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Substrate mediated elastic coupling between motile cells modulates inter–cell interactions and enhances cell–cell contact

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 with other neighbouring cells and form contacts, each of which require the cell to exert physical forces. Cells are known to exert contractile forces on underlying soft substrates. These stresses result in substrate deformation that can affect migratory behavior of cells as well as provide an avenue for cells to sense each other and coordinate their motion. The role of substrate mechanics, particularly its stiffness, in such biological processesis therefore a subject of active investigation. Recent progress in experimental techniques have enabled key insights into pairwise mechanical interactions that control cell motility when they move on compliant soft substrates. Analysis and modeling of such systemsis however still in its nascent stages. Motivated by the role modeling is expected to play in interpreting, informing and guiding experiments, we build a biophysical model for cell migration and cell–cell interactions. Our focus is on situations highly relevant to tissue engineering and regenerative medicine –when substrate traction stresses induced by motile cells enable substrate deformation and serve as a medium of communication. Using a generalizable agent–basedmodel, we compute key metrics of cell motile behavior such as the number of cell–cell contacts over a given time, dispersion of cell trajectories, and probability of permanent cell contact, and analyze how these depend on a cell motility parameter and on substrate stiffness. Our results provide a framework towards modeling the manner in which cells may sense each other mechanically via the substrate and use this information to generate coordinated movements across much longer length scales. Our results also provide a foundation to analyze experiments on the phenomenon known as durotaxis where single cells move preferentially towards regions of high stiffness on patterned substrates.