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Many types of animal cells exert active, contractile forces and mechanically deform their elastic substrate, to accomplish biological functions such as migration. These substrate deformations provide a mechanism in principle by which cells may sense other cells, leading to long-range mechanical inter–cell interactions and possible self-organization. Here, inspired by cell mechanobiology, we propose an active matter model comprising self-propelling particles that interact at a distance through their mutual deformations of an elastic substrate. By combining a minimal model for the motility of individual particles with a linear elastic model that accounts for substrate-mediated, inter–particle interactions, we examine emergent collective states that result from the interplay of motility and long-range elastic dipolar interactions. In particular, we show that particles self-assemble into flexible, motile chains which can cluster to form diverse larger-scale compact structures with polar order. By computing key structural and dynamical metrics, we distinguish between the collective states at weak and strong elastic interaction strength, as well as at low and high motility. We also show how these states are affected by confinement within a channel geometry–an important characteristic of the complex mechanical micro-environment inhabited by cells. Our model predictions may be generally applicable to active matter with dipolar interactions ranging from biological cells to synthetic colloids endowed with electric or magnetic dipole moments. 

The mechanical micro-environment of cells and tissues influences key aspects of cell structure and function, including cell motility. For proper tissue development, cells need to migrate, interact, and form contacts. Cells are known to exert contractile forces on underlying soft substrates and sense deformations in them. Here, we propose and analyze a minimal biophysical model for cell migration and long-range cell–cell interactions through mutual mechanical deformations of the substrate. We compute key metrics of cell motile behavior, such as the number of cell-cell contacts over a given time, the dispersion of cell trajectories, and the probability of permanent cell contact, and analyze how these depend on a cell motility parameter and substrate stiffness. Our results elucidate how cells may sense each other mechanically and generate coordinated movements and provide an extensible framework to further address both mechanical and short-range biophysical interactions.