Active spin model for cell assemblies on 1D substrates

The experimental use of micropatterned quasi-1D substrates has emerged as an useful experimental tool to study the nature of cell-cell interactions and gain insight on collective behaviour of cell colonies. Inspired by these experiments, we propose an active spin model to investigate the emergent properties of the cell assemblies. The lattice gas model incorporates the interplay of self-propulsion, polarity directional switching, intra-cellular attraction, and contact Inhibition Locomotion (CIL). In the absence of vacancies, which corresponds to a confluent cell packing on the substrate, the model reduces to an equilibrium spin model which can be solved exactly. In the presence of vacancies, the clustering is controlled by a dimensionless Peclet Number, Q - the ratio of magnitude of self-propulsion rate and directional switching rate of particles. In the absence of CIL interactions, we invoke a mapping to Katz-Lebowitz-Spohn(KLS) model to determine an exact analytical form of the cluster size distribution in the limit Q << 1. In the limit of Q >> 1, the cluster size distribution exhibits an universal scaling behaviour (in an approximate sense), such that the distribution function can be expressed as a scaled function of Q, particle density and CIL interaction strength. We characterize the phase behaviour of the system in terms of contour plots of average cluster size. The average cluster size exhibit a non-monotonic dependence on CIL interaction strength, attractive interaction strength, and self-propulsion.