In single-particle analysis of macromolecule images with the electron microscope, variations of projections are often observed that can be attributed to the changes of the particle’s orientation on the specimen grid (“rocking”). In the multivariate statistical analysis (MSA) of such projections, a single factor is often found that expresses a large portion of these variations. Successful angle calibration of this “rocking factor” would mean that correct angles can be assigned to a large number of particles, thus facilitating three-dimensional reconstruction.In a study to explore angle calibration in factor space, we used 40S ribosomal subunits, which are known to rock around an axis approximately coincident with their long axis. We analyzed micrographs of a field of these particles, taken with 20° tilt and without tilt, using the standard methods of alignment and MSA. The specimen was prepared with the double carbon-layer method, using uranyl acetate for negative staining. In the MSA analysis, the untilted-particle projections were used as active, the tilted-particle projections as inactive objects. Upon tilting, those particles whose rocking axes are parallel to the tilt axis will change their appearance in the same way as under the influence of rocking. Therefore, each vector, in factor space, joining a tilted and untilted projection of the same particle can be regarded as a local 20-degree calibration bar.
Signatures of a universal jump in the superfluid density of a two-dimensional Bose gas with a finite number of particles