PMC

Examples of angular and positional helical dispersion from simulated data. The instantaneous helical axes are plotted for each frame of the simulation. The longer, black axis is the optimal helical axis (i.e., the approximately mean helical axis) and the solid black dot is the optimal helical pivot point (i.e., the point in space that is closest to all instantaneous helical axes). A) Low angular dispersion (8.5°) and low positional dispersion (0.6 mm): the individual instantaneous helical axes are closely oriented with the optimal helical axis and all nearly intersect the optimal pivot. B) High angular dispersion (24.4°) and low positional dispersion (0.5 mm): the individual instantaneous helical axes deviate from the orientation of the optimal helical axis, but all nearly intersect the optimal pivot. C) Low angular dispersion (8.5°) and high positional dispersion (4.0 mm): the individual instantaneous helical axes are closely oriented with the optimal helical axis, but are scattered around (i.e., displaced from) the optimal helical pivot. D) High angular dispersion (24.4°) and high positional dispersion 3.0 mm): the individual instantaneous helical axes deviate from the orientation of the optimal helical axis and but are scattered around (i.e., displaced from) the optimal helical pivot.

(A) Interactions of the S domains of the NV subunits across the different icosahedral symmetry axes. The locations of these axes are shown by the corresponding numbers. Subunits A, B, and C are related by a quasi-threefold (shown by a triangle) and C and C₂ are related by an icosahedral twofold axis. Subunits A and B₅ are related by quasi-twofold axes, and C is related to B₅ and B₂ by quasi-sixfold symmetry. Subunits A and A₅ are related by a strict fivefold axis. The broken lines joining the icosahedral symmetry axes are the icosahedral interfaces indicated by arrows. The line (5-3) joining the fivefold and the threefold axes includes the A-B₅ (dimeric), A-A₅ (pentameric), and the C-B₅ (hexameric) interface regions while the line (3-3) joining the two threefold axes, includes the C-B₂ (hexameric) interface region. Similarly, the quasi-trimeric A-B, A-C, and the B-C interface regions lie on the boundaries between the A, B, and the C subunits. (B) NV conserved residues with reference to the secondary structure and icosahedral interfaces. Filled green arrow, β-strand; filled green cylinder, helix. The ACRs are shown in red along with their locations with respect to the icosahedral symmetry axes that are shown, using different symbols: oval, twofold axis; inverted triangle, threefold axis; hexagon, quasi-sixfold axis; pentagon, fivefold axis; and teardrop, quasi-threefold axis. A black border around the symmetry axes symbols indicates a buried residue, while no border around the symbol indicates an exposed residue. Multiple symbols on ACRs indicate the presence of multiple symmetry axes about which these residue(s) interact with other subunits.

(A–E) A. mackiei axes preserving connection between a leafy shoot axis, root-bearing axis and two rooting axes apices. (A) Photograph of thin section NHMUK 16433 showing a large A. mackiei axis with stellate xylem cut in transverse section in the top left and highlighted with the green arrowhead, and attached root-bearing axis. On the root-bearing axis (A) the position of a scale leaf (B), is highlighted with a blue arrowhead and the two rooting axes meristems are highlighted with white arrowheads. (C–E) Rooting axis meristems marked by white arrowheads in (A) the left arrowhead (C) and right (D, E). (D) Well-preserved rooting axis meristem showing continuous cell files from the central vascular trace into the apex, the tissues of the rooting axis are continuous with the root-bearing axis indicating that development was by anisotomous dichotomy. Scale bars, 5 mm (A), 0.5 mm (C, D) 0.2 mm (B, E). Specimen accession codes: NHMUK 16433 (A–E).

Cone-beam computed tomography. a Sagittal view. Green line: coronal axis. Red line: axial axis. The axes are incorrectly oriented with respect to tooth 3.7. b Green line: coronal axis. Red line: axial axis. The axes are correctly oriented (parallel and perpendicular to the longitudinal axis of the tooth 3.7). c Coronal view. Yellow line: sagittal axis. Red line: axial axis. The axes are oriented incorrectly regarding the tooth 3.7. d Yellow line: sagittal axis. Red line: axial axis. The axes are correctly oriented. Section shows radix entomolaris type III curvature Abbreviations, L:  lingual; B: buccal.