Single-particle electron cryomicroscopy (cryo-EM) is a powerful method for determining the structures of biological macromolecules. With automated microscopes, cryo-EM data can often be obtained in a few days. However, processing cryo-EM image data to reveal heterogeneity in the protein structure and to refine 3D maps to high resolution frequently becomes a severe bottleneck, requiring expert intervention, prior structural knowledge, and weeks of calculations on expensive computer clusters. Here we show that stochastic gradient descent (SGD) and branch-and-bound maximum likelihood optimization algorithms permit the major steps in cryo-EM structure determination to be performed in hours or minutes on an inexpensive desktop computer. Furthermore, SGD with Bayesian marginalization allows ab initio 3D classification, enabling automated analysis and discovery of unexpected structures without bias from a reference map. These algorithms are combined in a user-friendly computer program named cryoSPARC (http://www.cryosparc.com).

No abstract

ingle-particle cryo-EM has transformed rapidly into a mainstream technique in biological research 1. Cryo-EM images individual protein particles, rather than crystals and has therefore been particularly useful for structural studies of integral membrane proteins, which are difficult to crystallize 2. These molecules are critical for drug discovery, targeted by more than half of drugs today 3. Membrane proteins pose challenges in cryo-EM sample preparation, imaging and computational 3D reconstruction, as they are often of small size, appear in multiple conformations, have flexible subunits and are embedded in a detergent micelle or lipid nanodisc 2. These characteristics cause strong spatial variation in structural properties, such as rigidity and disorder, across the target molecule's 3D density. Traditional cryo-EM reconstruction algorithms, however, are based on the simplifying assumption of a uniform, rigid particle. We develop an algorithm that incorporates such domain knowledge in a principled way, improving 3D reconstruction quality and allowing single-particle cryo-EM to achieve higher-resolution structures of membrane proteins. This expands the range of proteins that can be effectively studied and is especially important for structure-based drug design 4,5. We begin by formulating a cross-validation (CV) regularization framework for single-particle cryo-EM refinement and use it to account for the spatial variability in resolution and disorder found in a typical molecular complex. The framework incorporates general domain knowledge about protein molecules, without specific knowledge of any particular molecule and critically, without need for manual user input. Through this framework we derive a new algorithm called non-uniform refinement, which automatically accounts for structural variability, while ensuring that key statistical properties for validation are maintained to mitigate the risk of over-fitting during 3D reconstruction. With a graphics processing unit-accelerated implementation of non-uniform refinement in the cryoSPARC software package 6 , we demonstrate improvements in resolution and map quality for a range of membrane proteins. We show results on a 48-kDa membrane protein in lipid nanodisc with a Fab bound, a 180-kDa membrane protein complex with a large detergent micelle and a 245-kDa sodium channel complex with flexible domains. Non-uniform refinement is reliable and automatic, requiring no change in parameters between datasets and is without reliance on handmade spatial masks or manual labels. Iterative refinement and regularization. In standard cryo-EM 3D structure determination 6-8 , a generative model describes the formation of two-dimensional (2D) electron microscope images from a target 3D protein density (Coulomb potential). According to the model, the target density is rotated, translated and projected along the direction of the electron beam. The 2D projection is modulated by a microscope contrast transfer function (CTF) and corrupted by additive noise. The goal of reconstruction ...

Single particle cryo-EM is a powerful method for studying proteins and other biological macromolecules. Many of these molecules comprise regions with varying structural properties including disorder, flexibility, and partial occupancy. These traits make computational 3D reconstruction from 2D images challenging. Detergent micelles and lipid nanodiscs, used to keep membrane proteins in solution, are common examples of locally disordered structures that can negatively affect existing iterative refinement algorithms which assume rigidity (or spatial uniformity). We introduce a cross-validation approach to derive non-uniform refinement, an algorithm that automatically regularizes 3D density maps during iterative refinement to account for spatial variability, yielding dramatically improved resolution and 3D map quality. We find that in common iterative refinement methods, regularization using spatially uniform filtering operations can simultaneously over-and under-regularize local regions of a 3D map. In contrast, non-uniform refinement removes noise in disordered regions while retaining signal useful for aligning particle images. Our results include state-of-the-art resolution 3D reconstructions of multiple membrane proteins with molecular weight as low as 90kDa. These results demonstrate that higher resolutions and improved 3D density map quality can be achieved even for small membrane proteins, an important use case for single particle cryo-EM, both in structural biology and drug discovery. Non-uniform refinement is implemented in the cryoSPARC software package and has already been used successfully in several notable structural studies.