THEORY OF DEFORMABLE SUBSTRATES DOR CELL MOTILITY STUDIES

Linear theory is used to relate the tractions F applied by a cell to t he resulting deformation of fluid, viscoelastic, or solid substrates. The theory is used to fit data in which the motion of a fluid surface in the neighborhood of a motile keratocyte is visualized with the aid of embedded beads. The data are best fit by modeling the surface layer as a two-dimensional, nearly incompressible fluid. The data favor thi s model over another plausible model, the planar free boundary of a th ree-dimensional fluid. In the resulting diagrams for the distribution of F, it is found that both curl F and div F are concentrated in the l ateral extrema of the lamellipodium. In a second investigation, a nonl inear theory of weak wrinkles in a solid substrate is proposed. The in -plane stress tensor plays the role of a metric. Compression wrinkles are found in regions where this metric is negative definite. Tension w rinkles arise, in linear approximation, at points on the boundary betw een positive definite and indefinite regions, and are conjectured to b e stabilized by nonlinear effects. Data for the wrinkles that would be produced by keratocyte traction are computed, and these agree qualita tively with observed keratocyte wrinkles.