  To initiate tumbling of an E. coli, one of the helical flagella reverses its
sense of rotation. It then transforms from its normal form first to the
transient semicoiled state and subsequently to the curly-I state. The dynamics
of polymorphism is effectively modeled by describing flagellar elasticity
through an extended Kirchhoff free energy. However, the complete landscape of
the free energy remains undetermined because the ground state energies of the
polymorphic forms are not known. We investigate how variations in these ground
state energies affect the dynamics of a reversely rotated flagellum of a
swimming bacterium. We find that the flagellum exhibits a number of distinct
dynamical states and comprehensively summarize them in a state diagram. As a
result, we conclude that tuning the landscape of the extended Kirchhoff free
energy alone cannot generate the intermediate full-length semicoiled state.
However, our model suggests an ad hoc method to realize the sequence of
polymorphic states as observed for a real bacterium. Since the elastic
properties of bacterial flagella are similar, our findings can easily be
extended to other peritrichous bacteria.
