  A common type of cytoskeletal morphology involves multiple converging
microbutubules with their minus ends collected and stabilized by a microtubule
organizing center (MTOC) in the interior of the cell. This arrangement enables
the ballistic transport of cargo bound to microtubules, both dynein mediated
transport towards the MTOC and kinesin mediated transport away from it,
interspersed with diffusion for unbound cargo-motor complexes. Spatial and
temporal positioning of the MTOC allows for bidirectional transport towards and
away from specific organelles and locations within the cell and also the
sequestering and subsequent dispersal of dynein transported cargo. The general
principles governing dynamics, efficiency and tunability of such transport in
the MTOC vicinity is not fully understood. To address this, we develop a
one-dimensional model that includes advective transport towards an attractor
(such as the MTOC), and diffusive transport that allows particles to reach
absorbing boundaries (such as cellular membranes). We calculated the mean first
passage time (MFPT) for cargo to reach the boundaries as a measure of the
effectiveness of sequestering (large MFPT) and diffusive dispersal (low MFPT).
The MFPT experiences a dramatic growth in magnitude, transitioning from a low
to high MFPT regime (dispersal to sequestering) over a window of cargo
attachment/detachment rates that is close to in vivo values. We find that
increasing either the attachment or detachment rate, while fixing the other,
can result in optimal dispersal when the attractor is placed asymmetrically.
Finally, we describe a rare event regime, where the escape location is
exponentially sensitive to the attractor positioning. Our results suggest that
structures such as the MTOC allow for the sensitive control of the spatial and
temporal features of transport and corresponding function under physiological
conditions.
