Versatility of Approximating Single-Particle Electron Microscopy Density Maps Using Pseudoatoms and Approximation-Accuracy Control

Abstract

Three-dimensional Gaussian functions have been shown useful in representing electron microscopy (EM) density maps for studying macromolecular structure and dynamics. Methods that require setting a desired number of Gaussian functions or a maximum number of iterations may result in suboptimal representations of the structure. An alternative is to set a desired error of approximation of the given EM map and then optimize the number of Gaussian functions to achieve this approximation error. In this article, we review different applications of such an approach that uses spherical Gaussian functions of fixed standard deviation, referred to as pseudoatoms. Some of these applications use EM-map normal mode analysis (NMA) with elastic network model (ENM) (applications such as predicting conformational changes of macromolecular complexes or exploring actual conformational changes by normal-mode-based analysis of experimental data) while some other do not use NMA (denoising of EM density maps). In applications based on NMA and ENM, the advantage of using pseudoatoms in EM-map coarse-grain models is that the ENM springs are easily assigned among neighboring grains thanks to their spherical shape and uniformed size. EM-map denoising based on the map coarse-graining was so far only shown using pseudoatoms as grains.

The first single particle analysis Map Challenge: A summary of the assessments

“…SJ analyzed the unfiltered maps by visual inspection in Chimera, as well as by quantitative evaluation of pairwise similarities among the maps and among Gaussian-based map approximations (Jonic and Sorzano, 2016). The pairwise similarities are based on the Pearson correlation coefficient (CC).…”

A methodology using Gaussian-based density map approximation to assess sets of cryo-electron microscopy density maps

“…The Gaussian-based map representations were obtained with the method proposed in (Jonic and Sorzano, 2016a). Several different applications of this method have already been shown, including normal-mode-based deformation modeling for continuous conformational variability analysis and EM map denoising (Jin et al, 2014;Jonic and Sorzano, 2016b;Sanchez Sorzano et al, 2016). Though this method can be used to fully denoise the maps , it should be noted that this method was here used with a different goal.…”

“…Smaller values of and result in larger numbers of Gaussian functions and vice versa. Their values (usual range: voxel and ) should be chosen to suit the target application of the method, as explained in (Jonic and Sorzano, 2016a;Jonic and Sorzano, 2016b). Small enough values of the minimum distance between Gaussian functions d min , the initial seeds parameter, and the grow seeds parameter will only affect the speed of convergence of the algorithm but not the maximum achievable accuracy of the density map approximation (Jonic and Sorzano, 2016a).…”

Gaussian mixture model decomposition of multivariate signals

“…In this work we are concerned with the related problem of approximating a non-negative but otherwise arbitrary signal by a sparse linear combination of potentially anisotropic Gaussians. Our interest in this problem stems mainly from its applications in transmission electron microscopy (TEM), where it is common to express the reconstructed 3D image as a linear combination of Gaussians [5][6][7][8]. Consequently, because the projection of a Gaussian is a Gaussian, TEM projection data can be treated as 2D images made up of linear combinations of Gaussians [14].…”