Fig. 2.

Unrolled cylindrical surface lattices of flagellar filaments at radius 45 Å. These have been constructed from schematic subunits that allow point contacts on the 11-start lines so as to make protofilaments, and extended contacts on the 5-start lines, by means of a bi-stable connection; however, there are no connections on the 6-start lines. Subunits are numbered in the order of building the filament; a selection of these numbers is shown here. Subunits 0, 11, 22 and 0, 5, 10 lie on typical 11- and 5-start lattice lines, respectively. Subunits 10, 11 and 5, 11 lie on single- and 6-start lattice lines, respectively. The 11 protofilaments may be identified as containing the subunits numbered 0, 1…10. (a) Straight filament with left-handed twist, n = 0: all bi-stable connections are of the L type. (b) Straight filament with right-handed twist, n = 11: all bi-stable connections have sheared by 2.5 Å into the R type and are marked by red lines. (c) Filament n = 2, the normal helical form (see Fig. 1). Here, there are two longitudinal strands of bi-stable 5-start connections of the R type—again marked by red lines—clustered together so as to minimize the overall elastic strain energy of distortion (Ref. 13). (d) Lt straight filament, formed when the polypeptide chain of flagellin is truncated so that the inner tube is not properly constructed.^8,17,18 All bi-stable connections are of the R type; the pattern of (b) has been altered by the introduction of a shear dislocation between two adjacent protofilaments. Subunit numbers are not given here, since there is no longer a single-start lattice line passing through all subunits.