  Analytical formulas for effective drift, diffusivity, run times, and run
lengths are derived for an intracellular transport system consisting of a cargo
attached to two cooperative but not identical molecular motors (for example,
kinesin-1 and kinesin-2) which can each attach and detach from a microtubule.
The dynamics of the motor and cargo in each phase are governed by stochastic
differential equations, and the switching rates depend on the spatial
configuration of the motor and cargo. This system is analyzed in a limit where
the detached motors have faster dynamics than the cargo, which in turn has
faster dynamics than the attached motors. The attachment and detachment rates
are also taken to be slow relative to the spatial dynamics. Through an
application of iterated stochastic averaging to this system, and the use of
renewal-reward theory to stitch together the progress within each switching
phase, we obtain explicit analytical expressions for the effective drift,
diffusivity, and processivity of the motor-cargo system. Our approach accounts
in particular for jumps in motor-cargo position that occur during attachment
and detachment events, as the cargo tracking variable makes a rapid adjustment
due to the averaged fast scales. The asymptotic formulas are in generally good
agreement with direct stochastic simulations of the detailed model based on
experimental parameters for various pairings of kinesin-1 and kinesin-2 under
assisting, hindering, or no load.
