Abstract
Helices are one of the most frequently encountered symmetries in biological assemblies. Helical symmetry has been exploited in electron microscopic studies as a limited number of filament images, in principle, can provide all the information needed to do a three-dimensional reconstruction of a polymer. Over the past 25 years, three-dimensional reconstructions of helical polymers from cryo-EM images have shifted completely from Fourier-Bessel methods to single-particle approaches. The single-particle approaches have allowed people to surmount the problem that very few biological polymers are crystalline in order, and despite the flexibility and heterogeneity present in most of these polymers, reaching a resolution where accurate atomic models can be built has now become the standard. While determining the correct helical symmetry may be very simple for something like F-actin, for many other polymers, particularly those formed from small peptides, it can be much more challenging. This review discusses why symmetry determination can be problematic, and why trial-and-error methods are still the best approach. Studies of many macromolecular assemblies, such as icosahedral capsids, have usually found that not imposing symmetry leads to a great reduction in resolution while at the same time revealing possibly interesting asymmetric features. We show that for certain helical assemblies asymmetric reconstructions can sometimes lead to greatly improved resolution. Further, in the case of supercoiled flagellar filaments from bacteria and archaea, we show that the imposition of helical symmetry can not only be wrong, but is not necessary, and obscures the mechanisms whereby these filaments supercoil.