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

  Chaviva Sirote  ,  Chvaiva Ssirote  ,  Yair Shokef  
Tel aviv university

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 two simple e_ective

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. We analytically calculate

the resulting interaction energy in linear elastic matrices, and study its dependence on the geometry,

on the cell's sti_ness, and on the cell's regulatory behavior. In nonlinear, strain sti_ening matrices,

we obtain numerical solutions and complement them by asymptotic analytical approximations