Permutation testing of Fourier shell correlation for resolution estimation of cryo-EM maps

Maximilian Beckers,Carsten Sachse

doi:10.1016/j.jsb.2020.107579

Abstract

Fourier shell correlation (FSC) has become a standard quantity for resolution estimation in electron cryo-microscopy. However, the resolution determination step is still subjective and not fully automated as it involves a series of map interventions before FSC computation and includes the selection of a common threshold. Here, we apply the statistical methods of permutation testing and false discovery rate (FDR) control to the resolution-dependent correlation measure. The approach allows fully automated and mask-free resolution determination based on statistical thresholding of FSC curves. We demonstrate the applicability for global, local and directional resolution estimation and show that the developed criterion termed FDR-FSC gives realistic resolution estimates based on statistical significance while eliminating the need of any map manipulations. The algorithms are implemented in a user-friendly GUI based software tool termed SPoC (https://github.com/MaximilianBeckers/SPOC).

Highlights

Electron cryo-microscopy is becoming established as one of the methods of choice for macromolecular structure determination
In order to minimize subjectivity and increase robustness of Fourier shell correlation (FSC) computations, we developed a new approach of adaptive thresholding for resolution determination using a combination of permutation sampling and p-value correction by false discovery rate control
Resolution estimation using statistical thresholding of the FSC In order to circumvent principal and practical problems of thresholding FSC curves, we developed a procedure for identifying the highest resolution shell of interpretable signal based on parameter-free permutation sampling and subsequent statistical inference

Summary

Introduction

Electron cryo-microscopy (cryo-EM) is becoming established as one of the methods of choice for macromolecular structure determination. The technique has undergone major improvements in hardware and software, allowing to determine 3D structures routinely at close-to-atomic resolution (Kühlbrandt et al, 2014; Bartesaghi et al, 2015; Weis et al, 2019). These resolutions provide the landmark features for atomic model building and the resulting atomic coordinates rationalize biological mechanism and function. FSCs were originally introduced to the field of cryo-electron microscopy (Harauz & Van Heel, 1986) and more recently were applied to related fields such as super-resolution microscopy (Nieuwenhuizen et al, 2013; Banterle et al, 2013)

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