# Job: Orientation Diagnostics

A new job in CryoSPARC v4.4+ to diagnose the presence of preferred orientation

Description

Orientation Diagnostics is a job **(new in CryoSPARC v4.4, updated in v4.5)** that can aid in diagnosing the presence of preferred orientation. It includes and builds upon 3DFSC (Tan et al., 2017) and Fourier Sampling (Baldwin & Lyumkis, 2020).

By default, Orientation Diagnostics reports the conical FSC area ratio, or **cFAR **(v4.4+) and **Relative signal **(v4.5+). cFAR values below 0.5 generally indicate the presence of preferred orientation. cFAR accounts for both the viewing direction distribution and the signal content present within each particle by quantifying the variance of directional half-map Fourier correlations across the viewing sphere.

Relative signal captures FSC variation as a function of viewing direction. Regions of low relative signal can help identify missing views whose absence has a deleterious effect on map anisotropy.

If particles are supplied, the job will also report the Sampling Compensation Factor or **SCF*** (Baldwin & Lyumkis, 2020 — see below for more information about the significance of the star). SCF* values below 0.81 generally indicate the presence of preferred orientation. SCF* characterizes the sampling of Fourier shells by considering the viewing directions of all particles, without accounting for the signal content contained therein. A junk particle is given equal weight to a real particle.

We provide a short summary of the two metrics below. Please see the detailed definitions at the end of this job guide or the **Orientation Diagnostics tutorial** for more information.

#### cFAR and SCF* at a glance...

Range | Anisotropy Threshold | A function of… | |
---|---|---|---|

cFAR | [0, 1] higher is better | 0.5 | alignments & particle images |

SCF* | [0, 1] higher is better | 0.81 | alignments only |

cFAR | SCF* | Conclusion |
---|---|---|

↑ | ↑ | No orientation bias |

↑ | ↓ | ? (inconclusive, perhaps a pathological alignment distribution) |

↓ | ↑ | Anisotropy due to junk or other contaminants |

↓ | ↓ | Anisotropy due to junk and/or preferred orientation |

## Input

Volume or Volumes (all classes)

**New in v4.5:**If Volumes (all classes) are supplied from an upstream classification job, orientation diagnostics will be computed for each class volume. Note that this input is a volumes group input.

[Optional] Particles

If supplied, Fourier sampling (and its associated metric, SCF*) will be computed along with other per-particle diagnostics

[Optional] Mask

If supplied, half-maps will be masked prior to the computation of conical FSCs

**NOTE: **The cFSC plot produced during the final iteration of all refinement jobs uses the auto-tightened mask (mask_fsc_auto). This mask is a low-level output of all refinements and will be automatically used by Orientation Diagnostics:

when connecting a refined volume group as an input to Orientation Diagnostics

when using the 'Build Orientation Diagnostics' quick action

To use a custom mask, connect the input mask group. Note that if a custom mask is connected, the results may differ from the output of an upstream refinement.

**Common Parameters**

**Common Parameters**

*Conical FSC*

**Number of Directions**The conical FSC Area Ratio (cFAR) metric is relatively robust to number of conical axis directions. However, reducing this number can speed up the job for volumes with large box sizes. Increasing this number will create denser spherical plots.

*Sampling Compensation Factor*

**Symmetry**Particle viewing directions will be expanded to account for symmetry. This parameter should be set to the symmetry applied in the upstream refinement.

## Output

3DFSC volume

A volume of radial cFSC curves interpolated at each 3D voxel location

## Common Next Steps

Particle picking (to find missing views)

## More details about cFAR, SCF*, and Relative Signal

### cFSC Weighted Area-under-Curve (wAuC)

Given a conical Fourier shell correlation, $C_r (\hat{v})$, (where $r$ is the Fourier radius in wave number and $\hat{v}$ is the conical axis), we define the wAuC as

\begin{align}\text{wAuC}(\hat{v}) &\overset{\Delta}{=} \sum_r w_r C_r(\hat{v}) \\ &= \sum_r 4 \pi r^2 C_r(\hat{v}). \end{align}

In this weighted sum, the Fourier radius, $r$, ranges from the DC component to the radius at which $C_r(\hat{v})$ first crosses 0.143. Intuitively, for each Fourier radius $r$, the correlation between the half maps is multiplied by the surface area of the Fourier shell at $r$. The final result is proportional to the ‘mass’ of the cone in units of correlation.

### cFSC Area Ratio (cFAR)

We define the cFSC as the ratio of the minimum to the maximum $\text{wAuC}(\hat{v})$ over $\hat{v}$, or

$\text{cFAR} \overset{\Delta}{=} \frac{\min_{\hat{v}} \text{wAuC}(\hat{v})}{\max_{\hat{v}} \text{wAuC}(\hat{v})}.$

*Sampling Compensation Factor (SCF*)* (Baldwin and Lyumkis, 2020)

*Sampling Compensation Factor (SCF*)*(Baldwin and Lyumkis, 2020)

SCF* measures orientation bias in particle viewing directions — it allows CryoSPARC to convert a potentially difficult-to-parse viewing distribution into a single metric.

SCF* is computed from the statistics of ‘Fourier sampling’. Given a single particle, Fourier sampling is a binary function that indicates which ‘slab’ (i.e., a stack of slices) of Fourier voxels are affected when the particle is used in back-projection. Summing this sampling over many particles allows one to see if large chunks of Fourier space are poorly sampled or missing completely. The degree to which this occurs is measured by the Sampling Compensation Factor—a single number that quantifies the extent to which anisotropic viewing direction distributions attenuate the global FSC value.

### Relative Signal

The conical sections used to compute cFSCs cannot be easily mapped to viewing directions. To map FSC values to viewing directions, we use a toroidal section. We define a toroidal section to be the volume swept out by a cone, whose axis is orthogonal to the viewing direction, as it spins about the viewing direction. A toroidal section contains the Fourier components that would be populated by a particle with the same viewing direction, dilated to account for some error (or 'wiggle') in the pose estimate. We set the toroidal half-angle such that its volume is approximately equal to a cone of the same half-angle.

Using these toroidal sections, we compute a set of FSC curves. This set then allows to define a number, which we call relative signal, for each viewing direction. Relative signal is the wAuC of each curve, normalized with respect to the maximum within the set. The curve with the greatest wAuC in the set has a relative signal of 1.0, while a theoretical curve with a wAuC that is 0 at every frequency would have a relative signal of 0.0.

## Plot Explanations

### Summary of cFSC curves

**Updated in v4.5**. We summarize all cFSC curves in this plot, visualizing statistics as a function of spatial frequency rather than conical axis. As of v4.5, this plot also displays the cFAR score.

### Relative signal

**New in v4.5. **Relative signal visualized in a 2D azimuth-elevation chart (left), and in a 3D coloured scatter plot (right) with a low-pass-filtered volume embedded within. Low relative signal (i.e., darker colours) indicates a region with under-represented views.

### Relative signal in azimuth / elevation regions

**New in v4.5. **Relative signal within twelve regions of the viewing sphere, defined by different limits on azimuth and elevation. For each region, we show the projection of the structure from the central viewing direction, as well as the mean relative signal withing that region. Regions with low relative signal represent missing or underrepresented views in the data.

### 3DFSC volume

The 3DFSC volume (Tan et. al, 2017) is another way to summarize cFSC curves by storing them in a volume whose voxels are interpolated from cFSC values at the nearest conical axis. In this plot, we visualize the 3DFSC volume via central slices. The ‘sphericity’ of the volume (which is output by the job) is a proxy for anisotropy.

### Fourier Sampling

(Only generated if particles are connected). These plots visualize the Fourier sampling accumulated over a random subset of the particle viewing directions (default: 10000) — Fourier sampling is anti-podally symmetric (and hence only has ~ $2 \pi R^2$ bins) so we visualize only the $z>0$ hemisphere, following the original publication (Baldwin, P. R., & Lyumkis, D., 2020). N.B., the elevation / azimuth plot on the left should be visually similar to the Posterior Precision plot as posterior precision measures Fourier sampling modulated by the CTF.

### Particle scale factor vs. viewing direction

(Only generated if particles are connected and per-particle scales are not all 1.0). This figure visualizes the average particle scale for a set of viewing directions (uniformly sampled on the viewing sphere).

## 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.

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