(
A) Projected filament cross section of a 52Å-long segment of the wild-type
L. Biflexa flagellar filament. (
B) Plot of the averaged cross-correlation between the image in A and
N rotated copies of itself, corresponding to rotations of 1*360°/
N, 2*360°/
N, … (
N-1)*360°/
N about the filament center. Thus, for an image containing an 11
-fold symmetric feature, the averaged cross-correlation value will be highest for symmetry order
N = 11. Systematically varying N in this calculation reveals a maximum corresponding to 11-fold radial symmetry, matching the symmetry of the
Salmonella flagellum. Cross-correlations were computed for the entire image (‘full projection’) as well as masked sub-regions corresponding to the core (‘core only’) and sheath (‘sheath only’). All three of these calculations yield a maximum score for
N = 11. (
C) The 11-fold symmetry operator identified in
B was used to average the projected map, reducing the effects of the missing wedge and substantially improving molecular features. Leftmost panel shows the original core region, center-left panel shows the result of adding four symmetry-related copies (N = 11; Φ = 0*360°/11, 1*360°/11, 2*360°/11, 3*360°/11) and center-right panel shows the result of adding 11 symmetry-related copies (resulting in an 11-fold symmetric image). Features in the averaged images (yellow shape) resemble the projected D0/D1 subdomain within a projected
Salmonella flagellar filament cross section (rightmost panel; synthetic image derived from PDB ID 3A5X). (
D) Results of three-dimensional cross-correlation analysis between the wild-type sub-tomographic average volume and rotated copies of itself. For each rotation value (Φ=0*360°/11, 1*360°/11, … 11*360°/11), a volume copy was rotated about an axis running through the center channel and masked to exclude all but the core region of a single 52 Å axial repeat. A 3D cross-correlation map was then computed between the resulting volume and the original reference, and the axial shift described by the top-scoring peak was plotted for each Φ rotation value. The resulting graph describes a staggered pattern of helical subunit positions closely matching the 11-start helical symmetry observed in several other reported bacterial flagella structures (
Namba et al., 1989;
Wang et al., 2017). The estimated pseudo-helical parameters (~26 Å helical pitch,~5.5 subunits per turn) closely match helical parameters established for several other flagellar filaments (i.e.
Salmonella:~25.5 Å – 27 Å helical pitch, 5.4x – 5.5x subunits per turn).