Deducing the symmetry of helical assemblies: Applications to membrane proteins

Helical reconstruction represents a convenient and powerful approach for structure determination of macromolecules that assemble into helical arrays. In the case of membrane proteins, formation of tubular crystals with helical symmetry represents an attractive alternative, especially when their small size precludes the use of single-particle analysis. An essential first step for helical reconstruction is to characterize the helical symmetry. This process is often daunting, due to the complexity of helical diffraction and to the low signal-to-noise ratio in images of individual assemblies. Furthermore, the large diameters of the tubular crystals produced by membrane proteins exacerbates the innate ambiguities that, if not resolved, will produce incorrect structures. In this report, we describe a set of tools that can be used to eliminate ambiguities and to validate the choice of symmetry. The first approach increases the signal-to-noise ratio along layer lines by incoherently summing data from multiple helical assemblies, thus producing several candidate indexing schemes. The second approach compares the layer lines from images with those from synthetic models built with the various candidate schemes. The third approach uses unit cell dimensions measured from collapsed tubes to distinguish between these candidate schemes. These approaches are illustrated with tubular crystals from a boron transporter from yeast, Bor1p, and a β-barrel channel from the outer membrane of E. coli, OmpF.