  We introduce DiffFit, a differentiable algorithm for fitting protein
atomistic structures into an experimental reconstructed Cryo-Electron
Microscopy (cryo-EM) volume map. In structural biology, this process is
necessary to semi-automatically composite large mesoscale models of complex
protein assemblies and complete cellular structures that are based on measured
cryo-EM data. The current approaches require manual fitting in three dimensions
to start, resulting in approximately aligned structures followed by an
automated fine-tuning of the alignment. The DiffFit approach enables domain
scientists to fit new structures automatically and visualize the results for
inspection and interactive revision. The fitting begins with differentiable
three-dimensional (3D) rigid transformations of the protein atom coordinates
followed by sampling the density values at the atom coordinates from the target
cryo-EM volume. To ensure a meaningful correlation between the sampled
densities and the protein structure, we proposed a novel loss function based on
a multi-resolution volume-array approach and the exploitation of the negative
space. This loss function serves as a critical metric for assessing the fitting
quality, ensuring the fitting accuracy and an improved visualization of the
results. We assessed the placement quality of DiffFit with several large,
realistic datasets and found it to be superior to that of previous methods. We
further evaluated our method in two use cases: automating the integration of
known composite structures into larger protein complexes and facilitating the
fitting of predicted protein domains into volume densities to aid researchers
in identifying unknown proteins. We implemented our algorithm as an open-source
plugin (github.com/nanovis/DiffFit) in ChimeraX, a leading visualization
software in the field. All supplemental materials are available at
osf.io/5tx4q.
