structural-biology/ai produced the result/Journal of Structural Biology 2012 · v2
Software works out protein shapes from electron microscope images using statistics
RELION builds three-dimensional maps of molecules from noisy electron microscope images. A statistical model learns the map, the signal and the noise from the data themselves, replacing settings a user would otherwise choose by hand.
spectrum · one line per step, placed by what the step does · bright lines used AI
RELION: Implementation of a Bayesian approach to cryo-EM structure determination
Journal of Structural Biology, 2012
doi:10.1016/j.jsb.2012.09.006 · record aix-00022 v2 · checked 2026-10-07
- AI was for
- Structure determination
- Model family
- Probabilistic graphical model
- Checked by
- Benchmark4 tested
- Code
- available
The finding the paper is about came from the AI.
What this research was about
Cryo-electron microscopy freezes copies of a molecule in ice and photographs them. Each copy lies at a random angle, and the images are extremely noisy, because a strong electron beam would destroy the sample. To recover the molecule's shape, software must work out which direction each particle was facing, then combine many thousands of views into one three-dimensional map. The angles are unknown, so the shape and the angles have to be found together: a better map improves the guessed angles, and better angles improve the map. Deciding how much to smooth the map along the way has traditionally depended on choices made by the person running the software.
The work describes an implementation that writes this problem as a single statistical target to be optimised. The map, the strength of the real signal at each level of detail and the strength of the noise are all estimated from the images rather than set by the user. The paper also describes faster ways to search over angles, a procedure that estimates how precisely each particle can be oriented, and a resolution check in which two maps are built from independent random halves of the data and compared. An automatic refinement protocol was run on four cryo-EM data sets, and the resulting maps were compared with published crystal structures.
Where AI came in
The statistical model is the instrument here, not a tool applied afterwards. The images are described in terms of hidden quantities nobody observed: each particle's orientation and which class it belongs to. For every particle the software works out how probable each sampled orientation is, given the current map and the estimated noise. Those probabilities then act as weights when the particle is added back into the map, and the same step updates the noise and signal estimates. The cycle repeats until it settles. No labelled examples are used; the model learns from the images alone, starting from a blurred initial map.
Several judgements a practitioner would normally make are folded into this fitting. The smoothing applied to the map comes from comparing the two half-data reconstructions rather than from a user's setting. The angular search is narrowed automatically: coarse probabilities pick out a small region worth examining in finer detail, and later rounds search only near the current best angles. The model is also queried directly, on a random subset of images, to estimate how accurately orientations can be assigned, and that estimate sets how finely angles are sampled next.
Written by AIxSci from the checked record below, to give context for readers outside the field. It is not part of the record.
The work
Technical · from the record
RELION refines cryo-EM single-particle reconstructions by optimising a single Bayesian target function, in which the 3D map together with the resolution-dependent signal and noise power spectra are estimated from the data by an expectation-maximization algorithm instead of being set by the user. The paper describes on-the-fly Fourier-space interpolation, an adaptive expectation-maximization scheme and local orientational searches, a procedure that uses the statistical model to estimate how accurately individual particles can be oriented, and a gold-standard Fourier shell correlation procedure in which two models are refined from independent random halves of the data. On a 5053-particle GroEL data set the adaptive expectation-maximization scheme gave speed-ups rising from 2-fold in the initial iterations to 24-fold in the final ones, with local angular searches giving an additional 8-fold acceleration during the last 10 iterations; the reconstruction from the gold-standard FSC run correlated up to 8.7 Angstrom with the symmetrized GroEL crystal structure, and that from the original MAP approach up to 10 Angstrom. An automated 3D auto-refine protocol was applied to four cryo-EM data sets and the resulting maps were compared with published crystal structures.
How AI was used
Particle images were normalised and windowed, and a low-pass filtered starting map supplied. The fitted model is a Bayesian latent-variable model of the images in Fourier space: for each particle the posterior probability of every discretely sampled orientation and class assignment is evaluated against the current 3D map and per-image noise estimates, and these probabilities then weight the back-projection that updates the map, the noise power spectrum and the signal power spectrum, with the cycle repeated until convergence. Orientations are sampled with HEALPix grids; an adaptive expectation-maximization scheme sorts the coarse-grid posterior values and re-evaluates only the sub-domain carrying a chosen fraction of the probability mass on a finer grid, and a truncated Gaussian prior on the hidden variables restricts later iterations to local angular searches. Two sets of model parameters are refined from independent random halves of the data, and the Fourier shell correlation between the two half-reconstructions is converted each iteration into the signal-power estimate used to filter the maps. The same statistical model is evaluated on a random subset of images, by perturbing Euler angles and translations until a posterior probability ratio criterion is met, to estimate orientational assignment accuracy and the contribution of each resolution shell to it; these estimates drive the automatic sampling-rate schedule of the 3D auto-refine protocol.
The shape of the work
Structural · the record, drawn
no AI
Assemble experimental and simulated particle data sets
Obtaining raw data, whether by measurement, download or retrieval.
an experimental cryo-EM data set of 5168 GroEL particles that is distributed as part of a workshop on the EMAN2 software packagewhere the paper describes this · verbatim
no AI
Normalise, window particles and filter starting model
Cleaning, filtering, normalising or labelling data already obtained.
all particles were normalized, 115 particles were discarded after initial sortingwhere the paper describes this · verbatim
AI
Evaluate posterior probabilities of orientation and class assignment
Running a trained model over new data to predict, classify or score. The AI stood in for conventional algorithm.
for every experimental image one has to evaluate the posterior probability Γikϕ(n) for all possible ϕ and kwhere the paper describes this · verbatim
AI
Update 3D map, noise and signal power spectra
Fitting model parameters, including fine-tuning an existing model. The AI stood in for expert judgement. Its result feeds back into an earlier step.
The model Θˆ, including all Vkl,σij2 and τkl2, that optimizes the posterior distribution P(Θ|X,Y) is called the maximum a posteriori (MAP) estimate.where the paper describes this · verbatim
no AI
Reduce orientation domain and schedule sampling rates
Iterative search over a space. Its result feeds back into an earlier step.
a sub-domain of all k and ϕ is selected that corresponds to the highest values of Γikϕ(n)where the paper describes this · verbatim
no AI
Gold-standard FSC between independent half-reconstructions
Testing outputs against ground truth. Its result feeds back into an earlier step.
At the end of every iteration, an FSC curve between the two independent reconstructions is calculatedwhere the paper describes this · verbatim
AI
Estimate orientational assignment accuracy from the model
Extracting understanding from model behaviour. The AI stood in for physical experiment.
one then modifies for each image each of the three Euler angles and two translations in small steps until RF/T<0.01where the paper describes this · verbatim
no AI
Assess reconstructions against crystal structures and phantoms
Testing outputs against ground truth.
Objective indications of reconstruction quality were obtained by FSC calculations against available crystal structureswhere the paper describes this · verbatim
What the record says
Technical · every part carries its own basis
+ in the paper~ our reading− not reported
How to read the quotations. A quotation shows where the paper describes something. It does not quote every value beside it: one passage locates a part of the work, and values without their own quotation are our reading of that passage.
The 3D reconstructions and resolution estimates the paper reports are produced by the MAP/expectation-maximization model itself; the model is the measurement instrument, not a downstream analysis of an independently obtained result.
the Bayesian approach iteratively learns most parameters of the statistical model from the data themselveswhere the paper describes this · verbatim
Objective indications of reconstruction quality were obtained by FSC calculations against available crystal structureswhere the paper describes this · verbatim
its open-source C++ code is available for download from http://www2.mrc-lmb.cam.ac.uk/relionwhere the paper describes this · verbatim
What this paper did not report
Technical · absence is published deliberately
- Trained model weightsWhether the trained model is available is not stated.
- DataWhether the data are available is not stated.
- Version of original MAP algorithm (Eq. 5 signal-power estimate), run as comparisonWhich version of the model was used is not stated.
About this article
Record aix-00022, version 2, checked by a person on 2026-10-07. The record describes the paper; it does not assess whether the paper's findings are right. The paper is published under CC-BY-3.0; quotations are at most 25 words. How we work · Report an error