudes of the highest resolution structure factors are too weak, if the population of high resolution reflections is too sparse, or if the signal-to-noise ratio of the high resolution data is too low. Calculated examples are presented here which illustrate how the apparent resolution in images of a membrane protein, bacteriorhodopsin, can be reduced from a nominal value of 3.5 A by weak amplitudes, sparse data or high noise levels. These calculations provide concrete examples which can serve as a guide when estimating whether the objective definition of image resolution is likely to correspond to a practical, structurally useful estimate of image resolution.