  Living cells respond to mechanical changes in the matrix surrounding them by
applying contractile forces that are in turn transmitted to distant cells. We
calculate the mechanical work that each cell performs in order to deform the
matrix, and study how that energy changes when a contracting cell is surrounded
by other cells with similar properties and behavior. We consider simple
effective geometries for the spatial arrangement of cells, with spherical and
with cylindrical symmetries, and model the presence of neighboring cells by
imposing zero-displacement at some distance from the cell, which represents the
surface of symmetry between neighboring cells. In linear elastic matrices, we
analytically study the dependence of the resulting interaction energy on the
geometry and on the stiffness and regulatory behavior of the cells. For cells
that regulate the active stress that they apply, in spherical geometry, the
deformation inside the cell is pure compression thus the interaction depends
only on their bulk modulus, while in cylindrical geometries the deformation
includes also shear and the interaction depends also on their shear modulus. In
nonlinear, strain stiffening matrices, our numerical solutions and analytical
approximations show how in the presence of other cells, cell contraction is
limited due to the divergence of the shear stress.
