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

TL;DR

This paper models how living cells mechanically interact through elastic matrices, analyzing energy transfer and deformation in linear and nonlinear materials, revealing geometry and material-dependent interaction behaviors.

Contribution

It provides analytical and numerical insights into cell-cell mechanical interactions considering complex geometries and nonlinear matrix behaviors, advancing understanding of tissue mechanics.

Findings

Interaction energy depends on cell geometry and matrix stiffness.

In nonlinear matrices, cell contraction is limited by shear stress divergence.

Deformation behavior varies with spherical or cylindrical symmetry.

Abstract

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.