Quasi- and nonequivalence in the structure of bacterial flagellar filament.

In supercoiled forms of flagellar filaments, which are thought to be produced by combinations of two distinct subunit lattices, the lattices are elastically deformed in 11 different ways, depending on their azimuthal positions on the circumference of a tube with 11 protofilaments. Those two interactions are nonequivalent as opposed to quasiequivalent ones in elastically deformed lattices of otherwise identical interactions. The term nonequivalence is defined to represent different bonding interactions, and quasiequivalent is used to describe deformed but conserved bonding interactions. By using two distinct lattices that were accurately determined by x-ray fiber diffraction, 10 possible supercoiled forms of flagellar filaments were simulated, based on a bistable-subunit packing model. Comparison to the observed forms showed good agreement, indicating that the model and determined lattice parameters effectively represent realistic features of the structure. The simulated quasiequivalent lattices have been compared to the two nonequivalent lattices, revealing an interesting feature: the maximum deviation in the intersubunit distance by elastic deformation is almost three-quarters of the difference between the two distinct lattices, demonstrating a balanced coexistence of a well-defined conformational distinction and extensive adaptability in the molecular structure of flagellin and its packing interactions.