  The motion of molecular motor is essential to the biophysical functioning of
living cells. In principle, this motion can be regraded as a multiple chemical
states process. In which, the molecular motor can jump between different
chemical states, and in each chemical state, the motor moves forward or
backward in a corresponding potential. So, mathematically, the motion of
molecular motor can be described by several coupled one-dimensional hopping
models or by several coupled Fokker-Planck equations. To know the basic
properties of molecular motor, in this paper, we will give detailed analysis
about the simplest cases: in which there are only two chemical states.
Actually, many of the existing models, such as the flashing ratchet model, can
be regarded as a two-state model. From the explicit expression of the mean
velocity, we find that the mean velocity of molecular motor might be nonzero
even if the potential in each state is periodic, which means that there is no
energy input to the molecular motor in each of the two states. At the same
time, the mean velocity might be zero even if there is energy input to the
molecular motor. Generally, the velocity of molecular motor depends not only on
the potentials (or corresponding forward and backward transition rates) in the
two states, but also on the transition rates between the two chemical states.
