Symmetry embedding in the reconstruction of macromolecular assemblies via the discrete Radon transform

In this paper we discuss the embedding of symmetry information in an algorithm for three-dimensional reconstruction, which is based on the discrete Radon transform. The original algorithm was designed for randomly oriented and in principal asymmetric particles. The expanded version presented here covers all symmetry point groups which can be exhibited by macromolecular protein assemblies. The orientations of all symmetry equivalent projections, based on the orientation of an experimental projection, are obtained using global group operators. Further, an improved interpolation scheme for the recovery of the three-dimensional discrete Radon transform has been designed for greater computational efficiency. The algorithm has been tested on phantom structures as well as on real data, a virus structure possessing icosahedral symmetry.