Alignment of 3D structures of macromolecular assemblies.

Abstract

A number of macromolecular assemblies are being reconstructed in 3D from electron micrographs. The analysis yields a 3D matrix representing the protein density map. In reconstruction processes and in comparing the results of different experiments, it is often necessary to obtain all models oriented the same way in three dimensions. The problem is not trivial since there exist no 3D counterpart of correlation analysis used for 2D images. It is usually solved by time consuming trial and error algorithms. 3D density distributions can be brought to a 'canonical' orientation. The tensor of inertia of the distribution is determined and its eigenvectors are oriented along the coordinate axes. The method is fast and essentially free of reference. It is suitable for structures whose inertial axes do not completely degenerate as they do in icosahedral viruses or if symmetry is cubic. Applications are presented for asymmetric objects and for molecules possessing symmetry axes higher than twofold. The implementation simply requires the accumulation of the inertial tensor and its diagonalisation. Volume data rotation has been already illustrated in this journal by the authors.