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 part icles. However, if the symmetry is not contrasted strongly, this proce dure may be inconclusive since the relevant peak may not be convincing ly higher than other spectral components. To some extent, this is a sa mpling problem since the number of repeating elements involved is usua lly small. We have devised more sensitive statistical tests for rotati onal 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 back ground areas. One method is based on the well known t-test which estim ates 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 ba ckground areas is calculated, and thence, the cumulative product of th ese ratios over all particles in the data set. If a symmetry is presen t, this product gradually diverges; otherwise, it converges to zero. A s a practical trial, the tests were applied to micrographs of negative ly stained hexons of herpes simplex virus and confirmed their 6-fold s ymmetry. Applied to negatively stained ''connector'' proteins of bacte riophage T7 purified from a plasmid expression system, both algorithms detected polymorphism with distinct subpopulations of both 13-fold an d 12-fold connectors.