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 regularization 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 that it exploits compares unfavorably with the knowledge about biological structures that has been accumulated over decades of research in structural biology. Here, a regularization framework for cryo-EM structure determination is presented that exploits prior knowledge about biological structures through a convolutional neural network that is trained on known macromolecular structures. This neural network is inserted into the iterative cryo-EM structure-determination process through an approach that is inspired by regularization by denoising. It is shown that the new regularization approach yields better reconstructions than the current state of the art for simulated data, and options to extend this work for application to experimental cryo-EM data are discussed.
Highlights
In cryo-EM single-particle analysis, the three-dimensional structure of biological macromolecules is reconstructed from two-dimensional projection images of multiple copies of these molecules in different relative orientations
We show in Appendix A that the mimimum mean-square estimator (MMSE) estimator f : CM ! CM under Gaussian noise with covariance À2 approximates the gradient of the log-prior according to rlogP(x) ’ f(x) À À2(x)
Synthetic training data were generated from 543 atomic structures that were downloaded from the Protein Data Bank (PDB; Berman et al, 2000)
Summary
In cryo-EM single-particle analysis, the three-dimensional structure of biological macromolecules is reconstructed from two-dimensional projection images of multiple copies of these molecules in different relative orientations. In response to these issues, Reehorst and Schniter proposed a new framework, score-matching by denoising (SMD), which showed that RED achieves its performance by approximating the ‘score’ or the gradient of the prior distribution This approach circumvents the requirement for an explicit prior expression and further does away with the abovementioned conditions on the denoiser function (Reehorst & Schniter, 2018). It serves as a general proof of principle that learned priors can improve cryo-EM reconstruction Future research directions, such as the exploration of alternative optimization algorithms and different strategies to design and train the neural networks, are discussed
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