Is there any possibility to add symmetry relaxation as a feature of local refinement (perhaps as a modification of the gaussian priors - allowing global search, but with tight gaussian priors around each sym-related orientation)? This would be a great help for pseudosymmetric complexes! I know it has been discussed before, but the last discussion seems to have been some time ago.

If so, perhaps it would also be possible to make it “tolerant” of symmetry expanded particle sets, by avoiding superimposing symmetry-expanded duplicates during the symmetry relaxation search?

Thanks for the request . We have planned investigation of how the refinement jobs handle pseudosymmetric complexes refined in C1, and will look at how well symmetry relaxation helps resolve pseudosymmetry. It would be planned to add this as a feature to homogeneous refinement jobs and local refinement too. Due to the branch-and-bound procedure, there’s a chance that with nearly symmetric complexes refined in C1, particles get misaligned to a symmetry-related position of the correct pose. Thus, with “symmetry relaxation search”, there would be an additional step after branch-and-bound to explicitly check all symmetry-related positions to the found pose (within some deltas around the previously optimal pose), and then use that pose for reconstruction. This is essentially what Daniel Asarnow described in the last paragraph of a previous post – symmetry relaxation without expanded particles.

The second case – making local refinement w/ symmetry relaxation tolerant of symmetry expanded particles – is a bit more complicated. I assume there’s two subcases, both of which I have questions about:

where all of the N symmetry-related particles from the expanded set are to contribute to the reconstruction after the “symmetry relaxation search”. (Under some constraint that duplicates aren’t superimposed. But is there a reason why the “symmetry relaxation search” is even needed here, since the particles are already expanded and hence already allowed to align independently of each other, centred around each symmetry related pose?)

where only one symmetry-related particle from the expanded set is to contribute to the reconstruction (the best scoring one, after branch-and-bound alignment. Since particles already cover all of the N symmetry-related poses, no symmetry relaxation search needed. Though, isn’t this just a more computationally expensive version of symmetry relaxation without expanded particles?).

The other complication is due to how particles are processed. Particles are portioned into mini-batches and are aligned via BnB and then immediately accumulated into the reconstruction at their best alignment. If we made this procedure tolerant to symmetry expanded sets, it means that a single mini-batch would have to hold all symmetry-related particles from each of the original particles, so that their alignments or log-probabilities can be compared immediately, in the first and second subcases, respectively. It’s technically possible, but I wonder if there’s a modification of the simpler first case that could result in basically the same behaviour without these complications.

Thinking about it a bit more, I think you are probably right - the combination of symm expansion & relaxation is probably not required (I was having a bit of a brain malfunction, sorry!). Because if a particle is truly asymmetric (e.g. a small asymmetric binding partner on a Cn framework), there is only one correct orientation - sym expansion will not help here.

In terms of what you describe for sym relaxation, this sounds good! I think it will probably be most useful as a feature of local refinement. What you want to do is first refine with the apparent higher symmetry enforced (e.g. C4), then do a local search around symmetry related orientations in C1.

Having this available in local refinement would allow one to first do a Cn (or Dn, etc) global refinement, and then perform a local “symmetry relaxed refinement” with a mask around the region where one suspects the symmetry is broken - allowing the asymmetric binding partner which is smeared around the different possible orientations in the framework to be resolved (thinking of a case like TRPV5 & CaM, for example).

For my TRPV5:CaM structure I used cisTEM to do a fine global search on Phi only, which actually works very well (also for some Spike:Ab datasets) but is expensive compared to symmetry relaxation. I haven’t tried that TRPV5 dataset again, I guess that would be a good test. The problem I’ve encountered with relaxation so far is that it seems like the symmetry usually doesn’t get broken and all the particles keep contributing a lot at all the related positions. I bet it wouldn’t be such an issue without marginalization, though, as then they’ll only contribute to one at the end.

If pseudosymmetry is implemented in local refinement, maybe there should be marginalization only around the best of the symmetry related poses?

Also, if it’s implemented into a global / BnB step, it seems like then the exact symmetry related positions can just be added to the list of poses to check even if they would otherwise be excluded? Maybe that is only a semantic difference from how @mmclean suggested doing it afterwards.

Fine global search on Phi would only work for apparent Cn symmetry though, right? Not for octahedral, icosahedral, etc?

Our experience with symm relaxation (as implemented in relion) is that it works superbly for some cases, and fails to resolve the issue for others, but definitely a useful option to have available!

If it is implemented in global (homogeneous/NU) refine, it would also be useful to add to heterogenous refinement perhaps - might be useful for classification in cases where the sample contains a mixture of truly symmetric and pseudosymmetric particles.

No, the initial reference was as refined in the higher symmetry, but in successful cases it pretty rapidly converged on the correct (asymmetric) solution

Hi @mmclean, great to hear you are considering implementing symmetry relaxation feature. As others commented already, this makes sense for local alignments only (using a refinement with symmetry as initial poses) and without symmetry expansion.

@Juha disagree, it would be good to keep the precise symmetry related positions in the list of poses to check during a global refinement as well, which is pretty much the same thing as symmetry relaxation. Lower case symmetries (“c3”) in Frealign could be used with either local or global searches.

@DanielAsarnow First to check that we use the terms the same way: By local alignment combined with symmetry relaxation, I mean local alignment around each symmetry related view direction (pose). To me global alignment means that all view directions are tested, not just the symmetry related directions (and their local neighborhoods). Then related to your comment (which is interesting!): In what refinement scenarios would it be beneficial to have the exact symmetry related directions plus all other possible directions in the list of poses?

I think (correct me if wrong!) Dan is referring to the fact that in the branch and bound algorithm (which is used in global refinement in cryoSPARC), poses that have already been excluded by the “bounds” for a given particle will not be searched.

In C1 refinement of a pseudosymmetric entity that can mean that each particle can end up trapped in a local minimum (one of the pseudosymmetry-related poses) which may not necessarily correspond to the true pose, and in these cases searching the pseudosymmetry related poses regardless of the current bounds may be worthwhile.

In the absence of symmetry relaxation in cryosparc, we have been performing 3D classification without alignments on symmetry expanded particle sets after refinement in the highest apparent symmetry point group, to separate out rotational states, and then rotating each state to match one reference state before combining using Volume Alignment Tools (applying the appropriate rotation to the particle set) and proceeding to local refinement in C1. This works quite well, but would still be great to have symm relaxation!

Yeah, exactly, as I think mentioned above there is no guarantee all other symmetry related poses are included in the sampling points, and cryoSPARC doesn’t limit the search space during symmetric refinements either.

Thanks for the explanation @olibclarke, that makes sense. Thanks for highlighting the case of pseudosymmetry and limitations of cryosparc in this case. I hadn’t appreciated that the issue was this severe, but even more reason to take this into account in cryosparc. Another use case is two components with different symmetries. One refines first using the symmetry of the larger structure, and then relaxes the symmetry to resolve the smaller structure. If the orientation of the smaller structure is locked relative to the larger one, one needs to search only the symmetry mates. If the orientation is not strictly locked, one needs to run a local refinement around each pose. We refer to this as “multi-modal priors” in our --sym_relax implementation in RELION.

Yes exactly! Right now the kind of clunky way we deal with this (within Csparc) is to run classification without alignments (with many classes, more than the number of symmetry mates) in order to split it into all the different orientations with respect to the higher symmetry framework, and then manually realign each subset using Volume Alignment Tools before local refinement in C1. This is awkward and imperfect though, and we would greatly benefit from a proper implementation of symmetry relaxation.

I wonder if this would be worth adding as an option for 3D classification in cryoSPARC - it would be more computationally expensive than classification without any search, but not much more - just searching N-1 additional discrete orientations for a Cn (pseudo)symmetric entity? Although I guess this is more or less equivalent to symmetry expansion followed by classification without alignments, or am I missing something there?

(EDIT: Thinking about it more - symmetry relaxed search should be cheaper in terms of number of classes. Let’s say an asymmetric component is bound to a C12 symmetric framework, where the consensus refinement is performed in C12. Let’s also assume it is bound in a manner that contacts multiple subunits, so one can’t simply mask out a single subunit. In this case for a symm relaxed search, there will effectively be two classes - bound and unbound - as particles can change orientations. In the case of symm expansion followed by classification without alignment, there are effectively 13 classes - all the possible orientations with respect to the C12 framework, plus an empty class. This adds to the cost of having to process a 12-fold larger dataset due to symmetry expansion.)

By the way, is the hADV-26 dataset on EMPIAR somewhere, or do you know of a similar dataset that is? It would be really useful as a dataset for testing different approaches to dealing with pseudo & local symmetry