Abstract
The effect of the nucleus on the cell mechanical behavior was investigated based on the dynamic indentation response of cells under a spherical tip. A “two-component” cell model (including cytoplasm and nucleus) is used, and the dynamic indentation behavior is studied by a semiempirical method, which is established based on fitting the numerical simulation results of the quasi-static indentation response of cells. We found that the “routine analysis” (based on the Hertz’s contact solution of homogeneous model) significantly overestimated the nucleus effect on the overall cell indentation response due to the effects of the Hertz contact radius and the substrate stiffening. These effects are significantly stronger in the “two-component” cell model than in the homogeneous model. The inaccuracy created by the “routine analysis” slightly increases with the modulus ratio of nucleus to cytoplasm and the volume fraction of nucleus. Finally, the error sensitivity to the geometrical parameters used in the model is discussed, which shows the indentation analysis is not very sensitive to these parameters, and the reasonable assumptions for these parameters are effective. This systematic analysis can provide a useful guideline to understanding the mechanical behavior of cells and nuclei.
Similar content being viewed by others
References
Bursa J, Lebis R et al (2006) FE models of stress-strain states in vascular smooth muscle cell. Technol Health Care 14(4–5): 311–320
Caille N, Tardy Y et al (1998) Assessment of strain field in endothelial cells subjected to uniaxial deformation of their substrate. Ann Biomed Eng 26(3): 409–416
Caille N, Thoumine O et al (2002) Contribution of the nucleus to the mechanical properties of endothelial cells. J Biomech 35: 177–187
Callies C, Schön P et al (2009) Simultaneous mechanical stiffness and electrical potential measurements of living vascular endothelial cells using combined atomic force and epifluorescence microscopy. Nanotechnology 20: 175104
Cao GX, Chandra N (2010) Evaluation of biological cell properties using dynamic indentation measurement. Phys Rev E 81(2): 021924
Carl P, Schillers H (2008) Elasticity measurement of living cells with an atomic force microscope: data acquisition and processing. Pflugers Arch Eur J Physiol 457: 551–559
Cross SE, Jin Y et al (2007) Nanomechanical analysis of cells from cancer patients. Nat Nanotechnol 2: 780–783
Dahl KN, Engler AJ et al (2005) Power-law rheology of isolated nuclei with deformation mapping of nuclear substructures. Biophys J 89(4): 2855–2864
Darling EM, Topel M et al (2008) Viscoelastic properties of human mesenchymally-derived stem cells and primary osteoblasts, chondrocytes, and adipocytes. J Biomech 41(2): 454–464
Deguchi S, Maeda K et al (2005) Flow-induced hardening of endothelial nucleus as an intracellular stress-bearing organelle. J Biomech 38: 1751–1759
Deguchi S, Yano M et al (2007) Assessment of the mechanical properties of the nucleus inside a spherical endothelial cell based on microtensile testing. J Mech Mater Struct 2(6): 1087–1102
Dimitriadis EK, Horkay F et al (2002) Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys J 82(5): 2798–2810
Dong C, Skalak R et al (1991) Cytoplasmic rheology of passive neutrophils. Biorheology 28(6): 557–567
Ferko MC, Bhatnagar A et al (2007) Finite-element stress analysis of a multicomponent model of sheared and focally-adhered endothelial cells. Ann Biomed Eng 35(2): 208–223
Guilak F, Tedrow JR et al (2000) Viscoelastic properties of the cell nucleus. Biochem Biophys Res Commun 269: 781–786
Gupta S, Carrillo F et al (2005) Simulated soft tissue nanoindentation: a finite element study. J Mater Res 20(8): 1979–1994
Hansen JC, Lim JY et al (2006) Effect of surface nanoscale topography on elastic modulus of individual osteoblastic cells as determined by atomic force microscopy. J Biomech 40: 2865–2871
Herbert EG, Oliver WC et al (2008) Nanoindentation and the dynamic characterization of viscoelastic solids. J Phys D Appl Phys 41(7): 074021
Jean RP, Chen CS et al (2005) Finite-element analysis of the adhesion-cytoskeleton-nucieus mechanotransduction pathway during endothelial cell rounding: axisymmetric model. J Biomech Eng Trans ASME 127(4): 594–600
Johnson KL (1985) Contact mechanics. Cambridge University Press, Cambridge
Kang I, Panneerselvam D et al (2008) Changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor-alpha. Biophys J 94(8): 3273–3285
Karcher H, Lammerding J et al (2003) A three-dimensional viscoelastic model for cell deformation with experimental verification. Biophys J 85(5): 3336–3349
Kuznetsova TG, Starodubtseva MN et al (2007) Atomic force microscopy probing of cell elasticity. Micron 38(8): 824–833
Lammerding J, Dahl KN et al (2007) Nuclear mechanics and methods. Cell Mech 83: 269–294
Leipzig ND, Athanasiou KA (2008) Static compression of single chondrocytes catabolically modifies single-cell gene expression. Biophys J 94(6): 2412–2422
Lim CT, Zhou EH et al (2006) Mechanical models for living cells—a review. J Biomech 39: 195–216
Lu YB, Franze K et al (2006) Viscoelastic properties of individual glial cells and neurons in the CNS. Proc Natl Acad Sci U S A 103(47): 17759–17764
Lulevich V, Zink R et al (2006) Cell mechanics using atomic force microscopy-based single-cell compression. Langmuir 22: 8151–8155
Mahaffy RE, Park S et al (2004) Quantitative analysis of the viscoelastic properties of thin regions of fibroblasts using atomic force microscopy. Biophys J 86(3): 1777–1793
Mahaffy RE, Shih CK et al (2000) Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells. Phys Rev Lett 85(4): 880–883
Maniotis AJ, Chen CS et al (1997) Demonstration of mechanical connections between integrins cytoskeletal filaments, and nucleoplasm that stabilize nuclear structure. Proc Natl Acad Sci U S A 94(3): 849–854
Odegard GM, Gates T et al (2005) Characterization of viscoelastic properties of polymeric materials through nanoindentation. Exp Mech 45(2): 130–136
Ofek G, Natoli RM et al (2009) In situ mechanical properties of the chondrocyte cytoplasm and nucleus. J Biomech 42(7): 873–877
Ohashi T, Ishii Y et al (2002) Experimental and numerical analyses of local mechanical properties measured by atomic force microscopy for sheared endothelial cells. Bio-Med Mater Eng 12(3): 319–327
Pajerowski JD, Dahl KN et al (2007) Physical plasticity of the nucleus in stem cell differentiation. Proc Natl Acad Sci U S A 104(40): 15619–15624
Radmacher M (2007) Studying the mechanics of cellular processes by atomic force microscopy. Methods Cell Biol 83: 347–372
Rico F, Roca-Cusachs P et al (2005) Probing mechanical properties of living cells by atomic force microscopy with blunted pyramidal cantilever tips. Phys Rev E Stat Nonlin Soft Matter Phys 72(2 Pt 1): 021914
Rowat AC, Lammerding J et al (2008) Towards an integrated understanding of the structure and mechanics of the cell nucleus. Bioessays 30(3): 226–236
Rowat AC, Lammerding J et al (2006) Mechanical properties of the cell nucleus and the effect of emerin deficiency. Biophys J 91(12): 4649–4664
Tseng Y, Lee JSH et al (2004) Micro-organization and visco-elasticity of the interphase nucleus revealed by particle nanotracking. J Cell Sci 117(10): 2159–2167
Vaziri A, Lee H et al (2006) Deformation of the cell nucleus under indentation: mechanics and mechanisms. J Mater Res 21(8): 2126–2135
Vaziri A, Mofrad MRK (2007) Mechanics and deformation of the nucleus in micropipette aspiration experiment. J Biomech 40(9): 2053–2062
White CC, Vanlandingham MR et al (2005) Viscoelastic characterization of polymers using instrumented indentation. II. Dynamic testing. J Polym Sci Part B Polym Phys 43(14): 1812–1824
Zhang CY, Zhang YW (2007) Effects of membrane pre-stress and intrinsic viscoelasticity on nanoindentation of cells using AFM. Philos Mag 87(23): 3415–3435
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cao, G., Sui, J. & Sun, S. Evaluating the nucleus effect on the dynamic indentation behavior of cells. Biomech Model Mechanobiol 12, 55–66 (2013). https://doi.org/10.1007/s10237-012-0381-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-012-0381-z