# Cryo-EM Map Anisotropy Can Be Attenuated by Map Post-Processing and a New Method for Its Estimation

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## Abstract

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## 1. Introduction

## 2. Results and Discussion

#### 2.1. Common Map Anisotropy Metrics Are Affected by the Shape of the Specimen

#### 2.2. New Anisotropy Method Results

#### 2.3. Nonlinear Post-Processing Methods Can Attenuate Map Anisotropy

## 3. Materials and Methods

#### 3.1. Datasets

#### 3.1.1. Artificial Anisotropy

#### 3.1.2. Experimental Maps

#### 3.2. FSC-3D Calculation

#### 3.3. New Anisotropy Method

#### 3.4. Map Post-Processing

#### 3.5. Map Visualisation

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**3D-FSC apparent anisotropy induced by the macromolecule shape. Each row shows an experimental cryo-EM map EMD-8910 (

**a**), EMD-29350 (

**b**) and EMD-13202 (

**c**) and corresponding slices of Fourier amplitudes along $z=0,y=0\mathrm{and}x=0$ Fourier planes. The black circles indicate a resolution of 4.0 Å. The colorbar represents Fourier amplitude values at Fourier slices.

**Figure 2.**Results obtained for the simulation of the soluble portion of the small influenza hemagglutinin (HA) trimer by the 3D-FSC [6] (

**a**), the efficiency [3] (

**b**), MonoDir [8] (

**c**–

**e**) and the approach proposed in this manuscript (

**f**). Note that in (

**f**) the colorbar represents the noise power of the noise masked map along different directions given by the elevation and azimuth angles and normalized by the value at the direction providing maximum noise power. Contrary to what it is expected for a perfectly isotropic map, the 3D-FSC per-cone standard deviation (

**a**) is not zero, the histogram (

**b**) of resolution per angle is not narrow and the different planes of local-directional resolution computed with MonoDir are not at the same values. On the contrary, our approach shows almost constant values near 0.95. Consequently, all the studied methods except our proposed approach consider that the resolution of the ideal simulated volume is anisotropic.

**Figure 3.**Results obtained by the proposed method for experimental maps obtained from untilted (

**a**) and 40° tilted single particles of the influenza hemagglutinin (HA) trimer (

**b**). The particle angular distribution as obtained by Relion is shown in (

**c**) as counts per orientation or as the logarithm of the counts in (

**e**), as reflected in the colorbar. The same plots are shown in (

**d**,

**f**) for the tilted case. The colorbars in (

**a**,

**b**) represent the noise power of the noise masked map along different directions given by the elevation and azimuth angles and normalized by the value at the direction providing maximum noise power. The elevations and azimuths are given in radians. The region selected in the black box in (

**a**,

**b**) corresponds to the whole plots in (

**c**–

**f**). The results obtained by the 3D FSC method are shown in (

**g**,

**h**) for the untilted and 40° tilted cases, respectively.

**Figure 4.**Results obtained for reconstructions of the β-galactosidase complex (EMPIAR-10061), consisting of a standard reconstruction of the β-galactosidase at 3.15 Å and two reconstructions in which anisotropy was artificially induced by removing 95% of the particles assigned to tilt angles above 80° or 70° (side views). The first row shows the results obtained by the proposed method. The black rectangles in the figures correspond to the regions shown in the 2D particle angular distributions displayed in the second (particle count) and third (logarithm of the particle count) rows. The colorbars represent the noise power of the noise masked map along different directions given by the elevation and azimuth angles and normalized by the value at the direction providing maximum noise power. The region selected in the black box in the top row corresponds to the whole plots in the other rows.

**Figure 5.**Per-cone FSC (map to model) standard deviation (

**top**) and mean (

**bottom**) calculated with 3D-FSC for three different versions of the β-galactosidase complex: reconstructed with all particles (

**left**) and reconstructed with 95% of the particles with tilt angle >80° (

**middle**) and >70° (

**right**) removed. The blue line represents the reconstructed map, whereas the brown, purple, red, orange and green lines represent the maps obtained when DeepEMhancer [21], LocScale2 [22,23], LocSpiral [24], Phenix [15] and LocalDeblur [25] are employed on the reconstructed map. The FSC global resolution is displayed as a dotted vertical line. See Supplementary Figure S3 for an alternative representation of the data.

**Figure 6.**Per-cone FSC standard deviation (

**top**) and mean (

**bottom**) calculated with 3D-FSC for the EMD-20794. The blue line represents the reconstructed map, whereas the brown, purple, red, orange and green lines represent the maps obtained when DeepEMhancer [21], LocScale2 [22,23], LocSpiral [24], Phenix [15] and LocalDeblur [25] are employed on the reconstructed map. The FSC global resolution is displayed as a dotted vertical line. See Supplementary Figure S4 for an alternative representation of the data.

**Figure 7.**Reconstructed map (grey) for the EMD-20794 and the results of applying DeepEMhancer (yellow, [21]), LocSpiral (cyan, [24]), LocalDeblur (purple, [25]), LocScale2 (pink, [22,23]) and Phenix anisotropic sharpening (salmon, [15]) to the reconstructed map. The atomic model 6UJA is shown for reference. Three different locations viewed from two different orientations are displayed. They correspond to chain A residues 10, 71 and 118, and are displayed. Contour levels were manually selected to maximize the level of side chain inclusion.

**Figure 8.**Per-cone FSC (map to model) standard deviation (

**top**) and mean (

**bottom**) calculated with 3D-FSC for two different versions of the influenza hemagglutinin trimer (HA); reconstructed with untilted micrographs (severe anisotropy problems) and reconstructed with micrographs tilted 40°. The blue line represents the reconstructed map, whereas the brown, purple, red, orange and green lines represent the standard deviation for the maps obtained when DeepEMhancer [21], LocScale2 [22,23], LocSpiral [24], Phenix [15] and LocalDeblur [25] are employed on the reconstructed map. The FSC global resolution is displayed as a dotted vertical line. See Supplementary Figure S5 for an alternative representation of the data.

**Figure 9.**Influenza hemagglutinin trimer (HA) map reconstructed from tilted micrographs (grey), and the results of applying DeepEMhancer (yellow, [21]), LocSpiral (cyan, [24]), LocalDeblur (purple, [25]), LocScale2 (pink, [22,23]) and Phenix anisotropic sharpening (salmon, [15]) to the reconstructed map. The atomic model 7VDF is shown as reference. Three different locations viewed from two different orientations are displayed. They correspond to chain B residues 245 and 431, and chain C 454 are displayed. Contour levels were manually selected to maximize the level of side chain inclusion.

**Figure 10.**Workflow of the proposed anisotropy estimation method. The real space reconstructed 3D map (

**a**) is filtered with a 3D spherical soft mask to filter out the macromolecular signal leaving only the noise (

**b**). The filtered map is then transformed to the Fourier space and its 3D power map is calculated computing the square modulus of each Fourier component (

**d**). Then, for each central slice of the power map the average noise power is calculated between given r

_{min}and r

_{max}resolutions (

**c**). The central slice at orientation j is used to fill up the value of the noise power orientation distribution at this orientation j. As a result, the noise power directional distribution at pixel j is obtained (

**e**). The values in this distribution are normalized as shown in Equation (2). High values are depicted in yellow, and low values in blue. Note that in (

**d**) we show the logarithm of the power map for visualization purposes.

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## Share and Cite

**MDPI and ACS Style**

Sanchez-Garcia, R.; Gaullier, G.; Cuadra-Troncoso, J.M.; Vargas, J.
Cryo-EM Map Anisotropy Can Be Attenuated by Map Post-Processing and a New Method for Its Estimation. *Int. J. Mol. Sci.* **2024**, *25*, 3959.
https://doi.org/10.3390/ijms25073959

**AMA Style**

Sanchez-Garcia R, Gaullier G, Cuadra-Troncoso JM, Vargas J.
Cryo-EM Map Anisotropy Can Be Attenuated by Map Post-Processing and a New Method for Its Estimation. *International Journal of Molecular Sciences*. 2024; 25(7):3959.
https://doi.org/10.3390/ijms25073959

**Chicago/Turabian Style**

Sanchez-Garcia, Ruben, Guillaume Gaullier, Jose Manuel Cuadra-Troncoso, and Javier Vargas.
2024. "Cryo-EM Map Anisotropy Can Be Attenuated by Map Post-Processing and a New Method for Its Estimation" *International Journal of Molecular Sciences* 25, no. 7: 3959.
https://doi.org/10.3390/ijms25073959