Abstract
We present a minimal continuum model of strongly adhering cells as active contractile isotropic media and use the model for studying the effect of the geometry of the adhesion patch in controlling the spatial distribution of traction and cellular stresses. Activity is introduced as a contractile, hence negative, spatially homogeneous contribution to the pressure. The model shows that patterning of adhesion regions can be used to control traction stress distribution and yields several results consistent with experimental observations. Specifically, the cell spread area is found to increase with substrate stiffness and an analytic expression of the dependence is obtained for circular cells. The correlation between the magnitude of traction stresses and cell boundary curvature is also demonstrated and analyzed.
Highlights
Living cells actively sense and respond to the physical geometry and stiffness of their environment, which in turn affects a variety of cellular processes, such as growth, differentiation, morphogenesis, spreading and motility [1]
The spatial distribution of traction stresses exerted by cells on substrate and the corresponding organization of stress and deformation inside the cell are affected by the geometry of adhesive patterns
We have used a continuum model of an adherent cell on a substrate as an active contractile medium to study the role of adhesion geometry in controlling cell shape, cell spreading and the spatial distribution of traction stresses
Summary
Living cells actively sense and respond to the physical geometry and stiffness of their environment, which in turn affects a variety of cellular processes, such as growth, differentiation, morphogenesis, spreading and motility [1]. The interplay between substrate stiffness, intracellular contractility and the extracellular adhesion forces controls the cell morphology and its mechanical behavior. The traction forces are obtained from by assuming a linear Hooke’s law relation between the measured bending and the forces [6] These experiments have demonstrated that the mechanical response of adherent cells is controlled by a complex interplay of substrate stiffness and geometry, myosin activity and extracellular matrix proteins. An interesting extension of our work will be to introduce nonlinearity in the continuum model to incorporate an asymmetric response to compression and stretching This asymmetry, arising from the nonlinear force-extension curve of actin filaments, is known to be important in controlling the contractile behavior of isotropic gels [18, 19] and may alter the stress distribution in adhering cells.
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