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# Job: Average Power Spectra

## Description

While processing helical samples, it is often helpful to examine the power spectra of particles associated with a given 2D class. These power spectra may be used to determine the helical symmetry present in the sample, via Fourier-space methods such as Fourier-Bessel analysis [1, 2]. External software tools such as HELIXPLORER [3] implement such methods, and may be used downstream on the results of this job.
This job takes the outputs of a Select 2D Classes job, and generates averaged power spectra for each desired class. Specifically, the power spectrum of each particle within the supplied 2D classes is computed. Then, the spectra from all particles belonging to a given 2D class are averaged together. Note that this is distinct from computing the power spectrum of a 2D class average, as in this job, the power spectra are computed before class-averaging takes place.

## Inputs

This job takes class averages and particles as inputs from a previous Select 2D Classes job. To avoid excessive computation, only the classes (and corresponding particles) for which averaged power spectra are desired should be passed to this job.

## Parameters

• Particle computational batch size: This controls the computational batch size of particles used during the reconstruction of power spectra. If memory errors or excessive swapping are encountered, this parameter can be lowered. Note that this parameter does not affect the results.
• Interpolation order: This controls the interpolation order of the spline interpolation used when averaging the particles’ power spectra together. By default, cubic spline interpolation is used.

## Output

• Averaged Power Spectra (including a mrc file containing the power spectra themselves, and a cs file containing their metadata, both located within the job directory)
• Note: Since these power spectra don’t currently have direct downstream uses within cryoSPARC, they are not registered as cryoSPARC outputs and hence are not visible within the UI. You can find the files in the job directory for further use.
• In the job directory, JX_power_spectra.cs will contain the metadata associated with each power spectrum: this includes the uid of the class average that generated it, as well as the sample spacing in
$Å^{-1}$
, the path to the mrc file, and the index of the power spectrum in the mrc file

## Example Images

Above is an example of an image from the stream log. This shows four 2D classes of the Tobacco Mosaic Virus (EMPIAR-10022), as well as their associated average power spectra. Note the power spectra images can be found in the job directory, and the 2D class images can be found in the job directory of the preceding 2D Classification job.

## Next Steps

One may use these averaged power spectra to initiate Fourier-space investigation of helical symmetry. A common software tool that aids in this procedure is HELIXPLORER. HELIXPLORER performs a grid search over helical symmetry parameters, and compares theoretically expected power spectra from an ideal helix to the provided power spectrum. For each symmetry parameter, a score is computed based on how closely the two power spectra agree, which is useful in obtaining a set of candidate symmetry parameters. More information on the theory and operation behind HELIXPLORER is available via their documentation. Note that the .mrc file output of this job may need to be converted to .jpg or .png format for use in other programs.

## References

[1] E. Egelman, "The iterative helical real space reconstruction method: Surmounting the problems posed by real polymers", Journal of Structural Biology, vol. 157, no. 1, pp. 83-94, 2007. Available: 10.1016/j.jsb.2006.05.015.
[2] L. Gambelli, M. Isupov and B. Daum, "Escaping the symmetry trap in helical reconstruction", Faraday Discussions, 2022. Available: 10.1039/d2fd00051b.
[3] L. Estrozi, A. Desfosses and G. Schoehn, "Helixplorer-1: Online Indexation Of Fibers And Helical Structures", Rico.ibs.fr, 2018. Available:http://rico.ibs.fr/helixplorer/help.htm.