Local refinement of a pentamer on the capsid after symmetry expansion

Hi all,

I applied symmetry expansion on my capsid particle (T=9) and did local refinement on the pentamer by applying a mask on the region. I was able to improve the local map on the pentamer from 4A(after NU-refinement with enforced icosahedral symmetry) to 3.3A resolution and there was clearly improvement on the map if you compare the maps before and after local refinement. I have done local refinement on the unexpanded particle stack but the map was only 5A. So clearly, the map was improved by doing symmetry expansion.

My question is:

  1. Do I need to extract the subvolume of the pentamer out and do the local refinement ? or simply a mask will do the job.
  2. what does symmetry expansion do? does it just rotate the original particles based on the symmetry ? for example, a capsid has 60 asymmetric units, after symmetry expansion, the original particle will rotate by asymmetric unit, which will end up with 60 rotations and 60-fold expanded particle stack?
  1. You don’t need to, but sometimes it can give better results, and will allow you to use a smaller box (faster refinements & classifications).

  2. Yes, that is exactly what it does - generates copies of each particle with symmetry operations applied.


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Hi Oli,
Thank you so much for the help.
I have another question: if I don’t extract the subvolume of the pentamer out, will I get redundant pentamer particles for my local refinement? if I simply put a mask on the pentamer, I will get one pentamer volume per particle. After expansion, for one original particle, I will get 60 pentamers, but there are 12 pentamers per capsid.
Also, if the capsid rotates based on the asymmetric unit, while a pentamer is not an asymmetric unit. how could a mask on one pentamer location will work for all the rotated expanded partcles.

I might have misunderstood some basics on symmetry expansion. I hope my questions are not confusing.

I saw a workflow in a published paper using Relion, they extracted all the pentamer subvolume and got rid of the redundant particles, but there were no workflow/details on how did they do it.

Hi Yumeng,

The intent of the symmetry expansion is to generate 59 copies (plus the original, for a total of 60) of each monomer of every pentamer (i.e. the asymmetric component of the pentamer). In principle, you could mask a single monomer from a pentamer in your icosahedral reconstruction and refine every individual monomer from every pentamer (i.e. 60 particles per capsid) from your entire dataset against it. It might be difficult to make a good mask for that, though.

It would be fine to mask the pentamer for refinement of your symmetry expanded-particles, in which case each of the monomers would already have a copy of every other monomer coincident with and ready to be refined against it. Just make sure not to apply additional (C5) symmetry averaging during the refinement. Alternatively, if you get the particles re-centered on the pentamer and re-extracted (allowing the smaller box that Oli mentioned), you could remove duplicates leaving only one particle per pentamer, then apply the C5 symmetry averaging as normal, consistent with the RELION paper you mentioned. This would, however, remove some pentamers when they are superimposed in the micrographs due to the orientation of the capsid, though it isn’t obvious to me if those are useful for refinement to begin with.

Hope this helps,


Thank you James, it makes sense. I got it now.