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.