Biology subjects

Urzhumtsev, A. G.

Publications and source records attributed to Urzhumtsev, A. G..

6 recordsLinked to original sources

bioRxiv2026

Variable Resolution Maps (VRM) in CCTBX and Phenix: Accounting For Local Resolution In cryoEM

Calculation of density maps from atomic models is essential for structural studies using crystallography and electron cryo-microscopy (cryoEM). These maps serve various purposes, including atomic model building, refinement, visualization, and validation. However, accurately comparing model-calculated maps to experimental data poses challenges, particularly because the resolution of cryoEM experimental maps varies across the map. Traditional crystallography methods generate finite-resolution maps with uniform resolution throughout the unit cell volume, while most modern software in cryoEM employ Gaussian-like functions to generate these maps, which does not adequately account for atomic model parameters and resolution. Recent work by Urzhumtsev & Lunin (2022, IUCr Journal, 9, 728-734) introduces a novel method for computing atomic model maps that incorporate local resolution and can be expressed as analytically differentiable functions of all atomic parameters. This approach enhances the accuracy of matching atomic models to experimental maps. In this paper, we detail the implementation of this method in CCTBX and Phenix. SynopsisNew tools implemented in CCTBX and Phenix allow the calculation of variable-resolution maps through a sum of atomic images expressed as analytic functions of all atomic parameters, along with their associated local resolution.

bioinformatics↗

bioRxiv2025

EXPLICIT CORRECTION OF SEVERELY NON-UNIFORM DISTRIBUTIONS OF CRYO-EM VIEWS

The quality of three-dimensional macromolecular image reconstructions by cryo electron microscopy strongly depends on the number and quality of respective two-dimensional projections and on their angular distribution in space. Distributions with one or a few strongly preferred particle orientations may result in maps deformed in certain directions. A simple removal of overrepresented views may improve the quality of the reconstructed maps when the level of noise in the two-dimensional projections is low and the dataset-size can afford this removal but is counterproductive or insufficient otherwise. Giving complementarily an increased weight to underrepresented views, or taking multiple copies of them during the reconstruction, may improve the results, naturally, depending on how much the views distribution is non-uniform. This work describes the results of three-dimensional reconstructions using an explicit correction of the number of over- and underrepresented projections for non-uniformly distributed sets. SynopsisAn explicit numerical leveling of non-uniformly distributed sets of 2D projections with the program VUE improves the 3D reconstructions and illustrate sources of image distortions.

molecular biology↗

bioRxiv2025

QUANTIFYING DISTRIBUTIONS OF CRYO-EM PROJECTIONS

In cryo-electron microscopy, a set of two-dimensional projections collected from different viewing directions may complicate image processing and subsequent model building if the distribution of these views is non-uniform. View distributions are traditionally represented as color-coded two-dimensional diagrams. However, such diagrams can introduce distortions, are cumbersome to manipulate, store, and compare across datasets; they do not provide a commonly accepted quantitative measure of uniformity. In this work, we propose a method to characterize these angular distributions quantitatively and to represent them as simple one-dimensional curves rather than two-dimensional colored diagrams. The suggested measures could be incorporated into databases such as the EMDB to provide a compact, standardized description of the angular distribution of particle views. SynopsisWe propose a numerical measure to quantify the deviation of a cryo-EM 2D view distribution from the uniform one. This approach allows the traditional two-dimensional projection diagrams to be replaced, or completed with simple, easily generated curves that are straightforward to analyze.

molecular biology↗

bioRxiv2025

Straightening FSC curves

The Fourier Shell Correlation (FSC) is traditionally calculated in resolution shells and plotted as a function of the inverse resolution. To ensure consistent statistics, these resolution shells should ideally contain an equal number of Fourier coefficients, at least approximately. This condition is naturally met when the shell boundaries are chosen uniformly in a scale based on the inverse cubic resolution. It has been observed that, in this scale, the FSC curves tend to exhibit local linearity. Using the new scale also zooms at the high-resolution shells allowing to extract values of interest more reliably. SynopsisCalculating and plotting FSC curves on a scale uniform in inverse cubic resolution ([A]-3) has several useful features.

biophysics↗

bioRxiv2023

Local heterogeneity analysis of crystallographic and cryo-EM maps using shell-approximation

In X-ray crystallography and cryo-EM, experimental maps can be heterogeneous, showing different regions of the structure with different level of details. In this work we interpret the heterogeneity in terms of two parameters, assigned individually for each atom, combining the conventional parameter of atomic displacement with the resolution of the atomic image in the map. We propose a local real-space procedure to estimate the values of these heterogeneity parameters, assuming that a fragment of the density map and preliminary values of atomic coordinates are given. The procedure is based on the representation of the atomic image in an analytical form, as a function of the inhomogeneity parameters and atomic coordinates. In this article, we report the results of the tests both with simulated maps and maps derived from experimental data. For simulated heterogeneous maps containing regions with different resolutions, the method determines the local map resolution near the atomic centers and the values of the atomic displacement parameter with reasonable accuracy. For experimental maps, obtained as a Fourier synthesis of a given global resolution, estimated values of the local resolution are close to the global one, and the values of the estimated displacement parameters are close to the respective values in the refined model. Shown examples of the application of the proposed method to the experimental crystallographic and cryo-EM maps can be seen as a practical proof of method.

biophysics↗

bioRxiv2022

Analytic representation of inhomogeneous-resolution maps of three-dimensional scalar fields

Refinement of macromolecular atomic models versus experimental maps in cryo-electron microscopy and crystallography is a critical step in structure solution. For an appropriate comparison, model maps should mimic imperfections of the experimental ones, mainly atomic disorder and its limited resolution, often inhomogeneous over the molecule. We construct these model maps as a sum of atomic contributions expressed through a specially designed function describing a solitary spherical wave. Thanks to this function, atomic contributions analytically depend on both an atomic disorder and the local resolution, a value associated now with each atom. Such fully analytic dependence of inhomogeneous-resolution map values on model parameters permits an efficient refinement of all these parameters together and, beyond structural biology, opens a way to solve similar problems in other research domains. One-Sentence SummaryAn analytic decomposition of 3D-oscillating functions results in efficient tools to calculate maps and refine atomic models.

molecular biology↗