Estimating accuracy of particle translations and rotations

3D Refinement
1

Hi!
I was wondering if there is a way to find out the estimated global accuracy of particle angles and offsets in both the Homogenous and NU refinement procedures. I cannot attribute anything printed out in the log to such parameters.

These parameters arise through signal-to-noise considerations in RELION and are used, along with FSCs, to determine the convergence of a 3D refinement. I am not sure if cryoSPARC relies on the same estimates for convergence.

Cheers,
Stefan

2

I’ve done some experimenting, and might have a “poor man’s solution”:

  1. After obtaining a NU Refine 2.81Å reconstruction, I exported the particles into RELION using csparc2star.py.
  2. I performed a round of 3D auto-refine with: initial angular sampling = 0.1, initial offset range and step = 0.001, local searches for auto samplig = 0.1. Basically, to prevent RELION from moving particles. I used the cryosparc output map and model, low pass filtered to 2.81Å as reference input.
  3. After 1 round of refinement, I got this output:

For optics_group 1, there are 298317 particles on the scratch disk.
Estimating initial noise spectra
3.78/3.77 min …~(,,">
Auto-refine: Iteration= 1
Auto-refine: Resolution= 2.81166 (no gain for 0 iter)
Auto-refine: Changes in angles= 999 degrees; and in offsets= 999 Angstroms (no gain for 0 iter)
CurrentResolution= 2.81166 Angstroms, which requires orientationSampling of at least 1.60714 degrees for a particle of diameter 200 Angstroms
Oversampling= 0 NrHiddenVariableSamplingPoints= 1305
OrientationalSampling= 0.234375 NrOrientations= 145
TranslationalSampling= 0.002592 NrTranslations= 9
=============================
Oversampling= 1 NrHiddenVariableSamplingPoints= 41760
OrientationalSampling= 0.117188 NrOrientations= 1160
TranslationalSampling= 0.001296 NrTranslations= 36
=============================
Expectation iteration 1
2.22/2.22 hrs …~(,,">
Averaging half-reconstructions up to 40 Angstrom resolution to prevent diverging orientations …
Note that only for higher resolutions the FSC-values are according to the gold-standard!
Calculating gold-standard FSC …
Maximization …
4.95/4.95 min …~(,,">
Auto-refine: Iteration= 2
Auto-refine: Resolution= 2.81166 (no gain for 1 iter)
Auto-refine: Changes in angles= 0.969269 degrees; and in offsets= 0.373906 Angstroms (no gain for 0 iter)
Estimating accuracies in the orientational assignment …
6/ 6 sec …~(,,">
Auto-refine: Estimated accuracy angles= 1.962 degrees; offsets= 0.688176 Angstroms
Auto-refine: Angular step= 0.117188 degrees; local searches= true
Auto-refine: Offset search range= 0.001296 Angstroms; offset step= 0.001296 Angstroms
CurrentResolution= 2.81166 Angstroms, which requires orientationSampling of at least 1.60714 degrees for a particle of diameter 200 Angstroms

Does the approach make sense? It does not seem like angles or offsets got refined. However, RELION refinements for this dataset typically converge with angular accuracy < 1 deg and offset accuracy less than < 0.5Å.

Am I even asking the right question? Or is it expected that different algorithms have different error accuracy refinement targets (especially NU), and therefore it is expected for RELION to “think” NU refined angles/offsets as less accurate?