Rapid automated superposition of shapes and macromolecular models using spherical harmonics. Issue 3 (16th May 2016) - Konarev, Petr V.; Petoukhov, Maxim V.; Svergun, Dmitri I.
Abstract : A method utilizing a spherical harmonics representation of the scattering amplitudes for a rapid superposition of three‐dimensional models is developed. Abstract : 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.