  Upon contact with antigen presenting cells (APCs) cytotoxic T lymphocytes (T
cells) establish a highly organized contact zone denoted as immunological
synapse (IS). The formation of the IS implies relocation of the microtubule
organizing center (MTOC) towards the contact zone, which necessitates a proper
connection between MTOC and IS via dynamic microtubules (MTs). The efficiency
of the MTs finding the IS within relevant time scale is, however, still
illusive. We investigate how MTs search the three-dimensional constrained
cellular volume for the IS and bind upon encounter to dynein anchored at the IS
cortex. The search efficiency is estimated by calculating the time required for
the MTs to reach the dynein-enriched region of the IS. In this study, we
develop simple mathematical and numerical models incorporating relevant
components of a cell and propose an optimal search strategy. Using the
mathematical model, we have quantified the average search time for a wide range
of model parameters and proposed an optimized set of values leading to the
minimum capture time. Our results show that search times are minimal when the
IS formed at the nearest or at the farthest sites on the cell surface, with
respect to the perinuclear MTOC. The search time increases monotonically away
from these two specific sites and are maximal at an intermediate position near
the equator of the cell. We observed that search time strongly depends on the
number of searching MTs and distance of the MTOC from the nuclear surface.
