Real space in cryo-EM: the future is local

Likelihood-based signal and noise analysis for docking of models into cryo-EM maps

Fast, reliable docking of models into cryo-EM maps requires understanding of the errors in the maps and the models. Likelihood-based approaches to errors have proven to be powerful and adaptable in experimental structural biology, finding applications in both crystallography and cryo-EM. Indeed, previous crystallographic work on the errors in structural models is directly applicable to likelihood targets in cryo-EM. Likelihood targets in Fourier space are derived here to characterize, based on the comparison of half-maps, the direction- and resolution-dependent variation in the strength of both signal and noise in the data. Because the signal depends on local features, the signal and noise are analysed in local regions of the cryo-EM reconstruction. The likelihood analysis extends to prediction of the signal that will be achieved in any docking calculation for a model of specified quality and completeness. A related calculation generalizes a previous measure of the information gained by making the cryo-EM reconstruction.

Analytic modeling of inhomogeneous-resolution maps in cryo-electron microscopy and crystallography

Refinement of macromolecular atomic models versus experimental maps in crystallography and cryo-electron microscopy is a critical step in structure solution. For an appropriate comparison, model maps should mimic the imperfections in the experimental maps, mainly atomic disorder and limited resolution, which are often inhomogeneous over the molecular region. In the suggested method, these model maps are calculated as the sum of atomic contributions expressed through a specifically designed function describing a solitary spherical wave. Thanks to this function, atomic contributions are analytically expressed through their atomic displacement parameter and local resolution, a value now associated with each atom. Such a full analytic dependence of inhomogeneous-resolution map values on model parameters permits the refinement of all of these parameters together.

Toward Real Real-Space Refinement of Atomic Models

High-quality atomic models providing structural information are the results of their refinement versus diffraction data (reciprocal-space refinement), or versus experimental or experimentally based maps (real-space refinement). A proper real-space refinement can be achieved by comparing such a map with a map calculated from the atomic model. Similar to density distributions, the maps of a limited and even inhomogeneous resolution can also be calculated as sums of terms, known as atomic images, which are three-dimensional peaky functions surrounded by Fourier ripples. These atomic images and, consequently, the maps for the respective models, can be expressed analytically as functions of coordinates, atomic displacement parameters, and the local resolution. This work discusses the practical feasibility of such calculation for the real-space refinement of macromolecular atomic models.