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 inSUPCOMBby 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 ofSUPCOMB. 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.
Laboratory of Reflectometry and Small-Angle Scattering, A.V. Shubnikov Institute of Crystallography of Federal Scientific Research Centre 'Crystallography and Photonics', Russian Academy of Sciences , Leninsky prospekt 59, Moscow, 119333, Russian Federation.
Petr V
PV
Konarev
Hamburg Outstation, European Molecular Biology Laboratory , Notkestrasse 85, Hamburg, 22607, Germany.
Maxim V
MV
Petoukhov
Hamburg Outstation, European Molecular Biology Laboratory , Notkestrasse 85, Hamburg, 22607, Germany.
Dmitri I
DI
Svergun
SUPALM; model superposition; protein structure; scattering amplitudes; small-angle scattering