Marcus A. Brubaker

cryoSPARC: algorithms for rapid unsupervised cryo-EM structure determination

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).

Lost! Leveraging the Crowd for Probabilistic Visual Self-Localization

In this paper we propose an affordable solution to self-localization, which utilizes visual odometry and road maps as the only inputs. To this end, we present a probabilistic model as well as an efficient approximate inference algorithm, which is able to utilize distributed computation to meet the real-time requirements of autonomous systems. Because of the probabilistic nature of the model we are able to cope with uncertainty due to noisy visual odometry and inherent ambiguities in the map (e.g., in a Manhattan world). By exploiting freely available, community developed maps and visual odometry measurements, we are able to localize a vehicle up to 3m after only a few seconds of driving on maps which contain more than 2,150km of drivable roads.

Alignment of cryo-EM movies of individual particles by optimization of image translations.

Direct detector device (DDD) cameras have revolutionized single particle electron cryomicroscopy (cryo-EM). In addition to an improved camera detective quantum efficiency, acquisition of DDD movies allows for correction of movement of the specimen, due to both instabilities in the microscope specimen stage and electron beam-induced movement. Unlike specimen stage drift, beam-induced movement is not always homogeneous within an image. Local correlation in the trajectories of nearby particles suggests that beam-induced motion is due to deformation of the ice layer. Algorithms have already been described that can correct movement for large regions of frames and for >1 MDa protein particles. Another algorithm allows individual <1 MDa protein particle trajectories to be estimated, but requires rolling averages to be calculated from frames and fits linear trajectories for particles. Here we describe an algorithm that allows for individual <1 MDa particle images to be aligned without frame averaging or linear trajectories. The algorithm maximizes the overall correlation of the shifted frames with the sum of the shifted frames. The optimum in this single objective function is found efficiently by making use of analytically calculated derivatives of the function. To smooth estimates of particle trajectories, rapid changes in particle positions between frames are penalized in the objective function and weighted averaging of nearby trajectories ensures local correlation in trajectories. This individual particle motion correction, in combination with weighting of Fourier components to account for increasing radiation damage in later frames, can be used to improve 3-D maps from single particle cryo-EM.

Physics-Based Person Tracking Using the Anthropomorphic Walker

We introduce a physics-based model for 3D person tracking. Based on a biomechanical characterization of lower-body dynamics, the model captures important physical properties of bipedal locomotion such as balance and ground contact. The model generalizes naturally to variations in style due to changes in speed, step-length, and mass, and avoids common problems (such as footskate) that arise with existing trackers. The dynamics comprise a two degree-of-freedom representation of human locomotion with inelastic ground contact. A stochastic controller generates impulsive forces during the toe-off stage of walking, and spring-like forces between the legs. A higher-dimensional kinematic body model is conditioned on the underlying dynamics. The combined model is used to track walking people in video, including examples with turning, occlusion, and varying gait. We also report quantitative monocular and binocular tracking results with the HumanEva dataset.

The Kneed Walker for human pose tracking

The Kneed Walker is a physics-based model derived from a planar biomechanical characterization of human locomotion. By controlling torques at the knees, hips and torso, the model captures a full range of walking motions with foot contact and balance. Constraints are used to properly handle ground collisions and joint limits. A prior density over walking motions is based on dynamics that are optimized for efficient cyclic gaits over a wide range of natural human walking speeds and step lengths, on different slopes. The generative model used for monocular tracking comprises the Kneed Walker prior, a 3D kinematic model constrained to be consistent with the underlying dynamics, and a simple measurement model in terms of appearance and optical flow. The tracker is applied to people walking with varying speeds, on hills, and with occlusion.

Estimating contact dynamics

Motion and interaction with the environment are fundamentally intertwined. Few people-tracking algorithms exploit such interactions, and those that do assume that surface geometry and dynamics are given. This paper concerns the converse problem, i.e., the inference of contact and environment properties from motion. For 3D human motion, with a 12-segment articulated body model, we show how one can estimate the forces acting on the body in terms of internal forces (joint torques), gravity, and the parameters of a contact model (e.g., the geometry and dynamics of a spring-based model). This is tested on motion capture data and video-based tracking data, with walking, jogging, cartwheels, and jumping.

Physics-Based Person Tracking Using Simplified Lower-Body Dynamics

We introduce a physics-based model for 3D person tracking. Based on a biomechanical characterization of lower-body dynamics, the model captures important physical properties of bipedal locomotion such as balance and ground contact, generalizes naturally to variations in style due to changes in speed, step-length, and mass, and avoids common problems such as footskate that arise with existing trackers. The model dynamics comprises a two degree-of-freedom representation of human locomotion with inelastic ground contact. A stochastic controller generates impulsive forces during the toe-off stage of walking and spring-like forces between the legs. A higher-dimensional kinematic observation model is then conditioned on the underlying dynamics. We use the model for tracking walking people from video, including examples with turning, occlusion, and varying gait.

Description and comparison of algorithms for correcting anisotropic magnification in cryo-EM images

Single particle electron cryomicroscopy (cryo-EM) allows for structures of proteins and protein complexes to be determined from images of non-crystalline specimens. Cryo-EM data analysis requires electron microscope images of randomly oriented ice-embedded protein particles to be rotated and translated to allow for coherent averaging when calculating three-dimensional (3D) structures. Rotation of 2D images is usually done with the assumption that the magnification of the electron microscope is the same in all directions. However, due to electron optical aberrations, this condition is not met with some electron microscopes when used with the settings necessary for cryo-EM with a direct detector device (DDD) camera. Correction of images by linear interpolation in real space has allowed high-resolution structures to be calculated from cryo-EM images for symmetric particles. Here we describe and compare a simple real space method, a simple Fourier space method, and a somewhat more sophisticated Fourier space method to correct images for a measured anisotropy in magnification. Further, anisotropic magnification causes contrast transfer function (CTF) parameters estimated from image power spectra to have an apparent systematic astigmatism. To address this problem we develop an approach to adjust CTF parameters measured from distorted images so that they can be used with corrected images. The effect of anisotropic magnification on CTF parameters provides a simple way of detecting magnification anisotropy in cryo-EM datasets.

Map-Based Probabilistic Visual Self-Localization

Accurate and efficient self-localization is a critical problem for autonomous systems. This paper describes an affordable solution to vehicle self-localization which uses odometry computed from two video cameras and road maps as the sole inputs. The core of the method is a probabilistic model for which an efficient approximate inference algorithm is derived. The inference algorithm is able to utilize distributed computation in order to meet the real-time requirements of autonomous systems in some instances. Because of the probabilistic nature of the model the method is capable of coping with various sources of uncertainty including noise in the visual odometry and inherent ambiguities in the map (e.g., in a Manhattan world). By exploiting freely available, community developed maps and visual odometry measurements, the proposed method is able to localize a vehicle to 4 m on average after 52 seconds of driving on maps which contain more than 2,150 km of drivable roads.

TMaCS: A hybrid template matching and classification system for partially-automated particle selection

Selection of particle images from electron micrographs presents a bottleneck in determining the structures of macromolecular assemblies by single particle electron cryomicroscopy (cryo-EM). The problem is particularly important when an experimentalist wants to improve the resolution of a 3D map by increasing by tens or hundreds of thousands of images the size of the dataset used for calculating the map. Although several existing methods for automatic particle image selection work well for large protein complexes that produce high-contrast images, it is well known in the cryo-EM community that small complexes that give low-contrast images are often refractory to existing automated particle image selection schemes. Here we develop a method for partially-automated particle image selection when an initial 3D map of the protein under investigation is already available. Candidate particle images are selected from micrographs by template matching with template images derived from projections of the existing 3D map. The candidate particle images are then used to train a support vector machine, which classifies the candidates as particle images or non-particle images. In a final step in the analysis, the selected particle images are subjected to projection matching against the initial 3D map, with the correlation coefficient between the particle image and the best matching map projection used to assess the reliability of the particle image. We show that this approach is able to rapidly select particle images from micrographs of a rotary ATPase, a type of membrane protein complex involved in many aspects of biology.