Identifying Components in 3D Density Maps of Protein Nanomachines by Multi-scale Segmentation

Segmentation of density maps obtained using cryo-electron microscopy (cryo-EM) is a challenging task, and is typically accomplished by time-intensive interactive methods. The goal of segmentation is to identify the regions inside the density map that correspond to individual components. We present a multi-scale segmentation method for accomplishing this task that requires very little user interaction. The method uses the concept of scale space, which is created by convolution of the input density map with a Gaussian filter. The latter process smoothes the density map. The standard deviation of the Gaussian filter is varied, with smaller values corresponding to finer scales and larger values to coarser scales. Each of the maps at different scales is segmented using the watershed method, which is very efficient, completely automatic, and does not require the specification of seed points. Some detail is lost in the smoothing process. A sharpening process reintroduces detail into the segmentation at the coarsest scale by using the segmentations at the finer scales. We apply the method to simulated density maps, where the exact segmentation (or ground truth) is known, and rigorously evaluate the accuracy of the resulting segmentations

Quantitative analysis of cryo-EM density map segmentation by watershed and scale-space filtering, and fitting of structures by alignment to regions

Cryo-electron microscopy produces 3D density maps of molecular machines, which consist of various molecular components such as proteins and RNA. Segmentation of individual components in such maps is a challenging task, and is mostly accomplished interactively. We present an approach based on the immersive watershed method and grouping of the resulting regions using progressively smoothed maps. The method requires only three parameters: the segmentation threshold, a smoothing step size, and the number of smoothing steps. We first apply the method to maps generated from molecular structures and use a quantitative metric to measure the segmentation accuracy. The method does not attain perfect accuracy, however it produces single or small groups of regions that roughly match individual proteins or subunits. We also present two methods for fitting of structures into density maps, based on aligning the structures with single regions or small groups of regions. The first method aligns centers and principal axes, whereas the second aligns centers and then rotates the structure to find the best fit. We describe both interactive and automated ways of using these two methods. Finally, we show segmentation and fitting results for several experimentally-obtained density maps.National Institutes of Health (U.S.) (Grant PN2EY016525)National Institutes of Health (U.S.) (Grant R01GM079429)National Institutes of Health (U.S.) (Grant P41RR02250)National Science Foundation (U.S.) (IIS-0705644

Lattice Transformations and Subunit Conformational Changes in Phage Capsid Maturation

A general feature of the pathways for the assembly of double-stranded DNA phages and viruses is the assembly of coat and scaffolding subunits into a precursor shell or procapsid, followed by packaging of the genomic DNA into the shell. Coupled to this DNA packaging process is the loss of the scaffolding subunits and expansion and re-organization of the procapsid lattice to the lattice of the mature virus. Such lattice transitions have also been observed with adenoviruses and herpesviruses. In re-organizing into the mature capsid lattice, each subunit of the precursor lattice must change its conformation, or its relationship with its neighbours, or both. We briefly review here recent structural data for phages P22 and HK97, and describe the motions and conformational changes associated with this lattice transition. Possible functions of such constrained transformations within the virus life-cycle are discussed

Abstract Bubble Mesh: Automated Triangular Meshing of Non-Manifold Geometry by Sphere Packing

This paper presents a new computational method for fully automated triangular mesh generation, consistently applicable to wire-frame, surface, solid, and nonmanifold geometries. The method, called bubble rrzeshing, is based on the observation that a pattern of tightly packed spheres mimics a Voronoi diagram, from which a set of well-shaped Delaunay triangles and tetrahedral can be created by connecting the centers of the spheres. Given a domain geometry and a node-spacing function, spheres are packed on geometric entities, namely, vertices, edges, faces, and volumes, in ascending order of dimension. Once the domain is filled with spheres, mesh nodes are placed at the centers of these spheres and are then connected by constrained Delaunay triangulation and tet rahedrizat ion. To obtain a closely packed configuration of spheres, the authors devised a technique for physically based mesh relaxation with adaptive population control, The process of mesh relaxation significantly reduces the number of ill-shaped triangles and tetrahedral.

Bubble Mesh: Automated Triangular Meshing of Non-Manifold Geometry by Sphere Packing

This paper presents a new computational method for fully automated triangular mesh generation, consistently applicable to wire-frame, surface, solid, and nonmanifold geometries. The method, called bubble meshing, is based on the observation that a pattern of tightly packed spheres mimics a Voronoi diagram, from which a set of well-shaped Delaunay triangles and tetrahedra can be created by connecting the centers of the spheres. Given a domain geometry and a node-spacing function, spheres are packed on geometric entities, namely, vertices, edges, faces, and volumes, in ascending order of dimension. Once the domain is filled with spheres, mesh nodes are placed at the centers of these spheres and are then connected by constrained Delaunay triangulation and tetrahedrization. To obtain a closely packed configuration of spheres, the authors devised a technique for physically based mesh relaxation with adaptive population control. The process of mesh relaxation significantly reduces the number of ill-shaped triangles and tetrahedra