Variable-resolution maps (VRMs) 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 employs Gaussian-like functions to generate these maps, which does not adequately account for atomic model parameters and resolution. Recent work by Urzhumtsev & Lunin [IUCrJ (2022), 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 atomic parameters. This approach enhances the accuracy of maps simulated from atomic models, allowing them to better reproduce features of the experimental maps. In this paper, we detail the implementation of this method in CCTBX and Phenix.