Three-dimensional matching of macromolecular structures obtained from electron microscopy: an application to the 70S and 50S E. coli ribosomal particles.
In this work we present a general computational method capable of finding the relative orientation of two structures represented by samples on a three-dimensional grid. It is shown that the three-dimensional shift and the three independent rotations necessary for the correct relative spatial placement of the two volumes can be obtained either from the auto-correlation function of the volumes or from a direct cross-correlation, depending on the specific problem to be solved. This method has been applied to the problem of fitting the 50S ribosomal subunit into the 70S monosome from E. coli, structures that were available as three-dimensional reconstructions from electron microscopical data.