Construction of bacterial flagellar filaments, and aspects of their conversion to different helical forms

The helical flagellar filaments of bacteria such as Salmonella typhimurium are constructed from subunits of a single protein called flagellin by a process of self-assembly. They are polymorphic, and change from one helical form to another in a variety of circumstances. This paper discusses, from a viewpoint of classical mechanics, two types of problem associated with these filaments. First is the general problem of how to construct a helical rod from identical subunits. There must be some variation in the pattern of packing of subunits; and it is demonstrated that a mechanically bi-stable but otherwise linear-elastic subunit can build filaments which are not only helical but also possess the observed polymorphic properties. The question of uniqueness of the design is discussed. The second problem concerns the hydrodynamic performance of a helical filament which can switch waveform when subjected to mechanical overload. Transitions which can be brought about in this way are reviewed briefly. An explanation is offered in terms of the mechanics of polymorphism for the behaviour of an anomalous and puzzling 'partly rotating' filament in Hotani's (1979) micro-video study of tethered filaments in fluid streams.