  Cryo-electron microscopy is a revolutionary technique that can provide 3D
density maps at near-atomic resolution. However, map validation is still an
open issue in the field. Despite several efforts from the community, it is
possible to overfit the reconstructions to noisy data. Here, inspired by modern
statistics, we develop a novel methodology that uses a small independent
particle set to validate the 3D maps. The main idea is to monitor how the map
probability evolves over the control set during the refinement. The method is
complementary to the gold-standard procedure, which generates two
reconstructions at each iteration. We low-pass filter the two reconstructions
for different frequency cutoffs, and we calculate the probability of each
filtered map given the control set. For high-quality maps, the probability
should increase as a function of the frequency cutoff and of the refinement
iteration. We also compute the similarity between the probability distributions
of the two reconstructions. As higher frequencies are added to the maps, more
dissimilar are the distributions. We optimized the BioEM software package to
perform these calculations, and tested the method on several systems, some
which were overfitted. Our results show that our method is able to discriminate
the overfitted sets from the non-overfitted ones. We conclude that having a
control particle set, not used for the refinement, is essential for
cross-validating cryo-EM maps.
