Exploiting prior knowledge about biological macromolecules in cryo-EM structure determination

Abstract

Three-dimensional reconstruction of the electron scattering potential of biological macromolecules from electron cryo-microscopy (cryo-EM) projection images is an ill-posed problem. The most popular cryo-EM software solutions to date rely on a regularisation approach that is based on the prior assumption that the scattering potential varies smoothly over three-dimensional space. Although this approach has been hugely successful in recent years, the amount of prior knowledge it exploits compares unfavourably to the knowledge about biological structures that has been accumulated over decades of research in Structural Biology. Here, we present a regularisation framework for cryo-EM structure determination that exploits prior knowledge about biological structures through a convolutional neural network that is trained on known macromolecular structures. We insert this neural network into the iterative cryo-EM structure determination process through an approach that is inspired by Regularisation by Denoising. We show that the new regularisation approach yields better reconstructions than the current state-of-the-art for simulated data and discuss options to extend this work for application to experimental cryo-EM data.

New tools for automated cryo-EM single-particle analysis in RELION-4.0

“…Although not illustrated here, the VDAM algorithm can also be used for 3D classification and 3D auto-refinement. The latter applications may be particularly interesting in the context of injecting more prior knowledge about protein structures into the 3D reconstruction process [54], which will be a direction of future research.…”

A Molecular Prior Distribution for Bayesian Inference Based on Wilson Statistics

“…Instead, an operator mimics the regularizer's action in an iterative algorithm (e.g., the operator may act as a gradient descent step [14,13] or a proximal operator [20,5]). One example in cryo-EM, implemented in RELION, uses a denoising neural network to regularize expectation-maximization iterations [8]. Another notable example, implemented in the non-uniform refinement option of cryoSPARC, regularizes the iteration using a smoothing kernel whose parameters are set adaptively by cross-validation [12].…”

“…Implicit regularization schemes are more general than regularization using an explicit prior and can leverage powerful machine learning techniques that sometimes yield impressive results, e.g. [8,12] both report that the prior nearly halves the attained resolution on some test cases compared to the traditional prior. On the other hand, implicit regularization schemes lose most theoretical guarantees and statistical interpretation granted by Bayesian inference, sometimes leading to overfitting.…”

Density modification of cryo-EM maps

“…Recently, efforts have been made to further improve the accuracy of cryo-EM maps by the incorporation of prior knowledge about expected characteristics of these maps (Scheres, 2012;Kimanius et al, 2020;Terwilliger, Ludtke et al, 2020), an approach sometimes known as 'density modification'. This density-modification approach is closely related to the procedure used in macromolecular crystallography with the same name (Wang, 1985;Podjarny et al, 1996;Terwilliger, 2001a;Cowtan, 2010).…”