  The cargo motion in living cells transported by two species of motor protein
with different intrinsic directionality is discussed in this study. Similar to
single motor movement, cargo steps forward and backward along microtubule
stochastically. Recent experiments found that, cargo transportation by two
motor species has a memory, it does not change its direction as frequently as
expected, which means that its forward and backward step rates depends on its
previous motion trajectory. By assuming cargo has only the least memory, i.e.
its step direction depends only on the direction of its last step, two cases of
cargo motion are detailed analyzed in this study: {\bf (I)} cargo motion under
constant external load; and {\bf (II)} cargo motion in one fixed optical trap.
Due to the existence of memory, for the first case, cargo can keep moving in
the same direction for a long distance. For the second case, the cargo will
oscillate in the trap. The oscillation period decreases and the oscillation
amplitude increases with the motor forward step rates, but both of them
decrease with the trap stiffness. The most likely location of cargo, where the
probability of finding the oscillated cargo is maximum, may be the same as or
may be different with the trap center, which depends on the step rates of the
two motor species. Meanwhile, if motors are robust, i.e. their forward to
backward step rate ratios are high, there may be two such most likely
locations, located on the two sides of the trap center respectively. The
probability of finding cargo in given location, the probability of cargo in
forward/backward motion state, and various mean first passage times of cargo to
give location or given state are also analyzed.
