Biology subjects

Lunin, V. Y.

Publications and source records attributed to Lunin, V. Y..

3 recordsLinked to original sources

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

Direct calculation of cryo EM and crystallographic model maps for real-space refinement

Real-space refinement of atomic models improves them by their fit to experimental scattering electrostatic potential maps in cryo electron microscopy and to electron density maps in crystallography. This procedure has a number of advantages in comparison with reciprocal-space refinement, is complementary to it in crystallographic studies and is the principal technique in cryo EM. An accurate real-space refinement of atomic models can be done by comparison of the model maps, calculated according to the respective theory, with the experimental ones, when the former mimic imperfections of the latter, mainly a limited resolution and an atomic disorder. Calculation of model maps as a sum of contributions of individual atoms means that these contributions - atomic images in the given map - should also be affected by the resolution and positional disorder. This blurs atomic images and surrounds their central peak by Fourier ripples. These ripples can be described by a specially designed function which allows combining both principal effects of map imperfection in an analytic way. The atomic images, at any resolution and with any value of the atomic displacement parameter, can be decomposed into a linear combination of such functions with the precalculated parameter values. As a consequence, each map value becomes an analytic function of atomic parameters including displacement parameter and a local resolution if required. Using the chain rule for the score function which compares the maps, such model results in analytic expressions for its partial derivatives with respect to all atomic parameters allowing an efficient real-space refinement. At the same time, for practical calculations atomic images are cut at some truncation distance, i.e., include a limited number of ripples. This introduced in the model maps errors which are not present in the experimental maps. Due to oscillating behavior of the atomic images, the choice of the value of this truncation distance is not straightforward and discussed in this work. SynopsisA new method is suggested to calculate maps of a limited and eventually inhomogeneous resolution as an analytic function of all atomic parameters, including local resolution.

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↗