RELION: implementation of a Bayesian approach to cryo-EM structure determination

Abstract

RELION, for REgularized LIkelihood OptimizatioN, is an open-source computer program for the refinement of macromolecular structures by single-particle analysis of electron cryo-microscopy (cryo-EM) data. Whereas alternative approaches often rely on user expertise for the tuning of parameters, RELION uses a Bayesian approach to infer parameters of a statistical model from the data. This paper describes developments that reduce the computational costs of the underlying maximum a posteriori (MAP) algorithm, as well as statistical considerations that yield new insights into the accuracy with which the relative orientations of individual particles may be determined. A so-called gold-standard Fourier shell correlation (FSC) procedure to prevent overfitting is also described. The resulting implementation yields high-quality reconstructions and reliable resolution estimates with minimal user intervention and at acceptable computational costs.

Fig.1

Accuracy of the projection/reconstruction cycle. (A) Central slices through the ribosome phantom and reconstructions made from 5000 noiseless projections in RELION and in SPIDER using commands BP3F or BP3G. All four images are on the same grey-scale. (B) As in A, but showing reconstructions made from 5000 noisy projections. (C) FSC curves between the phantom and reconstructions obtained from the noiseless projections in RELION (black), SPIDER BP3G (grey) and SPIDER BP3F (dashed grey). (D) As in C, but for reconstructions from the noisy projections. Note the difference in the Y-axis range between C and D.

Fig.2

Assessment of angular accuracies. (A) Three simulated GroEL particles. (B) The experimental counterparts of the particles in A. (C) Distribution of the angular errors after a single iteration of refinement of a 10 Å low-pass filtered version of the phantom against the simulated data, using an angular sampling rate of $15°$ (bold black), $7.5°$ (bold grey), $3.7°$ (solid black), $1.8°$ (solid grey) or $0.9°$ (dashed black). (D) FSC with the phantom for the reconstructions from the refinements in C. (E) Experimentally determined angular accuracies based on tilt pair analysis (grey circles) compared to estimated angular accuracies based on the $R_{F/T}$ criterion (black crosses). The samples analyzed by tilt-pair analysis were rotavirus double-layered particle (50 MDa), chicken anemia virus (2.7 MDa), 70S ribosome (2.7 MDa), fatty acid synthase (2.6 MDa), pyruvate dehydrogenase (1.6 MDa), V and F-type ATPase (0.6 MDa), DNA-dependent protein kinase (0.47 MDa) and β-galactosidase (0.45 MDa). The specimens analyzed in RELION were rotavirus recoated particle (60 MDa), hepatitis B capsid (4 MDa), 70S ribosome (2.7 MDa), GroEL (0.8 MDa) and β-galactosidase (0.45 MDa). (F) Contribution of the different resolution shells to the summation inside the exponential in Eq. (8) for projections of the GroEL phantom with an angular distance of 2.7° between ${\varphi }^T$ and ${\varphi }^F$. (G) Angular error distributions after alignment of the simulated GroEL particles against the phantom map using an angular sampling of 1.8°. The maximum resolution used in the alignment was varied between 20 Å (solid black), 10 Å (solid grey) and Nyquist (dashed black).

Fig.3

Reported resolutions for every iteration of a refinement using the original MAP algorithm (black) and a refinement using gold-standard FSCs (grey) to estimate signal strength.

Fig.4

Results obtained with the 3D auto-refine procedure for four cryo-EM data sets: (A) β-galactosidase, (B) GroEL, (C) hepatitis B capsid, and (D) recoated rotavirus. On the left are shown the resolution-dependent contributions to the orientability, i.e. to the sum inside the exponential in Eq. (8). On the right are shown representative pieces of reconstructed density (transparent yellow) with the corresponding fitted crystal structures inside (red). All maps were sharpened prior to visualization, using a B-factor of −1500, −750, −850 and −275 Å² for the β-galactosidase, GroEL, hepatitis B capsid, and recoated rotavirus reconstructions, respectively.