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Living cells respond to mechanical changes in the matrix surrounding them byapplying contractile forces that are in turn transmitted to distant cells. Wecalculate the mechanical work that each cell performs in order to deform thematrix, and study how that energy changes when a contracting cell is surroundedby other cells with similar properties and behavior. We consider simpleeffective geometries for the spatial arrangement of cells, with spherical andwith cylindrical symmetries, and model the presence of neighboring cells byimposing zero-displacement at some distance from the cell, which represents thesurface of symmetry between neighboring cells. In linear elastic matrices, weanalytically study the dependence of the resulting interaction energy on thegeometry and on the stiffness and regulatory behavior of the cells. For cellsthat regulate the active stress that they apply, in spherical geometry, thedeformation inside the cell is pure compression thus the interaction dependsonly on their bulk modulus, while in cylindrical geometries the deformationincludes also shear and the interaction depends also on their shear modulus. Innonlinear, strain stiffening matrices, our numerical solutions and analyticalapproximations show how in the presence of other cells, cell contraction islimited due to the divergence of the shear stress.

Mean-field interactions between living cells in linear and nonlinear elastic matrices