Matrix Strains Induced by Cells: Computing How Far Cells Can Feel

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Abstract
Many tissue cells exert contractile forces that mechanically couples them to elastic matrices and that influence cell adhesion, cytoskeletal organization, and even cell differentiation. However, strains within the depths of matrices are often unclear and are likely relevant not only to the fact that some matrices such as so-called basement membranes are thin relative to cell dimensions but also to defining how far cells can ‘feel’. Here we briefly present experimental results for cell spreading on thin, ligand-coated gels and for prestress in stem cells in relation to gel stiffness. We then introduce a finite element computation in which a cell is placed on an elastic matrix, while matrix elasticity and thickness are varied in order to compute and compare elastostatic deformations within the matrix. We focus on the response at the cell-matrix interface because this is the proximal location of likely tactile sensors, including focal adhesions and membrane channels. Average interfacial strains between cell and matrix show large deviations only when soft matrices are a fraction of the height and width of a cell, proving consistent with experiments. Three-dimensional (3D) cell morphologies that model stem cell-derived neurons, myoblasts, and osteoblasts show that a cylinder-shaped myoblast induces the highest strains, consistent with the prominent contractility of muscle. Groups of such cells show a weak crosstalk in matrix strains, but the cells must be much closer than a cell-width. Cells thus feel on length scales closer to that of adhesions than on cellular scales or higher.