Gap compression/extension mechanism of bacterial flagellar hook as the molecular universal joint

Bacterial flagellar hook acts as a molecular universal joint, transmitting torque produced by the flagellar basal body, a rotary motor, to the flagellar filament. The hook forms polymorphic supercoil structures and can be considered as an assembly of 11 circularly arranged protofilaments. We investigated the molecular mechanism of the universal joint function of the hook by a approximately two-million-atom molecular dynamics simulation. On the inner side of the supercoil, protein subunits are highly packed along the protofilament and no gaps remain for further compression, whereas subunits are slightly separated and are hydrogen bonded through one layer of water molecules on the outer side. As for the intersubunit interactions between protofilaments, subunits are packed along the 6-start helix in a left-handed supercoil whereas they are highly packed along the 5-start helix in a right-handed supercoil. We conclude that the supercoiled structures of the hook in the left- and right-handed forms make maximal use of the gaps between subunits, which we call "gap compression/extension mechanism". Mutual sliding of subunits at the subunit interface accompanying rearrangements of intersubunit hydrogen bonds is interpreted as a mechanism to allow continuous structural change of the hook during flagellar rotation at low energy cost.