# Tutorial: Orientation Diagnostics

Using the new Orientation Diagnostics job to assess preferred orientation with titled and untilted HA Trimer data

Orientation Diagnostics, a new job in CryoSPARC v4.4+, can help diagnose the presence of preferred orientation. In this tutorial, we’ll use the untilted and tilted **Influenza Hemagglutinin Trimer (HA Timer)** data (Tan et al. (2017); deposited in EMPIAR entries 10096 and 10097 respectively) to help elucidate the types of diagnostics one should expect to see with and without preferred orientation.

## HA Trimer Case Study

### Untilted dataset (EMPIAR 10096)

To begin, we’ll process the deposited 447 movies via a typical CryoSPARC processing workflow of Patch Motion, Patch CTF, Blob picking / curation, 2D classification, 2D class selection, and Ab-Initio reconstruction to arrive at a set of ~82 000 curated particles and an initial map. Refining this initial volume with homogeneous refinement with C3 symmetry yields a structure with a reported GSFSC resolution of ~3.1 Å (see figure below). By inspecting the volume visually, however, we see that the map lacks the features one would expect at this resolution.

What’s more, the vertical streaks in the map are clear indications that the poor quality may be due to the presence of preferred orientation within the particles. To assess further, we’ll take the refined volume, mask, and particles and connect it to an Orientation Diagnostics job, and set the symmetry parameter to C3.

#### Orientation Diagnostics

Once complete, orientation diagnostics will generate a number of visualizations. One natural starting point to investigate preferred orientation is to look at the conical FSC summary plot. This plot generalizes the GSFSC curves shown above to incorporate the notion of directional resolution. Note that this plot shows very similar information to the figure generated via the legacy 3DFSC job (Tan et al., 2017).

A conical FSC (cFSC) is a Fourier Shell Correlation of two half maps with a conical mask of a specified half angle and axis in Fourier space. To assess directional signal content, the Orientation Diagnostics job computes a set of cFSC curves with conical axes sampled along a uniform spherical distribution. The figure below illustrates this process for four cFSC cones. In blue, the cFSC summary plot visualizes the mean, minimum, maximum, and standard deviation value of the correlations at each spatial frequency. In green, we also overlay a histogram of 0.143 crossings, which correspond to the spread of resolution values over direction.

Although they can both be represented via azimuth and elevation angles, the conical axis of a cFSC should be carefully distinguished from viewing direction. Concretely, low cFSC values along a particular conical axis do not imply that more views are necessary from that direction. This is due to the fact that a particle contributes Fourier information to a Fourier slice whose components are orthogonal to the viewing direction — this fact is elucidated further in the mathematical definition of the SCF within the Orientation Diagnostics job page, and in the SCF publications (Baldwin and Lyumkis, 2020, 2021).

When cFSC curves do not vary significantly as function of conical axis, the structure has a directional resolution that is constant across the viewing sphere. Here, this is clearly not the case. In the worst case, we see a cFSC resolution worse than 11 Å!

To quantify orientation bias, Orientation Diagnostics provides two metrics: the conical FSC Area Ratio, or cFAR, and the Sampling Compensation Factor, or SCF*. Both metrics range from 0 to 1, where 0 indicates a strong orientation bias, and 1 indicates no bias.

cFAR is the ratio of the minimum to maximum area under the cFSC curves summarized above. To account for the fact that higher frequencies correspond to a larger shell of Fourier components, the area is weighted at each spatial frequency by the surface area of the corresponding shell in Fourier space. In other words, we summarize each cFSC with a weighted area-under-curve number (’wAuC’), that quantifies the total ‘mass’ of the cFSC cone in units of correlation. wAuC as a function of conical axis on the viewing sphere is shown in the plot above. The ratio of the minimum to the maximum value in this plot defines the cFAR. For a mathematical definition of cFAR and wAuC, please see the Orientation Diagnostics job page.

In this dataset, cFAR is 0.02, which indicates severe orientation bias. In general, we find that a cFAR value of 0.5 serves as a reasonable threshold for the presence, or lack thereof, of preferred orientation.

To complement cFAR, we also report the Sampling Compensation Factor (Baldwin & Lyumkis, 2020, 2021). The SCF assesses the degree to which certain Fourier voxels are under sampled by the set of particle alignments. It is important to note that SCF does not consider the signal content within each particle; junk particles and true particles contribute equally to the final metric. An SCF value of 0.81 corresponds to the case where we have one ‘band’ of viewing directions. As a result, the original authors of SCF (Baldwin and Lyumkis, 2021) argue that values above 0.81 generally indicate good sampling (though not necessarily isotropic signal content).

### Tilted dataset (EMPIAR 10097)

To see the effect of stage tilting on this data, we turn to the data deposited in EMPIAR entry 10097. As before, we process the raw movies using a typical CryoSPARC workflow to arrive at an initial volume and approximately 58,000 curated particles. We then apply homogeneous refinement with C3 symmetry and arrive at the map depicted below. Note that the global GSFSC resolution is actually worse than the untilted data, but visually the map quality is significantly improved.

Applying the Orientation Diagnostics job (with C3 symmetry set) to the outputs of this refinement, we see much higher cFAR and SCF scores, much smaller cFSC curve variation and directional resolutions that only differ by approximately 0.5 Å. We see further that in many cases, the cFAR score is more sensitive to directional anisotropy than SCF* as it accounts for both insufficient sampling of the Fourier domain, and for anisotropic distributions of signal (e.g., junk optimized into certain regions).

## References

Tan et al. (2017), Addressing preferred specimen orientation in single-particle cryo-EM through tilting. *Nat Methods* 14(8), 793-796.

Baldwin, P. R., & Lyumkis, D. (2020). Non-uniformity of projection distributions attenuates resolution in Cryo-EM. *Progress in biophysics and molecular biology* 150, 160-183.

Baldwin, P. R., & Lyumkis, D. (2021). Tools for visualizing and analyzing Fourier space sampling in Cryo-EM. *Progress in biophysics and molecular biology* 160, 53-65.

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