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Improvement of cryo-EM maps by density modification


A density-modification procedure for improving maps from single-particle electron cryogenic microscopy (cryo-EM) is presented. The theoretical basis of the method is identical to that of maximum-likelihood density modification, previously used to improve maps from macromolecular X-ray crystallography. Key differences from applications in crystallography are that the errors in Fourier coefficients are largely in the phases in crystallography but in both phases and amplitudes in cryo-EM, and that half-maps with independent errors are available in cryo-EM. These differences lead to a distinct approach for combination of information from starting maps with information obtained in the density-modification process. The density-modification procedure was applied to a set of 104 datasets and improved map-model correlation and increased the visibility of details in many of the maps. The procedure requires two unmasked half-maps and a sequence file or other source of information on the volume of the macromolecule that has been imaged.

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Fig. 1: Density modification of an apoferritin 3.1-Å map and evaluation using an apoferritin 1.8-Å map.
Fig. 2: Application of density modification to maps from the EMDB.
Fig. 3: Effect of a reconstruction procedure yielding more uniform noise on the outcome of density modification.

Data availability

The source data for Figs. 1 and 2 are available as Excel worksheets. The spreadsheet and underlying data used to generate the figures in this work and examples of the density-modified maps presented in the figures are available at


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This work was supported by the National Institutes of Health (grant no. GM063210 to P.D.A., R.J.R. and T.C.T. and grant no. R01-GM080139 to S.J.L.), the Wellcome Trust (grant no. 20947/Z/17/Z to R.J.R.) and the Phenix Industrial Consortium. This work was supported in part by the US Department of Energy under Contract No. DE-AC02-05CH11231 at the Lawrence Berkeley National Laboratory.

Author information




S.J.L. carried out image processing of test datasets to evaluate varying reconstruction procedures. R.J.R. and T.C.T. contributed ideas on the form of errors in cryo-EM. P.V.A. developed tools for the testing infrastructure. T.C.T. developed the software for error analysis. P.D.A. and T.C.T. supervised the work.

Corresponding author

Correspondence to Thomas C. Terwilliger.

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The authors declare no competing interests.

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Peer review information Arunima Singh was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

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Supplementary information

Source data

Source Data Fig. 1

Data used to generate Fig. 1AB

Source Data Fig. 2

Data used to generate Fig. 2AB

Source Data for Supplementary Fig. 9

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Terwilliger, T.C., Ludtke, S.J., Read, R.J. et al. Improvement of cryo-EM maps by density modification. Nat Methods 17, 923–927 (2020).

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