Sasakthi S. Abeysinghe

Modeling protein structure at near atomic resolutions with Gorgon.

Electron cryo-microscopy (cryo-EM) has played an increasingly important role in elucidating the structure and function of macromolecular assemblies in near native solution conditions. Typically, however, only non-atomic resolution reconstructions have been obtained for these large complexes, necessitating computational tools for integrating and extracting structural details. With recent advances in cryo-EM, maps at near-atomic resolutions have been achieved for several macromolecular assemblies from which models have been manually constructed. In this work, we describe a new interactive modeling toolkit called Gorgon targeted at intermediate to near-atomic resolution density maps (10-3.5 Å), particularly from cryo-EM. Gorgons de novo modeling procedure couples sequence-based secondary structure prediction with feature detection and geometric modeling techniques to generate initial protein backbone models. Beyond model building, Gorgon is an extensible interactive visualization platform with a variety of computational tools for annotating a wide variety of 3D volumes. Examples from cryo-EM maps of Rotavirus and Rice Dwarf Virus are used to demonstrate its applicability to modeling protein structure.

Segmentation-free skeletonization of grayscale volumes for shape understanding

Medical imaging has produced a large number of volumetric images capturing biological structures in 3D. Computer-based understanding of these structures can often benefit from the knowledge of shape components, particularly rod-like and plate-like parts, in such volumes. Previously, skeletons have been a common tool for identifying these shape components in a solid object. However, obtaining skeletons of a grayscale volume poses new challenges due to the lack of a clear boundary between object and background. In this paper, we present a new skeletonization algorithm on grayscale volumes typical to medical imaging (e.g., MRI, CT and EM scans), for the purpose of identifying shape components. Our algorithm does not require an explicit segmentation of the volume into object and background, and is capable of producing skeletal curves and surfaces that lie centered at rod-shaped and plate-shaped parts in the grayscale volume. Our method is demonstrated on both synthetic and medical data.

Interactive skeletonization of intensity volumes

We present an interactive approach for identifying skeletons (i.e. centerlines) in intensity volumes, such as those produced by biomedical imaging. While skeletons are very useful for a range of image analysis tasks, it is extremely difficult to obtain skeletons with correct connectivity and shape from noisy inputs using automatic skeletonization methods. In this paper we explore how easy-to-supply user inputs, such as simple mouse clicking and scribbling, can guide the creation of satisfactory skeletons. Our contributions include formulating the task of drawing 3D centerlines given 2D user inputs as a constrained optimization problem, solving this problem on a discrete graph using a shortest-path algorithm, building a graphical interface for interactive skeletonization and testing it on a range of biomedical data.

Shape modeling and matching in identifying 3D protein structures

In this paper, we describe a novel geometric approach in the process of recovering 3D protein structures from scalar volumes. The input to our method is a sequence of @a-helices that make up a protein, and a low-resolution protein density volume where possible locations of @a-helices have been detected. Our task is to identify the correspondence between the two sets of helices, which will shed light on how the protein folds in space. The central theme of our approach is to cast the correspondence problem as that of shape matching between the 3D volume and the 1D sequence. We model both shapes as attributed relational graphs, and formulate a constrained inexact graph matching problem. To compute the matching, we developed an optimal algorithm based on the A*-search with several choices of heuristic functions. As demonstrated in a suite of synthetic and authentic inputs, the shape-modeling approach is capable of identifying helix correspondences in noise-abundant volumes at high accuracy with minimal or no user intervention.

Shape modeling and matching in identifying protein structure from low-resolution images

In this paper, we describe a novel, shape-modeling approach to recovering 3D protein structures from volumetric images. The input to our method is a sequence of α-helices that make up a protein, and a low-resolution volumetric image of the protein where possible locations of α-helices have been detected. Our task is to identify the correspondence between the two sets of helices, which will shed light on how the protein folds in space. The central theme of our approach is to cast the correspondence problem as that of shape matching between the 3D volume and the 1D sequence. We model both the shapes as attributed relational graphs, and formulate a constrained inexact graph matching problem. To compute the matching, we developed an optimal algorithm based on the A*-search with several choices of heuristic functions. As demonstrated in a suite of real protein data, the shape-modeling approach is capable of correctly identifying helix correspondences in noise-abundant volumes with minimal or no user intervention.

Polygonizing extremal surfaces with manifold guarantees

Extremal surfaces are a class of implicit surfaces that have been found useful in a variety of geometry reconstruction applications. Compared to iso-surfaces, extremal surfaces are particularly challenging to construct in part due to the presence of boundaries and the lack of a consistent orientation. We present a novel, grid-based algorithm for constructing polygonal approximations of extremal surfaces that may be open or unorientable. The algorithm is simple to implement and applicable to both uniform and adaptive grid structures. More importantly, the resulting discrete surface preserves the structural property of the extremal surface in a grid-independent manner. The algorithm is applied to extract ridge surfaces from intensity volumes and reconstruct surfaces from point sets with unoriented normals.

Semi-isometric Registration of Line Features for Flexible Fitting of Protein Structures

In this paper, we study a registration problem that is motivated by a practical biology problem – fitting protein structures to low‐re solution density maps. We consider registration between two sets of lines features (e.g., helices in the proteins) that have undergone not a single, but multiple isometric transformations (e.g., hinge‐motions). The problem is further complicated by the presence of symmetry in each set. We formulate the problem as a clique‐finding problem in a product graph, and propose a heuristic solution that includes a fast clique‐finding algorithm unique to the structure of this graph. When tested on a suite of real protein structures, the algorithm achieved high accuracy even for very large inputs containing hundreds of helices.

A geometric approach for deciphering protein structure from cryo-em volumes

Electron Cryo-Microscopy or cryo-EM is an area that has received much attention in the recent past. Compared to the traditional methods of X-Ray Crystallography and NMR Spectroscopy, cryo-EM can be used to image much larger complexes, in many different conformations, and under a wide range of biochemical conditions. This is because it does not require the complex to be crystallisable [74, 89]. However, cryo-EM reconstructions are limited to intermediate resolutions, with the state-of-the-art being 3.6A [116], where secondary structure elements can be visually identified but not individual amino acid residues. This lack of atomic level resolution creates new computational challenges for protein structure identification. In this dissertation, we present a suite of geometric algorithms to address several aspects of protein modeling using cryo-EM density maps. Specifically, we develop novel methods to capture the shape of density volumes as geometric skeletons. We then use these skeletons to find secondary structure elements (SSEs) of a given protein, to identify the correspondence between these SSEs and those predicted from the primary sequence, and to register high-resolution protein structures onto the density volume. In addition, we designed and developed Gorgon[1], an interactive molecular modeling system, that integrates the above methods with other interactive routines to generate reliable and accurate protein backbone models.

Surface reconstruction from point set using projection operator

Step 1: Lay a grid over the input point set. Step 3: Mark all grid edges with projection vectors at their two ends pointing in opposite directions. Approximate the intersection points between the surface and these edges based on the magnitudes of their projection vectors. Step 4: For each grid cell, calculate a grid center as the average of all intersection points. For each marked edge, connect the centers of its incident cells to make a piece of the surface.

Shape-preserving gray-scale skeletonization on 3D density maps

The medial surface that lies within a solid object, better known as the skeleton, is a local shape descriptor which is capable of capturing the shape and topological properties of a complex object. Due to its simple, yet informational nature, the skeleton shape descriptor has been widely used in graphics and computer vision for matching purposes.