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

Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We consider simple effective geometries for the spatial arrangement of 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. Cells regulating the displacements that they generate are attracted to each other in a manner that does not depend on the cell's rigidity. Whereas cells regulating the active stress that they apply repel each other. This repulsion depends on the cell's bulk modulus in spherical geometry, while in cylindrical geometries the interaction depends also on their shear modulus. In nonlinear, strain-stiffening matrices, for displacement regulation, in the presence of other cells, cell contraction is limited due to the divergence of the shear stress. For stress regulation, the interaction energy drops at the nonlinear stiffening stress. Our theoretical work provides insight into matrixmediated interactions between contractile cells and on the role of their mechanical regulatory behavior.

Automated summary

Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are transmitted to distant cells. The mechanical work and energy changes of cells are calculated and studied based on the spatial arrangement and properties of the cells. Cells can be attracted or repelled by each other, depending on their behavior and properties, with different effects observed in different geometries.