Unsupervised cryo-EM data clustering through adaptively constrained K-means algorithm

In single-particle cryo-electron microscopy (cryo-EM), K-means clustering algorithm is widely used in unsupervised 2D classification of projection images of biological macromolecules. 3D ab initio reconstruction requires accurate unsupervised classification in order to separate molecular projections of distinct orientations. Due to background noise in single-particle images and uncertainty of molecular orientations, traditional K-means clustering algorithm may classify images into wrong classes and produce classes with a large variation in membership. Overcoming these limitations requires further development on clustering algorithms for cryo-EM data analysis. We propose a novel unsupervised data clustering method building upon the traditional K-means algorithm. By introducing an adaptive constraint term in the objective function, our algorithm not only avoids a large variation in class sizes but also produces more accurate data clustering. Applications of this approach to both simulated and experimental cryo-EM data demonstrate that our algorithm is a significantly improved alterative to the traditional K-means algorithm in single-particle cryo-EM analysis.Comment: 35 pages, 14 figure

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Nanoscale mosaicity revealed in peptide microcrystals by scanning electron nanodiffraction.

Changes in lattice structure across sub-regions of protein crystals are challenging to assess when relying on whole crystal measurements. Because of this difficulty, macromolecular structure determination from protein micro and nanocrystals requires assumptions of bulk crystallinity and domain block substructure. Here we map lattice structure across micron size areas of cryogenically preserved three-dimensional peptide crystals using a nano-focused electron beam. This approach produces diffraction from as few as 1500 molecules in a crystal, is sensitive to crystal thickness and three-dimensional lattice orientation. Real-space maps reconstructed from unsupervised classification of diffraction patterns across a crystal reveal regions of crystal order/disorder and three-dimensional lattice tilts on the sub-100nm scale. The nanoscale lattice reorientation observed in the micron-sized peptide crystal lattices studied here provides a direct view of their plasticity. Knowledge of these features facilitates an improved understanding of peptide assemblies that could aid in the determination of structures from nano- and microcrystals by single or serial crystal electron diffraction