Bacterial flagella rotating in bundles: a study in helical geometry.

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Abstract
Bacterial flagella are semi-rigid helices that undergo true rotation. In peritrichously flagellated bacteria (e.g., Escherichia and Salmonella) there are many flagella on each cell; during translational cell movement these operate as a coordinated bundle that actively disperses upon reversal of the rotation sense. The dynamic behavior of a set of helices originating on separate rotational axes is explored by a working model, geometrical analysis and hydrodynamic calculations. A critical relationship exists between the interaxial separation and phase difference of parallel helices with overlapping domains; in the subcritical case the filaments are not intertwisted, but in the supercritical case they are intertwisted in the same sense (left-handed) as the helices, with 1 twist/helical turn. During counter-clockwise rotation (the sense operative in forward swimming) any preexisting twists of this kind are automatically cancelled, and the helices are brought progressively into phase. Hydrodynamic calculations suggest that some wrapping then occurs in a right-handed sense, opposite to that of the helices; this necessitates a distortion from true helical geometry which is minimized by maintaining a coaxial in-phase relationship. A highly coordinated helical bundle results that is capable of operating smoothly for an indefinite period, in agreement with the observed behavior of swimming bacteria. During reverse rotation the supercritical case develops to cause jamming of the bundle, as was observed with bacteria in high-viscosity medium. The explosive dispersal of the bundle during reversal in low-viscosity medium is a consequence of a complicating phenomenon, namely, a drastic change in flagellar quaternary structure. The bundle formation and function are perfectly compatible with a rotational mechanism for the individual flagella.