Abstract
A new method to estimate the trajectories of particle motion and the amount of cumulative beam damage in electron cryo-microscopy (cryo-EM) single-particle analysis is presented. The motion within the sample is modelled through the use of Gaussian process regression. This allows a prior likelihood that favours spatially and temporally smooth motion to be associated with each hypothetical set of particle trajectories without imposing hard constraints. This formulation enables the a posteriori likelihood of a set of particle trajectories to be expressed as a product of that prior likelihood and an observation likelihood given by the data, and this a posteriori likelihood to then be maximized. Since the smoothness prior requires three parameters that describe the statistics of the observed motion, an efficient stochastic method to estimate these parameters is also proposed. Finally, a practical algorithm is proposed that estimates the average amount of cumulative radiation damage as a function of radiation dose and spatial frequency, and then fits relative B factors to that damage in a robust way. The method is evaluated on three publicly available data sets, and its usefulness is illustrated by comparison with state-of-the-art methods and previously published results. The new method has been implemented as Bayesian polishing in RELION-3, where it replaces the existing particle-polishing method, as it outperforms the latter in all tests conducted.
Highlights
Recent advances in electron-detector technology have allowed cryo-EM single-particle analysis to uncover the structures of many biological macromolecules to resolutions sufficient for de novo atomic modelling
The primary impediment to highresolution reconstruction is the radiation damage that is inflicted on the molecules when they are exposed to an electron beam
We have presented Bayesian polishing, a new method for the estimation of particle motion and of the corresponding perframe relative B factors
Summary
Recent advances in electron-detector technology have allowed cryo-EM single-particle analysis to uncover the structures of many biological macromolecules to resolutions sufficient for de novo atomic modelling. Because the new detectors allow multi-frame movies to be captured during exposure of the sample, it is possible to estimate and correct for beam-induced motion This requires sufficient signal in the individual movie frames, which is challenging as each frame only contains a fraction of the total electron dose, resulting in even lower signal-to-noise ratios. The earliest approaches to beam-induced motion correction were performed in FREALIGN (Brilot et al, 2012; Campbell et al, 2012) and RELION (Bai et al, 2013), and estimated particle positions and orientations independently in each movie frame and for each particle Both programs averaged the signal over multiple adjacent frames to boost the low signal-to-noise ratios. We will refer to this property as the spatial smoothness of motion
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