The bacterial flagellum as an imperfect cylindrical crystal: flagellar geometry, movement and polymorphism, and the role of partial dislocations

A pairing attraction between helical turns of subunits in a cylindrical crystal, like that in the dahlemense strain of tobacco mosaic virus, can cause the axis of the rod or crystal to become helical. This is true only if the number of helices is odd. The shape of a bacterial flagellum can be accounted for then if, as Caspar &; Holmes and Klug have suggested, rows of its subunits exhibit such a pairing interaction. Klug's thoughts on bacterial flagella are developed and extended into a model that accounts qualitatively for geometry, movement and polymorphism of flagella. If the number of helices between which there is a pairing interaction is odd, then the crystal is an imperfect cylindrical crystal. The geometry of such crystals is described. They contain a line defect, termed here an antiphase boundary, across which the pairing interaction is reversed. The boundary is a line of expansion on the convex side of a curved filament. Movement of flagella is explained by circumferential displacement of the antiphase boundary. One polymorphic form can convert to another if a dislocation passes along it. Straight flagella are perfect cylindrical crystals with no antiphase boundary.