The elastic basis for the shape of Borrelia burgdorferi.

The mechanisms that determine bacterial shape are in many ways poorly understood. A prime example is the Lyme disease spirochete, Borrelia burgdorferi (B. burgdorferi), which mechanically couples its motility organelles, helical flagella, to its rod-shaped cell body, producing a striking flat-wave morphology. A mathematical model is developed here that accounts for the elastic coupling of the flagella to the cell cylinder and shows that the flat-wave morphology is in fact a natural consequence of the geometrical and material properties of the components. Observations of purified periplasmic flagella show two flagellar conformations. The mathematical model suggests that the larger waveform flagellum is the more relevant for determining the shape of B. burgdorferi. Optical trapping experiments were used to measure directly the mechanical properties of these spirochetes. These results imply relative stiffnesses of the two components, which confirm the predictions of the model and show that the morphology of B. burgdorferi is completely determined by the elastic properties of the flagella and cell body. This approach is applicable to a variety of other structures in which the shape of the composite system is markedly different from that of the individual components, such as coiled-coil domains in proteins and the eukaryotic axoneme.

The shape and dynamics of the Leptospiraceae.

Most swimming bacteria produce thrust by rotating helical filaments called flagella. Typically, the flagella stick out into the external fluid environment; however, in the spirochetes, a unique group that includes some highly pathogenic species of bacteria, the flagella are internalized, being incased in the periplasmic space; i.e., between the outer membrane and the cell wall. This coupling between the periplasmic flagella and the cell wall allows the flagella to serve a skeletal, as well as a motile, function. In this article, we propose a mathematical model for spirochete morphology based on the elastic interaction between the cell body and the periplasmic flagella. This model describes the mechanics of the composite structure of the cell cylinder and periplasmic flagella and accounts for the morphology of Leptospiraceae. This model predicts that the cell cylinder should be roughly seven times stiffer than the flagellum. In addition, we explore how rotation of the periplasmic flagellum deforms the cell cylinder during motility. We show that the transition between hook-shaped and spiral-shaped ends is purely a consequence of the change in direction of the flagellar motor and does not require flagellar polymorphism.