Elastic interactions of mechanically-polarizable cells

Elastic interactions between cells have been studied both experimentally and theoretically but the mechanisms by which local deformations of the environment drive changes in nearby cell orientations, polarity, force generation, and propensity to self-associate are poorly understood. We present a theoretical study of cell-cell elastic interactions on two-dimensional substrates. The cells are modeled as polarizable point force dipoles that actively adapt their force patterns in response to the local elastic strain. The theory reveals a generic short-range elastic interaction between cells - an induced-dipole interaction - analogous to the van der Waals interactions among molecules. We demonstrate these interactions to be strictly attractive for cells that upregulate contractility more strongly along than across the local principal strain direction. Furthermore, unlike the long-ranged fixed-dipole interaction, which optimizes for intermediate stiffness, the induced-dipole interaction monotonically intensifies on softer substrates and can reverse the nature of interaction from being repulsive at long distances and stiff environments to being attractive at short cell separations on soft substrates. The identification of generic, short-range, attractive elastic interactions among cells is important for understanding cell behavior at short cell separations and provides a new mechanism that drives cell accumulation on soft substrates.