Abstract
A substantial body of work has been reported in which the mechanical properties of adherent cells were characterized using compression testing in tandem with computational modeling. However, a number of important issues remain to be addressed. In the current study, using computational analyses, the effect of cell compressibility on the force required to deform spread cells is investigated and the possibility that stiffening of the cell cytoplasm occurs during spreading is examined based on published experimental compression test data. The effect of viscoelasticity on cell compression is considered and difficulties in performing a complete characterization of the viscoelastic properties of a cell nucleus and cytoplasm by this method are highlighted. Finally, a non-linear force-deformation response is simulated using differing linear viscoelastic properties for the cell nucleus and the cell cytoplasm.
References
Baaijens, F. P. T., W. R. Trickey, T. A. Laursen, and F. Guilak. Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte. Ann. Biomed. Eng. 33:494–501, 2005.
Bausch, A., W. Möller, and E. Sackmann. Measurement of local viscoelasticity and forces in living cells by magnetic tweezers. Biophys. J. 76:573–579, 1999.
Bausch, A., F. Ziemann, A. Boulbitch, K. Jacobson, and E. Sackmann. Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry. Biophys. J. 75:2038–2049, 1998.
Caille, N., O. Thoumine, Y. Tardy, and J.-J. Meister. Contribution of the nucleus to the mechanical properties of endothelial cells. J. Biomech. 35:177–187, 2002.
Dahl, K., A. Engler, J. Pajerowski, and D. Discher. Power-law rheology of isolated nuclei with deformation mapping of nuclear substructures. Biophys. J. 89:2855–2864, 2005.
Darling, E., M. Topel, S. Zauscher, T. Vail, and F. Guilak. Viscoelastic properties of human mesenchymally-derived stem cells and primary osteoblasts, chondrocytes, and adipocytes. J. Biomech. 41:454–464, 2008.
Deshpande, V., R. McMeeking, and A. Evans. A bio-chemo-mechanical model for cell contractility. Proc. Natl Acad. Sci. 103:14015, 2006.
Guilak, F. Compression-induced changes in the shape and volume of the chondrocyte nucleus. J. Biomech. 28:1529–1541, 1995.
Guilak, F., G. R. Erickson, and H. P. Ting-Beall. The effects of osmotic stress on the viscoelastic and physical properties of articular chondrocytes. Biophys. J. 82:720–727, 2002.
Hayashi, K. Tensile properties and local stiffness of cells. In: Mechanics of Biological Tissue, edited by G. A. Holzapfel, and R. W. Ogden. Springer-Verlag, 2006, pp. 137–152.
Hochmuth, R. M. Micropipette aspiration of living cells. J. Biomech. 33:15–22, 2000.
Huang, W., B. Anvari, J. Torres, R. Lebaron, and K. Athanasiou. Temporal effects of cell adhesion on mechanical characteristics of the single chondrocyte. J. Orthop. Res. 21:88–95.
Icard-Arcizet, D., O. Cardoso, A. Richert, and S. Henon. Cell stiffening in response to external stress is correlated to actin recruitment. Biophys. J. 94:2906–2913, 2008.
Jones, W. R., H. P. Ting-Beall, G. M. Lee, S. S. Kelley, R. M. Hochmuth, and F. Guilak. Alterations in the Young’s modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage. J. Biomech. 32:119–127, 1999.
Koay, E. J., A. C. Shieh, and K. A. Athanasiou. Creep indentation of single cells. J. Biomech. Eng. 125:334–341, 2003.
Kole, T., Y. Tseng, I. Jiang, J. Katz, and D. Wirtz. Intracellular mechanics of migrating fibroblasts. Mol. Biol. Cell 16:328–338, 2005.
Leipzig, N., and K. Athanasiou. Static compression of single chondrocytes catabolically modifies single-cell gene expression. Biophys. J. 94:2412–2422, 2008.
Lo, C. M., H. B. Wang, M. Dembo, and Y. L. Wang. Cell movement is guided by the rigidity of the substrate. Biophys. J. 79:144–152, 2000.
McGarry, J. P., J. Fu, M. T. Yang, C. S. Chen, R. M. McMeeking, A. G. Evans, and V. S. Deshpande. Simulation of the contractile response of cells on an array of micro-posts. Phil. Trans. R. Soc. A 367:3477–3497, 2009.
McGarry, J. P., and P. E. McHugh. Modelling of in vitro chondrocyte detachment. J. Mech. Phys. Solids 56:1554–1565, 2008.
McGarry, J. P., B. P. Murphy, and P. E. McHugh. Computational mechanics modelling of cell–substrate contact during cyclic substrate deformation. J. Mech. Phys. Solids 53:2597–2637, 2005.
Nguyen, V., Z. Zhang, C. Thomas, Q. G. Wang, N. Kuiper, and A. El Haj. Mechanical properties of single chondrocytes and chondrons determined by microcompression technique and numerical modelling. Trans. Orthop. Res. Soc. 34:323, 2009.
Ofek, G., D. C. Wiltz, and K. A. Athanasiou. Contribution of the cytoskeleton to the compressive properties and recovery behavior of single cells. Biophys. J., 2009, accepted for publication.
Ofek, G., R. Natoli, and K. Athanasiou. In situ mechanical properties of the chondrocyte cytoplasm and nucleus. J. Biomech., 2009
Ohashi, T., Y. Ishii, Y. Ishikawa, T. Matsumoto, and M. Sato. Experimental and numerical analyses of local mechanical properties measured by atomic force microscopy for sheared endothelial cells. Biomed. Mater. Eng. 12:319–327, 2002.
Pathak, A., V. Deshpande, R. McMeeking, and A. Evans. The simulation of stress fibre and focal adhesion development in cells on patterned substrates. J. R. Soc. Interface 5:507–524, 2008.
Peeters, E. A. G., C. V. C. Bouten, C. W. J. Oomens, D. L. Bader, L. H. E. H. Snoeckx, and F. P. T. Baaijens. Anisotropic, three-dimensional deformation of single attached cells under compression. Ann. Biomed. Eng. 32:1443–1452, 2004.
Peeters, E. A. G., C. W. J. Oomens, C. V. C. Bouten, D. L. Bader, and F. P. T. Baaijens. Mechanical and failure properties of single attached cells under compression. J. Biomech. 38:1685–1693, 2005.
Peeters, E. A. G., C. W. J. Oomens, C. V. C. Bouten, D. L. Bader, and F. P. T. Baaijens. Viscoelastic properties of single attached cells under compression. J. Biomech. Eng. 127:237–243, 2005.
Pelham, R. J., and Y.-L. Wang. Cell locomotion and focal adhesions are regulated by substrate flexibility. Proc. Natl Acad. Sci. USA 94:13661–13665, 1997.
Roca-Cusachs, P., J. Alcaraz, R. Sunyer, J. Samitier, R. Farre, and D. Navajas. Micropatterning of single endothelial cell shape reveals a tight coupling between nuclear volume in G1 and proliferation. Biophys. J. 94:4984–4995, 2008.
Rowat, A., L. Foster, M. Nielsen, M. Weiss, and J. Ipsen. Characterization of the elastic properties of the nuclear envelope. J. R. Soc. Interface 2:63–69, 2005.
Sato, M., K. Nagayama, N. Kataoka, M. Sasaki, and K. Hane. Local mechanical properties measured by atomic force microscopy for cultured bovine endothelial cells exposed to shear stress. J. Biomech. 33:127–135, 2000.
Sato, M., D. P. Theret, L. T. Wheeler, N. Ohshima, and R. M. Nerem. Application of the micropipette technique to the measurement of cultured porcine aortic endothelial cell viscoelastic properties. J. Biomech. Eng. 112:263–268, 1990.
Shieh, A. C., and K. A. Athanasiou. Dynamic compression of single cells. Osteoarthritis Cartilage 15:328–334, 2007.
Shiu, C., Z. Zhang, and C. R. Thomas. A novel technique for the study of bacterial cell mechanical properties. Biotechnol. Tech. 13:707–713, 1999.
Tan, J. L., J. Tien, D. M. Pirone, D. S. Gray, K. Bhadriraju, and C. S. Chen. Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proc. Natl Acad. Sci. USA 100:1484–1489, 2003.
Theret, D., M. Levesque, M. Sato, R. Nerem, and L. Wheeler. The application of a homogeneous half-space model in the analysis of endothelial cell micropipette measurements. J. Biomech. Eng. 110:190, 1988.
Thomas, C., J. Collier, C. Sfeir, and K. Healy. Engineering gene expression and protein synthesis by modulation of nuclear shape. Proc. Natl Acad. Sci. 99:1972, 2002.
Thoumine, O. Time scale dependent viscoelastic and contractile regimes in fibroblasts probed by microplate manipulation. J. Cell Sci. 110:2109–2116, 1997.
Trickey, W., F. Baaijens, T. Laursen, L. Alexopoulos, and F. Guilak. Determination of the Poisson’s ratio of the cell: recovery properties of chondrocytes after release from complete micropipette aspiration. J. Biomech. 39:78–87, 2006.
Trickey, W., G. Lee, and F. Guilak. Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage. J. Orthop. Res. 18:891–898.
Trickey, W., T. Vail, and F. Guilak. The role of the cytoskeleton in the viscoelastic properties of human articular chondrocytes. J. Orthop. Res. 22:131–139, 2004.
Vaziri, A., H. Lee, and M. Kaazempur Mofrad. Deformation of the cell nucleus under indentation: mechanics and mechanisms. J. Mater. Res. 21:2126–2135, 2006.
Vaziri, A., and M. Mofrad. Mechanics and deformation of the nucleus in micropipette aspiration experiment. J. Biomech. 40:2053–2062, 2007.
Wakatsuki, T., B. Schwab, N. C. Thompson, and E. L. Elson. Effects of cytochalasin D and latrunculin B on mechanical properties of cells. J. Cell Sci. 114:1025–1036, 2001.
Wakatsuki, T., R. Wysolmerski, and E. Elson. Mechanics of cell spreading: role of myosin II. J. Cell Sci. 116:1617–1625, 2003.
Wang, J., P. Goldschmidt-Clermont, J. Wille, and F. Yin. Specificity of endothelial cell reorientation in response to cyclic mechanical stretching. J. Biomech. 34:1563–1572, 2001.
Wang, Q. G., B. Nguyen, C. Thomas, A. El Haj, Z. Zhang, and N. Kuiper. The Relationship between mechanical forces and gene expression of single chondrocytes and chondrons. Trans. Orthop. Res. Soc. 34:297, 2009.
Yeung, T., P. Georges, L. Flanagan, B. Marg, M. Ortiz, M. Funaki, N. Zahir, W. Ming, V. Weaver, and P. Janmey. Effects of substrate stiffness on cell morphology, cytoskeletal structure, and adhesion. Cell Motil. Cytoskeleton 60:24–34, 2005.
Acknowledgments
The author would like to thank Prof. K.A. Athanasiou, Dr. G. Ofek and Prof. P.E. McHugh for insightful discussions. Funding was provided in part by the Science Foundation Ireland Research Frontiers Programme (SFI-RFP/ENM1726), and in part by an Irish Council for Science Engineering and Technology (IRCSET) Postdoctoral Fellowship.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
McGarry, J.P. Characterization of Cell Mechanical Properties by Computational Modeling of Parallel Plate Compression. Ann Biomed Eng 37, 2317–2325 (2009). https://doi.org/10.1007/s10439-009-9772-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10439-009-9772-4