Active spin model for cell assemblies on 1D substrates

The experimental use of micropatterned quasi-one-dimensional substrates has emerged as a useful experimental tool to study the nature of cell-cell interactions and gain insight on collective behavior 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, intracellular 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 that can be solved exactly. In the presence of vacancies, the clustering is controlled by a dimensionless Peclét Number, Q-the ratio of magnitude of self-propulsion rate to directional switching rate of particles. In the absence of CIL interactions, we invoke a mapping to Katz-Lebowitz-Spohn 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 a universal scaling behavior (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 behavior of the system in terms of contour plots of average cluster size. These measures exhibit a nonmonotonic dependence on CIL interaction strength, attractive interaction strength, and self-propulsion.