Switch interactions control energy frustration and multiple flagellar filament structures.

Bacterial flagellar filament is a macromolecular assembly consisting of a single protein, flagellin. Bacterial swimming is controlled by the conformational transitions of this filament between left- and right-handed supercoils induced by the flagellar motor torque. We present a massive molecular dynamics simulation that was successful in constructing the atomic-level supercoil structures consistent with various experimental data and further in elucidating the detailed underlying molecular mechanisms of the polymorphic supercoiling. We have found that the following three types of interactions are keys to understanding the supercoiling mechanism. "Permanent" interactions are always maintained between subunits in the various supercoil structures. "Sliding" interactions are formed between variable hydrophilic or hydrophobic residue pairs, allowing intersubunit shear without large change in energy. The formation and breakage of "switch" interactions stabilize inter- and intrasubunit interactions, respectively. We conclude that polymorphic supercoiling is due to the energy frustration between them. The transition between supercoils is achieved by a "transform and relax" mechanism: the filament structure is geometrically transformed rapidly and then slowly relaxes to energetically metastable states by rearranging interactions.