Hook and flagellar deformations in bacterial flicks*

Flexibility of the hook and flagellum affects the bacterial motility and run-reverse-flick motility of single-flagellated bacteria. Previously we have neglected hydrodynamic interactions between the cell body and flagellum and developed an efficient spring model with bending and torsional stiffnesses for the hook by linearizing Kirchhoff rod model. We have reported critical hook parameter that describes transition from stable orbits to precession. Then, we included the flexibility of the flagellar filaments and found that these flexibilities initiate dynamical buckling and flick in single-flagellated bacteria. Many other previous studies replaced the hook by a linear spring which does not have torsional response. Here, we study how including the torsional spring effects of our linearization alters swimming dynamics of organisms. We also investigate the role of hydrodynamic interactions between the cell body and flagellum and find that including hydrodynamic interactions makes hooks more susceptible to buckling instabilities. Finally, we model complete flick events, investigating the buckling angle and reorientations of the swimming cells due to time dependent hook flexibility while including flexibility of the flagellar filament