Ab initio high-resolution single-particle 3D reconstructions: The symmetry adapted functions way

A protocol to attain high-resolution single-particle reconstructions is presented. The protocol is the concatenation of two procedures: one to obtain an ab initio low-resolution reconstruction, the other to determine a fixed point of the consecutive applications of fast projection matching and 3D reconstruction. It is a reciprocal space formulation where the Fourier coefficients of the 3D scattering density are expressed in terms of symmetry adapted functions and the 2D particle images are represented by their Fourier-Bessel transforms. The new protocol shows advantages in terms of speed and accuracy when compared to other methods currently in use. We illustrate its performance as applied to high-resolution cryo-electron micrographs of rotavirus.