  We develop a stochastic kinetic model of a pre-formed attachment of a
mictrotuble (MT) with a cell cortex, in which the MT is tethered to the cell by
a group of active motor proteins. Such an attachment is a particularly unique
case of ligand-receptor bonds: The MT ligand changes its length (and thus
binding sites) with time by polymerization-depolymerization kinetics, while
multiple motor receptors tend to walk actively along the MT length. These
processes, combined with force-mediated unbinding of the motors, result in an
elaborate behavior of the MT connection to the cell cortex. We present results
for the strength and lifetime of the system through the well-established
force-clamp and force-ramp protocols when external tension is applied to the
MT. The simulation results reveal that the MT-cell attachment behaves as a
catch-bond or slip-bond depending on system parameters. We provide analytical
approximations of the lifetime and discuss implications of our results on
in-vitro experiments.
