הרצאת אורח המחלקה להנדסה ביו רפואית

Mechanical Interactions between Live Cells

Dr. Yair Shokef
School of Mechanical Engineering, Tel Aviv University, Israel

The elastic cytoskeleton contains molecular motors that produce mechanical forces by which cells attach to and pull on their surroundings. This mechanical interaction is responsible for many aspects of cellular function, from cell spreading and proliferation to stem-cell differentiation and tissue development. Both the cytoskeleton and the extracellular matrix comprise cross-linked, semi-flexible polymeric filaments, and as such they exhibit very nonlinear viscoelastic behavior that includes a power-law stiffening of the elastic moduli with increasing stress. We theoretically consider active force-dipoles embedded in a nonlinear elastic medium, with constitutive relations inspired by fracture mechanics, which obey the strain-stiffening scaling laws of biopolymers. For strong nonlinearity, the differential shear modulus diverges at finite strain, and we may employ a small strain (but strongly nonlinear) expansion. We find that for a single spherical force-dipole, strains change sign with distance, indicating that even around a contractile cell or single molecular motor complex there is radial compression; it is only at long distance that one recovers the linear response in which the medium is radially stretched. The renormalization of the far-field strain field implies that the material's nonlinearity causes the active force dipole to be equivalent to one which is dramatically larger and stronger. To investigate the mechanical interaction between several such cells in a nonlinear medium, we consider an array of active cells. Assuming the deformation around each cell is spherically symmetric, we connect the far-field strain field to the boundary condition of vanishing displacement on the plane of symmetry between neighboring cells. Our results explain experimental measurements of long-distance inter-cellular interactions on fibrin coated substrates, and suggest novel interpretations of the important question of whether cells regulate the stress that they exert or the deformation around them. Finally, we test our spherical model by considering the interactions between cells that regulate their anisotropic active contractile forces in a manner that ensures that in the presence of other such active cells they will preserve their shape