PF2 fit: Polar Fast Fourier Matched Alignment of Atomistic Structures with 3D Electron Microscopy Maps

Abstract

There continue to be increasing occurrences of both atomistic structure models in the PDB (possibly reconstructed from X-ray diffraction or NMR data), and 3D reconstructed cryo-electron microscopy (3D EM) maps (albeit at coarser resolution) of the same or homologous molecule or molecular assembly, deposited in the EMDB. To obtain the best possible structural model of the molecule at the best achievable resolution, and without any missing gaps, one typically aligns (match and fits) the atomistic structure model with the 3D EM map. We discuss a new algorithm and generalized framework, named PF2 fit (Polar Fast Fourier Fitting) for the best possible structural alignment of atomistic structures with 3D EM. While PF2 fit enables only a rigid, six dimensional (6D) alignment method, it augments prior work on 6D X-ray structure and 3D EM alignment in multiple ways: Scoring. PF2 fit includes a new scoring scheme that, in addition to rewarding overlaps between the volumes occupied by the atomistic structure and 3D EM map, rewards overlaps between the volumes complementary to them. We quantitatively demonstrate how this new complementary scoring scheme improves upon existing approaches. PF2 fit also includes two scoring functions, the non-uniform exterior penalty and the skeleton-secondary structure score, and implements the scattering potential score as an alternative to traditional Gaussian blurring. Search. PF2 fit utilizes a fast polar Fourier search scheme, whose main advantage is the ability to search over uniformly and adaptively sampled subsets of the space of rigid-body motions. PF2 fit also implements a new reranking search and scoring methodology that considerably improves alignment metrics in results obtained from the initial search.

Defining the limits and reliability of rigid-body fitting in cryo-EM maps using multi-scale image pyramids

“…Further optimization of the fit can then be tried using the Fit in Map routines in UCSF Chimera. Many advances have been made in both sensitivity and speed of cross-correlation based rigid body fitting (Bettadapura et al, 2015;Chacón and Wriggers, 2002;Derevyanko and Grudinin, 2014;Farabella et al, 2015;Garzón et al, 2007;Hoang et al, 2013;Hrabe et al, 2012;Roseman, 2000;Volkmann and Hanein, 1999;Volkmann, 2009;Wu et al, 2003). Recently, we introduced the coreweighted local cross-correlation scores in our rigid-body fitting package PowerFit .…”

EMNUSS: a deep learning framework for secondary structure annotation in cryo-EM maps

“…Protein secondary structure information, which can be extracted from maps, is demonstrated to be beneficial for both template-based fitting and de novo modeling [ 26 ]. PF2fit, which is a rigid fitting method, matches the detected secondary structures of the density map with the secondary structure units of the atomic model [ 28 ]. In 2017, Dou et al [ 29 ] developed a flexible fitting method guided by the correspondence between the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\alpha $\end{document} -helices in the cryo-EM map and those in the model.…”

Advances in Structure Modeling Methods for Cryo-Electron Microscopy Maps

“…Also, surface-based scores such as normal vector score (NVA), which computes the difference in angle between the normal vectors of EM maps, and the chamfer distance score (CDAgdt), which calculates the average distance between closest surface points of two EM maps [81,82]. Another possible score is skeleton-secondary structure score that depends on matching the skeleton of detected secondary structures of the density map with the secondary structure units of the atomic model [35].…”

“…In general, rigid-body fitting methods search for the best placement of an atomic model in a density map. Search algorithms that have been used for rigid fitting include Fast Fourier transform-based (FFT) [14,32,35], grid-threading Monte Carlo (GTMC) [16], spherical harmonic-based search [20], and geometric hashing [27]. FFT is a fast search scheme that accelerates the 3-D translational search [14].…”

“…HermiteFit speeds up the rotation step in the FFT by representing densities as three-dimensional orthogonal Hermite functions and performing rotation in the Hermite space [32]. Fast polar Fourier search is a variation of FFT, which is based on non-uniform SO(3) Fourier Transforms [35]. Its principal advantage is the ability to search efficiently and uniformly over a set of samples of the conformational space.…”