Rapid automated superposition of shapes and macromolecular models using spherical harmonics

A rapid algorithm to superimpose macromolecular models in Fourier space is proposed and implemented (SUPALM). The method uses a normalized integrated cross-term of the scattering amplitudes as a proximity measure between two three-dimensional objects. The reciprocal-space algorithm allows for direct matching of heterogeneous objects including high- and low-resolution models represented by atomic coordinates, beads or dummy residue chains as well as electron microscopy density maps and inhomogeneous multi-phase models (e.g. of protein–nucleic acid complexes). Using spherical harmonics for the computation of the amplitudes, the method is up to an order of magnitude faster than the real-space algorithm implemented in SUPCOMB by Kozin & Svergun [J. Appl. Cryst. (2001 ▸), 34, 33–41]. The utility of the new method is demonstrated in a number of test cases and compared with the results of SUPCOMB. The spherical harmonics algorithm is best suited for low-resolution shape models, e.g. those provided by solution scattering experiments, but also facilitates a rapid cross-validation against structural models obtained by other methods.