What if one would have many noisy 2D projections of assumedly identical 3D objects in unknown orientations, and one woul

Regularised likelihood optimisation for electron cryo-microscopy Sjors Scheres MRC Laboratory of Molecular Biology What if one would have many noisy 2D projections of assumedly identical 3D objects in unknown orientations, and one would want to know that 3D structure? A statistical approach...

Single-particle reconstruction
An intuitive explanation

Anexample“proteincomplex” Jan

Experimental setup e- sample detector

Electron microscopy imaging e- We collect data in 2D, but we want 3D info! 3D object Inverse problem 2D projection

Furtherinconveniences Embeddedrandomly in ice: manyunknownorientations Incomplete problem

Further inconveniences Microscopeimperfections: artefacts Limitedelectrondose: largeamounts of noise Ill-posed problem

Projection matching Initial 3D model

maxCC with all projections compare Projection matching

3D reconstruction

Iterative refinement

Single-particle reconstruction
A statistical view

So... We collect 2D projections (not 3D), which are extremely noisy have unknown relative orientations Incomplete, ill-posed inverse problem

A statistical approach Handle incompleteness by marginalisation Handle ill-posedness by regularisation Regularised likelihood optimisation

The forward model i Independent Gaussian noisewith standard deviations sisi unknown 2D Fourier Transform of observed image i=1,...,N (all independent) Contrast Transfer Function imaging artefacts: may be zero! known 3D Fourier Transformof underlying objectV unknown Operator that takes 2D slice out of 3D Fourier Transformin orientation ffi unknown

Marginal likelihood Treat orientations f as hidden variables 2D Fourier transforms components j=1,...,J

Prior: smoothness All 3D Fourier componentsVl are independent, Gaussian distributed with zero mean and (unknown) standard deviations tl

Bayes’ law

Expectation maximization Wiener filter for 3D reconstruction Estimate resolution-dependent power of noise from the data Estimate resolution-dependent power of signal from the data “Fuzzy” orientationalassignments

So what? … Probability-weighted angular assignments Don’t take discrete decision if the noise impedes this Better convergence behaviour Optimal weighting in alignment No arbitrary sharpening and/or filtering of raw data Don’t adjust the data to your program: adjust the program to your data! Optimal 3D filter on map (i.e. best 3D SSNR) Also for anisostropic CTFs, uneven orientational distributions, etc No arbitrary parameters, e.g. Wiener constant, or filter shapes! Learns parameters from the data Objective, no user-expertise required Excellent maps: easy& objective!

REgularisedLIkelihoodOptimisatioN http://www2.mrc-lmb.cam.ac.uk/relion

A recent example
Yeast ribosome structure

An 80S data set

Acknowledgements HepB data Tony Crowther Greg McMullan Ribosomes XiaochenBai Israel Sanchez Fernandez Greg McMullan VenkiRamakrishnan Computing Jake Grimmett Toby Darling Some code in RELION Xmipp (Carazo et al.) Bsoft (Heymann) Discussions LMB colleagues Funding

What if one would have many noisy 2D projections of assumedly identical 3D objects in unknown orientations, and one woul