Cellular and Molecular Bioengineering

, Volume 3, Issue 1, pp 68–75 | Cite as

Substrate Stiffness and Cell Area Predict Cellular Traction Stresses in Single Cells and Cells in Contact

Article

Abstract

Cells generate traction stresses against their substrate during adhesion and migration, and traction stresses are used in part by the cell to sense the substrate. While it is clear that traction stresses, substrate stiffness, and cell area are related, it is unclear whether or how area and substrate stiffness affect force generation in cells. Moreover, multiple studies have investigated traction stresses of single cells, but few have focused on forces exerted by cells in contact, which more closely mimics the in vivo environment. Here, cellular traction forces were measured where cell area was modulated by ligand density or substrate stiffness. We coupled these measurements with a multilinear regression model to show that both projected cell area and underlying substrate stiffness are significant predictors of traction forces in endothelial cells, and interestingly, substrate ligand density is not. We further explored the effect of cell–cell contact on the interplay between cell area, substrate stiffness, and force generation and found that again both area and stiffness play a significant role in cell force generation. These data indicate that cellular traction force cannot be determined by cell area alone and that underlying substrate stiffness is a significant contributor to traction force generation.

Keywords

Endothelial cell Polyacrylamide gel Linear regression model Cell–cell interaction Traction force 

References

  1. 1.
    An, S. S., et al. Do biophysical properties of the airway smooth muscle in culture predict airway hyperresponsiveness? Am. J. Respir. Cell Mol. Biol. 35(1):55–64, 2006.CrossRefGoogle Scholar
  2. 2.
    Califano, J. P., and C. A. Reinhart-King. A balance of substrate mechanics and matrix chemistry regulates endothelial cell network assembly. Cel. Mol. Bioeng. 1(2–3):122–132, 2008.CrossRefGoogle Scholar
  3. 3.
    Califano, J. P., and C. A. Reinhart-King. Exogenous and endogenous force regulation of endothelial cell behavior. J. Biomech., 2009. doi:10.1016/j.jbiomech.2009.09.012.
  4. 4.
    Chen, C. S. Mechanotransduction—a field pulling together? J. Cell Sci. 121(Pt 20):3285–3292, 2008.CrossRefGoogle Scholar
  5. 5.
    Dembo, M., et al. Imaging the traction stresses exerted by locomoting cells with the elastic substratum method. Biophys. J. 70(4):2008–2022, 1996.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Dembo, M., and Y. L. Wang. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys. J. 76(4):2307–2316, 1999.CrossRefGoogle Scholar
  7. 7.
    du Roure, O., et al. Force mapping in epithelial cell migration. Proc. Natl Acad. Sci. USA 102(7):2390–2395, 2005.CrossRefGoogle Scholar
  8. 8.
    Engler, A., et al. Substrate compliance versus ligand density in cell on gel responses. Biophys. J. 86(1 Pt 1):617–628, 2004.CrossRefGoogle Scholar
  9. 9.
    Engler, A., L. Richert, J. Wong, C. Picart, and D. Discher. Surface probe measurements of the elasticity of sectioned tissue, thin gels and polyelectrolyte multilayer films: correlations between substrate stiffness and cell adhesion. Surf. Sci. 570:142–154, 2004.CrossRefGoogle Scholar
  10. 10.
    Georges, P. C., and P. A. Janmey. Cell type-specific response to growth on soft materials. J. Appl. Physiol. 98(4):1547–1553, 2005.CrossRefGoogle Scholar
  11. 11.
    Guo, W. H., et al. Substrate rigidity regulates the formation and maintenance of tissues. Biophys. J. 90(6):2213–2220, 2006.CrossRefGoogle Scholar
  12. 12.
    Lemmon, C. A., C. S. Chen, and L. H. Romer. Cell traction forces direct fibronectin matrix assembly. Biophys. J. 96(2):729–738, 2009.CrossRefGoogle Scholar
  13. 13.
    Lemmon, C. A., et al. Shear force at the cell-matrix interface: enhanced analysis for microfabricated post array detectors. Mech. Chem. Biosyst. 2(1):1–16, 2005.Google Scholar
  14. 14.
    Li, B., et al. Spatial patterning of cell proliferation and differentiation depends on mechanical stress magnitude. J. Biomech. 42(11):1622–1627, 2009.CrossRefGoogle Scholar
  15. 15.
    Li, Y., Z. B. Hu, and C. F. Li. New method for measuring poisson ratio in polymer gels. J. Appl. Polym. Sci. 50(6):1107–1111, 1993.CrossRefGoogle Scholar
  16. 16.
    Lo, C. M., et al. Cell movement is guided by the rigidity of the substrate. Biophys. J. 79(1):144–152, 2000.CrossRefGoogle Scholar
  17. 17.
    Marganski, W. A., M. Dembo, and Y. L. Wang. Measurements of cell-generated deformations on flexible substrata using correlation-based optical flow. Methods Enzymol. 361:197–211, 2003.CrossRefGoogle Scholar
  18. 18.
    Munevar, S., Y. Wang, and M. Dembo. Traction force microscopy of migrating normal and H-ras transformed 3T3 fibroblasts. Biophys. J. 80(4):1744–1757, 2001.CrossRefGoogle Scholar
  19. 19.
    Nelson, C. M., et al. Emergent patterns of growth controlled by multicellular form and mechanics. Proc. Natl Acad. Sci. USA 102(33):11594–11599, 2005.CrossRefGoogle Scholar
  20. 20.
    Ott, R. L., and M. Longnecker. An Introduction to Statistical Methods and Data Analysis. Pacific Grove, CA: Duxbury Press, 2001, 1184 pp.Google Scholar
  21. 21.
    Paszek, M. J., and V. M. Weaver. The tension mounts: mechanics meets morphogenesis and malignancy. J. Mammary Gland. Biol. Neoplasia 9(4):325–342, 2004.CrossRefGoogle Scholar
  22. 22.
    Paszek, M. J., et al. Tensional homeostasis and the malignant phenotype. Cancer Cell 8(3):241–254, 2005.CrossRefMathSciNetGoogle Scholar
  23. 23.
    Pless, D. D., et al. Specific cell adhesion to immobilized glycoproteins demonstrated using new reagents for protein and glycoprotein immobilization. J. Biol. Chem. 258(4):2340–2349, 1983.Google Scholar
  24. 24.
    Reinhart-King, C. A. Endothelial cell adhesion and migration. Methods Enzymol. 443:45–64, 2008.CrossRefGoogle Scholar
  25. 25.
    Reinhart-King, C. A., M. Dembo, and D. A. Hammer. Endothelial cell traction forces on RGD-derivatized polyacrylamide substrata. Langmuir 19(5):1573–1579, 2003.CrossRefGoogle Scholar
  26. 26.
    Reinhart-King, C. A., M. Dembo, and D. A. Hammer. The dynamics and mechanics of endothelial cell spreading. Biophys. J. 89(1):676–689, 2005.CrossRefGoogle Scholar
  27. 27.
    Reinhart-King, C. A., M. Dembo, and D. A. Hammer. Cell-cell mechanical communication through compliant substrates. Biophys. J. 95(12):6044–6051, 2008.CrossRefGoogle Scholar
  28. 28.
    Tsai, J., and L. Kam. Rigidity-dependent cross talk between integrin and cadherin signaling. Biophys. J. 96(6):L39–L41, 2009.CrossRefGoogle Scholar
  29. 29.
    Wang, N., et al. Micropatterning tractional forces in living cells. Cell Motil. Cytoskeleton 52(2):97–106, 2002.CrossRefGoogle Scholar
  30. 30.
    Wang, Y., et al. Integrins regulate VE-cadherin and catenins: dependence of this regulation on Src, but not on Ras. Proc. Natl Acad. Sci. USA 103(6):1774–1779, 2006.CrossRefGoogle Scholar
  31. 31.
    Wang, Y. L., and R. J. Pelham, Jr. Preparation of a flexible, porous polyacrylamide substrate for mechanical studies of cultured cells. Methods Enzymol. 298:489–496, 1998.CrossRefGoogle Scholar
  32. 32.
    Yeung, T., et al. Effects of substrate stiffness on cell morphology, cytoskeletal structure, and adhesion. Cell Motil. Cytoskeleton 60(1):24–34, 2005.CrossRefGoogle Scholar
  33. 33.
    Zemel, A., and S. A. Safran. Active self-polarization of contractile cells in asymmetrically shaped domains. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2 Pt 1):021905, 2007.Google Scholar

Copyright information

© Biomedical Engineering Society 2010

Authors and Affiliations

  • Joseph P. Califano
    • 1
  • Cynthia A. Reinhart-King
    • 1
  1. 1.Department of Biomedical EngineeringCornell UniversityIthacaUSA

Personalised recommendations