How to correct relative voxel scale factors for calculations of vector-difference Fourier maps in cryo-EM

The atomic coordinates derived from cryo-electron microscopy (cryo-EM) maps can be inaccurate when the voxel scaling factors are not properly calibrated. Here, we describe a method for correcting relative voxel scaling factors between pairs of cryo-EM maps for the same or similar structures that are expanded or contracted relative to each other. We find that the correction of scaling factors reduces the amplitude differences of Fourier-inverted structure factors from voxel-rescaled maps by up to 20-30%, as shown by two cryo-EM maps of the SARS-CoV-2 spike protein measured at pH 4.0 and pH 8.0. This allows for the calculation of the difference map after properly scaling, revealing differences between the two structures for individual amino acid residues. Unexpectedly, the analysis uncovers two previously overlooked differences of amino acid residues in structures and their local structural changes. Furthermore, we demonstrate the method as applied to two cryo-EM maps of monomeric apo-photosystem II from the cyanobacteria Synechocystis sp. PCC 6803 and Thermosynechococcus elongatus. The resulting difference maps reveal many changes in the peripheral transmembrane PsbX subunit between the two species.