  Experiments performed using micro-patterned one dimensional collision assays
have allowed a precise quantitative analysis of the collective manifestation of
contact inhibition locomotion (CIL) wherein, individual migrating cells
reorient their direction of motion when they come in contact with other cells.
Inspired by these experiments, we present a discrete, minimal 1D Active spin
model that mimics the CIL interaction between cells in one dimensional
channels. We analyze the emergent collective behaviour of migrating cells in
such confined geometries, as well as the sensitivity of the emergent patterns
to driving forces that couple to cell motion. In the absence of vacancies, akin
to dense cell packing, the translation dynamics is arrested and the model
reduces to an equilibrium spin model which can be solved exactly. In the
presence of vacancies, the interplay of activity-driven translation, cell
polarity switching, and CIL results in an exponential steady cluster size
distribution. We define a dimensionless P\'eclet number Q - the ratio of the
translation rate and directional switching rate of particles in the absence of
CIL. While the average cluster size increases monotonically as a function of Q,
it exhibits a non-monotonic dependence on CIL strength, when the Q is
sufficiently high. In the high Q limit, an analytical form of average cluster
size can be obtained approximately by effectively mapping the system to an
equivalent equilibrium process involving clusters of different sizes wherein
the cluster size distribution is obtained by minimizing an effective Helmholtz
free energy for the system. The resultant prediction of exponential dependence
on CIL strength of the average cluster size and Q^{1/2} dependence of the
average cluster size is borne out to reasonable accuracy as long as the CIL
strength is not very large.
