A fast mathematical programming procedure for simultaneous fitting of assembly components into cryoEM density maps

Motivation: Single-particle cryo electron microscopy (cryoEM) typically produces density maps of macromolecular assemblies at intermediate to low resolution (∼5–30 Å). By fitting high-resolution structures of assembly components into these maps, pseudo-atomic models can be obtained. Optimizing the quality-of-fit of all components simultaneously is challenging due to the large search space that makes the exhaustive search over all possible component configurations computationally unfeasible. Results: We developed an efficient mathematical programming algorithm that simultaneously fits all component structures into an assembly density map. The fitting is formulated as a point set matching problem involving several point sets that represent component and assembly densities at a reduced complexity level. In contrast to other point matching algorithms, our algorithm is able to match multiple point sets simultaneously and not only based on their geometrical equivalence, but also based on the similarity of the density in the immediate point neighborhood. In addition, we present an efficient refinement method based on the Iterative Closest Point registration algorithm. The integer quadratic programming method generates an assembly configuration in a few seconds. This efficiency allows the generation of an ensemble of candidate solutions that can be assessed by an independent scoring function. We benchmarked the method using simulated density maps of 11 protein assemblies at 20 Å, and an experimental cryoEM map at 23.5 Å resolution. Our method was able to generate assembly structures with root-mean-square errors <6.5 Å, which have been further reduced to <1.8 Å by the local refinement procedure. Availability: The program is available upon request as a Matlab code package. Contact: alber@usc.edu and m.topf@cryst.bbk.ac.uk Supplementary information: Supplementary data are available at Bioinformatics Online.