# The Resolution in X-ray Crystallography and Single-Particle Cryogenic Electron Microscopy

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## Abstract

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## 1. Introduction

## 2. X-ray Crystallography

#### 2.1. Resolution Cutoff

#### 2.2. Resolution of the Dataset

## 3. Electron Microscopy

#### 3.1. Fourier Shell Correlation

_{C}of 1 (SNR

_{C}being the signal-to-noise ratio in the particular Fourier shell) [45]. However, this threshold value of 0.5 is said to underestimate the resolution [47,48], as during this procedure the data are split randomly in halves. This means that during refinement there are half less particles than when the complete dataset were used. Having fewer particles makes the dataset noisier, as there are fewer particles to average with. To overcome this problem, a new processing method (named the “gold standard” method) was introduced [47,48], which currently is the most accepted and widely used in the EM community. The resolution determined by the gold standard method is often the one reported for structures in the PDB or the Electron Microscopy Data Bank (EMDB). In this gold standard method the models derived from each half dataset are refined independently opposed to having two maps and a single model. This decreases unintended correlation of the compared maps and lessens the effect of data overfitting but does not eliminate it entirely [48,49]. The suggested threshold value of 0.143 originates from a 0.5 value of correlation of the complete dataset and an unknown perfect map of the macromolecule. The threshold of 0.5 for the estimated correlation was chosen for two main reasons. First, the estimated correlation can be written out as a function of the phase error. This is equivalent to an X-ray crystallographic measure of the accuracy of the phases, the figure of merit (FOM). The FOM is commonly used in X-ray crystallography as an indication if the map is interpretable enough to build a structure in it. A value of 0.5 corresponds to a phase error of $60deg$ which is considered as interpretable enough to build a structure into the density map [50]. Second, the FSC can be related to the real space correlation coefficient (R), a measure of similarity between two density maps. When there are no amplitude errors present, the real space correlation coefficient R corresponds to the estimated correlation of the complete dataset and the unknown perfect map. Using this, one can predict if the addition of a Fourier shell will have a positive effect on the correlation of the map and the perfect map and thus improve the map itself with 0.5 being the threshold [50].

#### 3.2. Spectral Signal-To-Noise Ratio

_{k}denotes the amount of Fourier components per voxel and ${\sigma}^{r}$ is equal to ${N}_{n}^{k}{}^{2}$. This is the ratio of the energy of the signal and the energy of the noise, and it is adjusted with the size of the dataset. However, this cannot be known because ${F}_{T}^{k}$ cannot be known. Therefore, the SSNR is estimated using:

#### 3.3. Fourier Neighbor Correlation

#### 3.4. Local Resolution

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Dubach, V.R.A.; Guskov, A.
The Resolution in X-ray Crystallography and Single-Particle Cryogenic Electron Microscopy. *Crystals* **2020**, *10*, 580.
https://doi.org/10.3390/cryst10070580

**AMA Style**

Dubach VRA, Guskov A.
The Resolution in X-ray Crystallography and Single-Particle Cryogenic Electron Microscopy. *Crystals*. 2020; 10(7):580.
https://doi.org/10.3390/cryst10070580

**Chicago/Turabian Style**

Dubach, Victor R.A., and Albert Guskov.
2020. "The Resolution in X-ray Crystallography and Single-Particle Cryogenic Electron Microscopy" *Crystals* 10, no. 7: 580.
https://doi.org/10.3390/cryst10070580