Elastic interactions of mechanically polarizable cells

Cells mechanically interact through the deformations they generate in their surrounding extracellular matrix. We present an analytical theory of the elastic interactions between cells that actively adapt their forces in response to local deformations of their environment. Cells are represented as localized contractile force generators, modeled as polarizable point force dipoles, whose adaptive forces are determined self-consistently with those of surrounding cells. Analysis of the associated elastic interaction energy identifies a generic short-ranged interaction arising from the mutual adaptation of cellular forces. This induced-dipole interaction is analogous to the van der Waals interaction between molecules and likewise is shown to be generally attractive for cells that enhance contractility in response to stretch. Furthermore, unlike the long-ranged elastic interaction between nonpolarizable force-dipoles, that peaks at intermediate matrix stiffness and then weakens as the matrix softens, the induced-dipole interaction strengthens monotonically as the matrix softens and can reverse the interaction from being repulsive at long cell distances to being attractive at short separations. Analytical calculations are presented to illustrate the mutual polarization of forces in pairs of interacting cells on a substrate. The identification of a generic, short-range cohesive elastic interaction between cells is important for understanding cell behavior at short separations and provides a physical mechanism driving cell accumulation on soft substrates.