Before cell division, two identical copies of chromosome need to
be segregated accurately. Each chromosome is connected to a ``nano-ring''
(dam1) by ``rods'' (Ndc80). For accurate chromosome segregation, the two
chromosomes are pulled apart in the opposite directions by two sets of
``nano-hooks'', formed by microtubules (MTs), that are inserted into these
rings. An externally applied tension can lead to detachment of the hooks
from the ring; the mean lifetime of such an attachment is essentially a
mean first-passage time. Recent pioneering in-vitro  experiments with
reconstituted nano hook-ring device established that the mean lifetimes of
such attachments vary non-monotonically with increasing tension. In this
talk I'll explain the counter-intuitive stabilization of the attachments by
small tension with a unified  model that we have developed very
recently. The catch-bond-like mechanism emerges naturally in this model
from the interplay of tension-dependence of (i) the potential landscape and
(ii) MT depolymerization rate. I'll also show how the distribution of
lifetimes of the hook-ring attachment depends on (a) the structure, (b)
energetics, and (c) kinetics of the coupling.