Elastic interactions of cells and their role in cellular self-association

Cell adhesion to the extracellular matrix is commonly accompanied by an active generation of elastic stresses in the cells` cytoskeleton. These stresses not only acquire the cells with their active mechano-sensitivity, but, provided the environment is sufficiently soft, they may also affect other cells and thus give rise to elastic interactions among the cells. These interactions have been studied both experimentally and theoretically but the precise mechanism by which local stresses and strains bring about changes in nearby cell orientation, polarity, force generation, and the propensity to self-associate is still largely unknown. We here present a theoretical investigation of cell cell elastic interactions on 2D elastic substrates, focusing first on pairs of cells in interaction and then on large ensembles of cells. The cells are modeled as polarizable point force dipoles that may actively adjust their force pattern in response to the local elastic field. Our model predicts that the strength of cell interactions should maximize for an intermediate rigidity of the substrate that is comparable to that of the cells. In addition, we demonstrate that the generic ability of cellular forces to polarize with the local elastic field creates a universal short range attractive interaction among the cells that scales similarly to the van der Waals intermolecular forces. A statistical mechanics model of cell cell elastic interactions is presented to predict the effects of these interactions on the propensity of cells to self-associate on the substrate.