Bacterial ?agella have a remarkable – and small – set of interconvertible supercoiled helical forms. An intact flagellum contains a long helical portion composed of tens of thousands of copies a flagellin protein (FliC in E. coli), coupled to a flexible hook which couples to a rod that is inserted into the bacterial motor. Here we discuss the physical properties of the flagellin homopolymer, also known as the flagellar filament. Though the details vary depending on the strain of bacterium, the filament’s allowed forms generally include several left-handed helices of varying pitch and several right-handed helices of varying pitch. Some of these are thermodynamically stable when the environment’s salt, pH or temperature is varied; others are predicted based on a geometrical model by Calladine but only observed when an external twisting or pulling force is applied. Under normal conditions (near-neutral pH, up to a few tenths of M salt, and low applied forces and torques) 2 out of the 11 protofilaments composing the flagellum are in the “L” state and the remaining 9 are in the “R” state. This produces a left-handed helix with a pitch angle of close to 45º: close to optimal for producing thrust.
Using reconstituted Salmonella flagellar filaments, I induced transformations between different flagellar states by pulling on filaments using an optical trap. Each of the sudden dips in the figure was caused by a section of filament transforming from the normal (2:9) form to unnamed hyperextended form (1:10). This typically takes several pN of force, but the exact force and exact site of transformation was varied from pull to pull. Filaments subject to slower pulling rates transformed at lower forces This is consistent with a statistical process controlled by an energy barrier: the Calladine states are local minima of free energy; the global minimum can be shifted by applying external force, but the local barriers between states remain. Transformation is therefore a thermally activated, statistical process. Full details of this research can be found here.
In the future, I would like to extend the current geometric and elastic model to give a complete thermodynamic description of ?agellar morphology. Flagella are simple enough homopolymers that I should be able to give a complete description of the energy landscape that governs their metastable folding states.