# Job: Symmetry Expansion

Symmetry expansion.

## Description

Symmetry expansion enables the creation of a new particle dataset that duplicates the original particles' poses around a point group or helical symmetry. The primary use of symmetry expansion is in generating a new particle stack to be used by a Local Refinement or a 3D Variability job, with the goal of resolving symmetry-breaking features. The original particle dataset must have been aligned previously to a reference, meaning one of the global refinement jobs (e.g., Homogeneous or Non-uniform Refinement) must have previously been run with the input particle stack. Note that the volume and particles must be previously aligned to the conventional symmetry axes, which will be the case if the upstream refinement job had symmetry enforced (otherwise, this may be done via Volume Alignment Tools). The new particle dataset refers back to the image data of the original particle dataset, meaning no new images are written to disk by this job.

Note that reconstructions and refinements with global pose searches (e.g., Ab-Initio Reconstruction, and Homogeneous, Heterogeneous, Non-uniform, and Helical refinements) should *not* be run with the output dataset, as it will cause particle duplication and hence mis-estimation of Fourier Shell Correlation values. Only Local Refinement, 3D Variability, 3D Classification, and Flexible Refinement jobs should be used after a symmetry expansion.

Similarly, refinements, classifications, and variability analysis on symmetry expanded datasets should *generally* only be performed without symmetry enforced (i.e. with C1 symmetry), since the input particles have already been expanded. In advanced cases, such as local symmetry centered around a subunit of the structure, this rule may be excepted.

**Input**

**Input**

Particles (

`alignments3D`

are required).

**Parameters**

**Parameters**

`Symmetry group`

The desired point group symmetry string (e.g., D7, C4, T, O, I).

Helical symmetry parameters:

`Helical twist (degrees)`

: The helical twist in degrees, if helical symmetry is present in the particle stack.`Helical rise (Angstroms)`

: The helical rise in Angstroms, if helical symmetry is present in the particle stack.`Helical symmetry order (integer)`

: The helical symmetry order. This can be found at the end of the streamlog from the source Helical Refinement job, underneath "Final Helical Parameters".Note: for symmetry expansion with helical symmetry, particles must be from a source Helical Refinement job to ensure they are properly aligned with the helical symmetry axis.

Before running symmetry expansion with helical symmetry, it is strongly recommended to run the source Helical Refinement with the "Limit shifts along the helical axis" parameter activated. This ensures that the particles are aligned such that the shifts along the helical axis are minimized.

`Split output by symmetry operator`

Activate this parameter to split the expanded particles by the applied symmetry operator. If activated this will generate one particle stack for each applied symmetry operator. The number of output particle stacks will be equal to the symmetry order; for example, if a

`C6`

symmetry is specified, this will produce six output particle stacks.

**Output**

**Output**

Particles (expanded stack)

The size of the output particle stack will be equal to the size of the input particle stack, multiplied by the symmetry order. For example, for a particle stack of size 10,000 symmetry expanded with D7 symmetry, the output particle stack will have size 140,000.

## Common Next Steps

After symmetry expansion, the next steps usually involve running a 3D Variability Analysis job, or a Local Refinement job. Both can help resolve symmetry-breaking features, such as inter-subunit flexibility.

Local Refinement may help resolve features when there exists flexibility between symmetry-related subunits. The main difference between enforcing symmetry during Local Refinement, and using symmetry expansion with C1 local refinement instead, is that the former enforces perfect symmetry whereas the latter allows each expanded image to align independently. For example, enforcing C2 symmetry means the output map will have perfect 180º rotational symmetry, whereas with expanded particles, this is not guaranteed and it’s possible to improve resolution if there is flexibility. For more information about Local Refinements, refer to the guide page for a detailed job description and case study.

Using symmetry expanded particles with 3D Variability Analysis boosts the signal available to the algorithm, compared to using a non-expanded stack. For more information on 3D Variability Analysis, including this use case of the symmetry expansion job, refer to the 3D Variability Analysis tutorial (both part 1 and part 2). Homogeneous Reconstruction jobs (with specified symmetry of C1) can also be run with the symmetry expanded particle stack, to ensure that the symmetry expansion was successful.

In some cases, one may need to "undo" symmetry expansion, via taking the full expanded particle stack and selecting only one particle from each symmetry expanded copy. This may be helpful when the symmetry expanded particles have been used for downstream processing (e.g. 3D Variability Display in the `cluster`

or `intermediates`

modes) and a subset of the expanded particle stack has been selected for further processing. In this case, if one wants to subsequently perform a symmetry-enforced refinement, they will need to remove the extraneous symmetry-expanded copies. This may be done via the Remove Duplicate Particles job.

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