Detection of secondary and supersecondary structures of proteins from cryo-electron microscopy

Abstract

Recent advances in three-dimensional electron microscopy (3D EM) have enabled the quantitative visualization of the structural building blocks of proteins at improved resolutions. We provide algorithms to detect the secondary structures (α-helices and β-sheets) from proteins for which the volumetric maps are reconstructed at 6–10Å resolution. Additionally, we show that when the resolution is coarser than 10Å, some of the super-secondary structures can be detected from 3D EM maps. For both these algorithms, we employ tools from computational geometry and differential topology, specifically the computation of stable/unstable manifolds of certain critical points of the distance function induced by the molecular surface. Our results connect mathematically well-defined constructions with bio-chemically induced structures observed in proteins.

Macromolecular structure modeling from 3D EM using VolRover 2.0

“…The simplest way to validate results from secondary structure detection is to count the number of helices and sheets detected. If the crystal structure of the molecule is available, one can count false positives and false negatives, as in Jiang et al,29 Kong et al,30 and Bajaj et al36…”

“…The volume‐based secondary structure elements identification ( VBSSI )2 detects secondary structure elements from an input 3D maps. Boundary‐based secondary structural elements identification ( BBSSI )36, 37 detects secondary structures from a suitable surface extracted from the 3D map. Evolution‐based secondary structure elements identification ( EBSSI ),38 evolves an initial surface obtained from the density map in the normal direction to obtain the skeleton.…”

Cryo-electron microscopy as a functional instrument for systems biology, structural analysis and experimental manipulations with living cells. A comprehensive analytical review of the current works

“…To date the structural methods of cryo-electron microscopy have been involved in characterization of a number of supramolecular structures and complexes: from the well-studied fibrillar collagen structures [92], intraflagillar transport complexes of protozoa [91], tubulin in microtubules [125] and some other fibrillar and filamentous structures with the relative molecular weight of about gigadalton [101] up to such subtle elements of biological machinery as ribosomal complexes (e.g. those involved in cotranslational folding and translocation [62]), elements of secondary [95] and supersecondary protein structure [7], as well as the conformational effects in molecular mechanisms of their folding [25] and the mechanisms of expression in the complexes of encoding semantides [109] (in terms of Zuckerkandl and Pauling [133]). In addition to the conventional cryo-electron microscopy, modern structural analysis, particularly the determination of the protein secondary structure, requires the use of its precision 3D analogcryo-electron tomography [9], which enables structure visualization at a wide scale / range of sizes, including the all-atom mapping [88] and a nanoscale cytophysiological ultrastructure analysis (so-called nanoimaging [63].…”

High-quality topological structure extraction of volumetric data on C2-continuous framework

“…Most of the time the purpose of computing the MS complex is to extract a summary skeleton of the volumetric data. The skeleton can be visualized directly to reflect the topology (Beketayev et al, 2011;Correa et al, 2011), or provides information to enhance the volume rendering result via improving the transfer function (Takahashi et al, 2004). The geometric features of the skeleton are also used for further analysis, for example, the structures of protein molecules can be learnt from the MS complex skeleton (Bajaj et al, 2012).…”