  Bacterial flagellar motor (BFM) is one of the ion-driven molecular machines,
which drives the rotation of flagellar filaments and enable bacteria to swim in
viscous solutions. Understanding its mechanism is one challenge in biophysics.
Based on previous models and inspired by the idea used in description of motor
proteins, in this study one two-state model is provided. Meanwhile, according
to corresponding experimental data, mathematical relationship between BFM
membrane voltage and pH value of the environment, and relationship between
internal and external sodium concentrations are given. Therefore, with model
parameter values obtained by fitting theoretical results of torque-speed
relation to recent experimental data, many biophysical properties of bacterial
flagellar motor can be obtained for any pH values and any external sodium
concentrations. Including the rotation speed, stall torque (i.e. the torque
generated by BFM), rotation dispersion, and rotation randomness. In this study,
the single-stator BFM will be firstly analyzed, and then properties of
multiple-stator BFM are addressed briefly.
