Abstract
Three-dimensional (3D) structure determination by single-particle analysis of cryo-electron microscopy (cryo-EM) images requires ab initio 3D reconstruction of density volume(s) from 2D images (particles). This large-scale inverse problem requires the determination of many million degrees of freedom from extremely noisy experimental measurements. Here, we introduce a new approach to probabilistic multi-volume ab initio 3D reconstruction for simultaneous estimation of the relative particle 3D orientations and partitioning of the particles into groups with distinct structural states. To account for further structural variability within the discrete state groups, due to for example regional disorder, flexibility or partial occupancy of associating ligands, we introduce a new method for adaptive non-uniform regularization based on iterated conditional modes (ICMs). Our ICM regularization approach can be viewed as a spatially varying real-space prior that optimizes the connectivity of the reconstructed density map(s). Our method is designed to run in real time as the microscope collects the data, which puts significant constraints on algorithm scalability and flexibility with regard to how new particles are incorporated. We describe the probabilistic optimization and non-uniform regularization theory in detail. Finally, we provide numerous benchmarking examples, both on publicly available standard test data sets and on data sets acquired at our cryo-EM facility at the National Cancer Institute, National Institutes of Health. The implementation of our new multi-volume ab initio 3D reconstruction approach is part of the SIMPLE software suite, which is provided open source at https://github.com/hael/SIMPLE.