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.