Improved methods for determination of rotational symmetries in macromolecules

Rotational symmetries of macromolecules are most clearly perceived in the en face projection and may be assessed by inspection of rotational power spectra calculated from electron micrographs of individual particles. However, if the symmetry is not contrasted strongly, this procedure may be inconclusive since the relevant peak may not be convincingly higher than other spectral components. To some extent, this is a sampling problem since the number of repeating elements involved is usually small. We have devised more sensitive statistical tests for rotational symmetry that pool the information contents of entire populations of particles. Both tests involve combining the rotational spectra of many particles and comparing them with the spectra of surrounding background areas. One method is based on the well known t-test which estimates whether two populations differ at a given significance level. In the second test, the ratio between the intensity of each component of the rotational spectrum and the average corresponding intensity for background areas is calculated, and thence, the cumulative product of these ratios over all particles in the data set. If a symmetry is present, this product gradually diverges; otherwise, it converges to zero. As a practical trial, the tests were applied to micrographs of negatively stained hexons of herpes simplex virus and confirmed their 6-fold symmetry. Applied to negatively stained “connector” proteins of bacteriophage T7 purified from a plasmid expression system, both algorithms detected polymorphism with distinct subpopulations of both 13-fold and 12-fold connectors.