  The organization of live cells to tissues is associated with the mechanical
interaction between cells, which is mediated through their elastic environment.
We model cells as spherical active force dipoles surrounded by an infinite
elastic matrix, and analytically evaluate the interaction energy for different
scenarios of their regulatory behavior. We obtain attraction for homeostatic
(set point) forces and repulsion for homeostatic displacements. When the
translational motion of the cells is regulated, the interaction energy decays
with distance as $1/d^4$, while when it is not regulated the energy decays as
$1/d^6$. This arises from the same reasons as the van der Waals interaction
between induced electric dipoles.
