PF2 fit: Polar Fast Fourier Matched Alignment of Atomistic Structures with 3D Electron Microscopy Maps

There continue to be increasing occurrences of both atomistic structure models in the PDB (possibly reconstructed from X-ray diffraction or NMR data), and 3D reconstructed cryo-electron microscopy (3D EM) maps (albeit at coarser resolution) of the same or homologous molecule or molecular assembly, deposited in the EMDB. To obtain the best possible structural model of the molecule at the best achievable resolution, and without any missing gaps, one typically aligns (match and fits) the atomistic structure model with the 3D EM map. We discuss a new algorithm and generalized framework, named PF2 fit (Polar Fast Fourier Fitting) for the best possible structural alignment of atomistic structures with 3D EM. While PF2 fit enables only a rigid, six dimensional (6D) alignment method, it augments prior work on 6D X-ray structure and 3D EM alignment in multiple ways:Scoring. PF2 fit includes a new scoring scheme that, in addition to rewarding overlaps between the volumes occupied by the atomistic structure and 3D EM map, rewards overlaps between the volumes complementary to them. We quantitatively demonstrate how this new complementary scoring scheme improves upon existing approaches. PF2 fit also includes two scoring functions, the non-uniform exterior penalty and the skeleton-secondary structure score, and implements the scattering potential score as an alternative to traditional Gaussian blurring.Search. PF2 fit utilizes a fast polar Fourier search scheme, whose main advantage is the ability to search over uniformly and adaptively sampled subsets of the space of rigid-body motions. PF2 fit also implements a new reranking search and scoring methodology that considerably improves alignment metrics in results obtained from the initial search.Author Summary: In recent years, advances in cryo-electron microscopy (cryoEM) and three-dimensional (3D) image reconstruction have made it possible to determine the structures of molecular complexes, to sub-nanometer resolutions. These reconstructed 3D cryoEM maps provide a unique challenge, since the resolutions are often sufficient to resolve a subset of the secondary structural features (e.g., long α-helices), but not high enough to unambiguously identify others (e.g., short α-helices, β-sheets, α-helix pitch, or overall connectivity of proteins). Various types of hierarchical structure refinement models of the data, including the atomistic model match and fitting, which is the subject of this paper are crucial in helping derive a more complete understanding of the structure and function relationships of biological complexes. Our protocol offers several advantages over existing fitting techniques. We introduce three new scoring terms to evaluate the quality of fitting, and the optimization of these functions lead to better predictions than existing tools like ADP-EM and Colores. Furthermore, we have adopted a non-uniform FFT-based search which is not only faster than regular FFT, but it also enables one to selectively perform more refined searches in localized regions, which is specially useful when fitting a small molecular component into a larger symmetric or asymmetric macromolecular structure.