Cellular and Molecular Bioengineering

, Volume 2, Issue 1, pp 39–48

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


DOI: 10.1007/s12195-009-0052-z

Cite this article as:
Sen, S., Engler, A.J. & Discher, D.E. Cel. Mol. Bioeng. (2009) 2: 39. doi:10.1007/s12195-009-0052-z


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.


Substrate stiffnessCell prestress

Supplementary material

12195_2009_52_MOESM1_ESM.docx (67 kb)
Figure S1Cell displacements on thick matrices. Similar to trends observed with 〈ε〉, 〈u〉 scales with Egel in a power-law dependent manner, with stem cells being maximally mechanosensitive. (a) Lateral propagation of displacements for a stem cell on gels of different stiffness. The common, characteristic decay length is ~0.25 Rcell. (DOCX 67 kb)
12195_2009_52_MOESM2_ESM.docx (300 kb)
Figure S2Depth sensing: gel strain distributions. Individual interfacial strain components (〈εrr〉, 〈εzz〉, 〈εrz〉, 〈εθθ〉) plotted versus gel thickness for different values of Egel exhibit different transition regimes. (DOCX 300 kb)
12195_2009_52_MOESM3_ESM.docx (108 kb)
Figure S3Comparison of prestress distributions (soft gel). Uniform prestress distribution, used in this paper is compared with edge prestress and interfacial prestress to study differences in the displacement and strain maps. In comparison to edge prestress, where peak displacements and strain compare well with those obtained with uniform prestress, interfacial prestress produces very low displacement and strains. (DOCX 109 kb)

Copyright information

© Biomedical Engineering Society 2009

Authors and Affiliations

  • Shamik Sen
    • 1
  • Adam J. Engler
    • 2
  • Dennis E. Discher
    • 1
  1. 1.Biophysical Engineering LabUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Laboratory for Stem Cell Biology & BioengineeringUniversity of CaliforniaSan DiegoUSA