An accelerated ISAF algorithm with the fast mapping strategy

ISAF (icosahedral symmetry-adapted functions) is a new approach used for 3D reconstruction of icosahedral macromolecules, which can achieve better resolutions compared with the commonly used Fourier-Bessel algorithm. However, ISAF is significantly slow. Among all reasons, the operation that rotating each image sixty times costs lots of running time. By analyzing the sixty symmetrical characteristics of icosahedrons in Fourier space, we proved that the positions of sixty mapped points derived from one sampling point are all the same in asymmetric unit. Thus, the sixty symmetrical rotating of each image can be removed and the reconstruction speed is increased. This accelerating strategy was validated by means of experiments with simulated data and experimental Cryo-EM data. The results showed that the speedup of this strategy was up to 41 times and it could grow up with the increase of the maximum Fourier radius and the number of images at the premise of maintenance of accuracy. Its running speed is about 9 times as great as that of Fourier-Bessel algorithm and is about 3 times than that of recISAFs algorithm.