Mechanical analysis of phase transition experiments of the bacterial flagellar filament

Bacterial flagellar filaments can undergo a polymorphic phase transition in both vitro and vivo environments. Each bacterial flagellar filament has 12 different helical forms which are macroscopically represented by different pitch lengths and helix radii. For external mechanical force induced filament phase transitions, there is so far only one experiment performed by Hotani in 1982, who showed a very beautiful cyclic phase transition phenomenon in his experiment on isolated flagellar filaments. In the present paper, we give a detailed mechanical analysis on Hotani's experiments. Through theoretical computations, we obtained a phase transition rule based on the phase transition mechanism. The theoretical analysis provides a foundation facilitating the establishment of phase transition theory for bacterial flagellar filaments