Use of triple correlations for the sign determinations of expansion coefficients of symmetric approximations to the diffraction volumes of regular viruses

An X-ray free electron laser is a new source of x-rays some 10 × 10(9) times brighter than any previous X-ray source, giving rise to the possibility of structure determination of individual biological particles without crystallization. Some of the earliest samples used in the X-ray free electron laser are viruses because they are about the largest of reproducible bioparticles. We show how common virus near-symmetries can be exploited to find a first approximation to their structures to give a starting point for a perturbation approach to determine their structures.