title: HermiteFit: fast-fitting atomic structures into a low-resolution density map using three-dimensional orthogonal Hermite functions.
abstract: HermiteFit, a novel algorithm for fitting a protein structure into a low-resolution electron-density map, is presented. The algorithm accelerates the rotation of the Fourier image of the electron density by using three-dimensional orthogonal Hermite functions. As part of the new method, an algorithm for the rotation of the density in the Hermite basis and an algorithm for the conversion of the expansion coefficients into the Fourier basis are presented. HermiteFit was implemented using the cross-correlation or the Laplacian-filtered cross-correlation as the fitting criterion. It is demonstrated that in the Hermite basis the Laplacian filter has a particularly simple form. To assess the quality of density encoding in the Hermite basis, an analytical way of computing the crystallographic R factor is presented. Finally, the algorithm is validated using two examples and its efficiency is compared with two widely used fitting methods, ADP_EM and colores from the Situs package. HermiteFit will be made available at http://nano-d.inrialpes.fr/software/HermiteFit or upon request from the authors.
authors.affiliation: Institute of Complex Systems (ICS-6), Forschungszentrum Jülich, Jülich, Germany.
authors.forename: Georgy
authors.initials: G
authors.lastname: Derevyanko
authors.affiliation: Université Grenoble Alpes, LJK, F-38000 Grenoble, France.
authors.forename: Sergei
authors.initials: S
authors.lastname: Grudinin
mesh_terms: D000465:Algorithms; D018834:Chaperonin 60 / Q000737:chemistry; D020916:Conotoxins / Q000737:chemistry; D003461:Crystallography; D011487:Protein Conformation
chemical_list: D018834:Chaperonin 60; D020916:Conotoxins
keywords: Cryo-EM; Hermite orthogonal polynomials; HermiteFit; density fitting; fast Fourier transform; spherical harmonics