Bayesian perspective for orientation determination in cryo-EM with application to structural heterogeneity analysis

Xu, S.; Balanov, A.; Singer, A.; Bendory, T.

doi:10.1107/S2059798326001415

Figure 5
Comparison of 3D structure reconstruction in cryo-ET subtomogram averaging using the MMSE and MLE rotation estimators. Iterative structure-reconstruction procedures with the MMSE estimator ( $[{\hat g}_{\rm {MMSE}}]$ ) and MLE estimator ( $[{\hat g}_{\rm {MLE}}]$ ) are defined in equations (31)

and (32)

, respectively. At high SNR levels, a low-resolution structure emerges due to finite grid sampling of the rotation group $[{\sf{SO}}(3)]$ , effectively acting as a low-pass filter. The 3D reconstruction using the MMSE estimator consistently outperforms the reconstruction using the MLE estimator. For high-SNR conditions (i.e. σ → 0), both estimators yield similar 3D structures, as expected from Proposition 2

. The SNR values used for the panels (from right to left) are 10⁻², 2 × 10⁻³, 7 × 10⁻⁴ and 2 × 10⁻⁴, with a volume size of 32 × 32 × 32. The boxes highlighted in purple resemble the true input structure (80S ribosome; Wong et al., 2014

), while the orange-highlighted boxes are more similar to the initial template (β-galactosidase; Bartesaghi et al., 2014

), illustrating the `Einstein from Noise' phenomenon. Notably, at very low SNRs, the `Einstein from Noise' effect is evident with the MLE estimator but not with the MMSE estimator.

STRUCTURAL
BIOLOGY

ISSN: 2059-7983

Volume 82| Part 4| April 2026| Pages 274-294

https://doi.org/10.1107/S2059798326001415

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