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A combined experimental atomic force microscopy-based nanoindentation and computational modeling approach to unravel the key contributors to the time-dependent mechanical behavior of single cells

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Abstract

Cellular responses to mechanical stimuli are influenced by the mechanical properties of cells and the surrounding tissue matrix. Cells exhibit viscoelastic behavior in response to an applied stress. This has been attributed to fluid flow-dependent and flow-independent mechanisms. However, the particular mechanism that controls the local time-dependent behavior of cells is unknown. Here, a combined approach of experimental AFM nanoindentation with computational modeling is proposed, taking into account complex material behavior. Three constitutive models (porohyperelastic, viscohyperelastic, poroviscohyperelastic) in tandem with optimization algorithms were employed to capture the experimental stress relaxation data of chondrocytes at 5 % strain. The poroviscohyperelastic models with and without fluid flow allowed through the cell membrane provided excellent description of the experimental time-dependent cell responses (normalized mean squared error (NMSE) of 0.003 between the model and experiments). The viscohyperelastic model without fluid could not follow the entire experimental data that well (NMSE = 0.005), while the porohyperelastic model could not capture it at all (NMSE = 0.383). We also show by parametric analysis that the fluid flow has a small, but essential effect on the loading phase and short-term cell relaxation response, while the solid viscoelasticity controls the longer-term responses. We suggest that the local time-dependent cell mechanical response is determined by the combined effects of intrinsic viscoelasticity of the cytoskeleton and fluid flow redistribution in the cells, although the contribution of fluid flow is smaller when using a nanosized probe and moderate indentation rate. The present approach provides new insights into viscoelastic responses of chondrocytes, important for further understanding cell mechanobiological mechanisms in health and disease.

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References

  • Ateshian GA, Costa KD, Hung CT (2007) A theoretical analysis of water transport through chondrocytes. Biomech Model Mechanobiol 6:91–101. doi:10.1007/s10237-006-0039-9

    Article  Google Scholar 

  • Bidhendi AJ, Korhonen RK (2012) A finite element study of micropipette aspiration of single cells: effect of compressibility. Comput Math Methods Med 2012:192618. doi:10.1155/2012/192618

  • Biot MA (1941) Consolidation settlement under a rectangular load distribution. J Appl Phys 12:578–581. doi:10.1063/1.1712921

    Article  MATH  Google Scholar 

  • Carl P, Schillers H (2008) Elasticity measurement of living cells with an atomic force microscope: data acquisition and processing. Pflugers Arch 457:551–9. doi:10.1007/s00424-008-0524-3

    Article  Google Scholar 

  • Chahine NO, Blanchette C, Thomas CB et al (2013) Effect of age and cytoskeletal elements on the indentation-dependent mechanical properties of chondrocytes. PLoS One 8:e61651. doi:10.1371/journal.pone.0061651

    Article  Google Scholar 

  • Charras GT, Horton MA (2002) Determination of cellular strains by combined atomic force microscopy and finite element modeling. Biophys J 83:858–79. doi:10.1016/S0006-3495(02)75214-4

    Article  Google Scholar 

  • Chiravarambath S, Simha NK, Namani R, Lewis JL (2009) Poroviscoelastic cartilage properties in the mouse from indentation. J Biomech Eng 131:011004. doi:10.1115/1.3005199

    Article  Google Scholar 

  • Costa KD, Ho MY, Hung CT (2003) Multi-scale measurement of mechanical properties of soft samples with atomic force microscopy. In: Summer bioengineering conference

  • Darling EM, Zauscher S, Guilak F (2006) Viscoelastic properties of zonal articular chondrocytes measured by atomic force microscopy. Osteoarthr Cartil 14:571–579. doi:10.1016/j.joca.2005.12.003

    Article  Google Scholar 

  • Darling EM, Zauscher S, Block JA, Guilak F (2007) A thin-layer model for viscoelastic, stress relaxation testing of cells using atomic force microscopy: do cell properties reflect metastatic potential? Biophys J 92:1784–91. doi:10.1529/biophysj.106.083097

  • Darling EM, Topel M, Zauscher S et al (2008) Viscoelastic properties of human mesenchymally-derived stem cells and primary osteoblasts, chondrocytes, and adipocytes. J Biomech 41:454–64. doi:10.1016/j.jbiomech.2007.06.019

    Article  Google Scholar 

  • Darling EM, Pritchett PE, Evans BA et al (2009) Mechanical properties and gene expression of chondrocytes on micropatterned substrates following dedifferentiation in monolayer. Cell Mol Bioeng 2:395–404. doi:10.1007/s12195-009-0077-3

    Article  Google Scholar 

  • Deshpande VS, McMeeking RM, Evans AG (2006) A bio-chemo-mechanical model for cell contractility. Proc Natl Acad Sci U S A 103:14015–20. doi:10.1073/pnas.0605837103

  • Digel I, Maggakis-Kelemen C, Zerlin KF et al (2006) Body temperature-related structural transitions of monotremal and human hemoglobin. Biophys J 91:3014–21. doi:10.1529/biophysj.106.087809

    Article  Google Scholar 

  • Dimitriadis EK, Horkay F, Maresca J et al (2002) Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys J 82:2798–810. doi:10.1016/S0006-3495(02)75620-8

    Article  Google Scholar 

  • DiSilvestro MR, Suh JK (2001) A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation, and confined compression. J Biomech 34:519–25. doi:10.1016/S0021-9290(00)00224-4

    Article  Google Scholar 

  • Dowling EP, Ronan W, McGarry JP (2013) Computational investigation of in situ chondrocyte deformation and actin cytoskeleton remodelling under physiological loading. Acta Biomater 9:5943–55. doi:10.1016/j.actbio.2012.12.021

  • Florea C, Mononen ME, Fick JM et al (2015) How does the actin cytoskeleton modulate the local elastic and time-dependent properties of chondrocytes during AFM nanoindentation? Trans Orthop Res Soc. 40:0144

    Google Scholar 

  • Galli M, Comley KSC, Shean TAV, Oyen ML (2011) Viscoelastic and poroelastic mechanical characterization of hydrated gels. J Mater Res 24:973–979. doi:10.1557/jmr.2009.0129

    Article  Google Scholar 

  • Grodzinsky AJ (2011) Fields, forces, and flows in biological systems, 1st edn. Garland Science. Taylor and Francis, New York, 259–272

  • Grodzinsky AJ, Levenston ME, Jin M, Frank EH (2000) Cartilage tissue remodeling in response to mechanical forces. Annu Rev Biomed Eng 2:691–713. doi:10.1146/annurev.bioeng.2.1.691

    Article  Google Scholar 

  • Guilak F (2000) The deformation behavior and viscoelastic properties of chondrocytes in articular cartilage. Biorheology 37:27–44. doi:10.1115/1.4000938

    Google Scholar 

  • Guilak F, Tedrow JR, Burgkart R (2000) Viscoelastic properties of the cell nucleus. Biochem Biophys Res Commun 269:781–6. doi:10.1006/bbrc.2000.2360

    Article  Google Scholar 

  • Haider MA, Guilak F (2000) An axisymmetric boundary integral model for incompressible linear viscoelasticity: application to the micropipette aspiration contact problem. J Biomech Eng 122:236–44. doi:10.1115/1.4000938

    Article  Google Scholar 

  • Harris AR, Charras GT (2011) Experimental validation of atomic force microscopy-based cell elasticity measurements. Nanotechnology 22:345102. doi:10.1088/0957-4484/22/34/345102

    Article  Google Scholar 

  • Hochmuth RM (2000) Micropipette aspiration of living cells. J Biomech 33:15–22. doi:10.1016/S0021-9290(99)00175-X

  • Janmey PA, McCulloch CA (2007) Cell mechanics: integrating cell responses to mechanical stimuli. Annu Rev Biomed Eng 9:1–34. doi:10.1146/annurev.bioeng.9.060906.151927

    Article  Google Scholar 

  • Janovjak H, Struckmeier J, Müller DJ (2005) Hydrodynamic effects in fast AFM single-molecule force measurements. Eur Biophys J 34:91–6. doi:10.1007/s00249-004-0430-3

    Article  Google Scholar 

  • Jones WR, Ting-Beall HP, Lee GM et al (1999) Alterations in the Young’s modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage. J Biomech 32:119–27. doi:10.1016/S0021-9290(98)00166-3

    Article  Google Scholar 

  • Jortikka MO, Inkinen RI, Tammi MI et al (1997) Immobilisation causes longlasting matrix changes both in the immobilised and contralateral joint cartilage. Ann Rheum Dis 56:255–61. doi:10.1136/ard.56.4.255

    Article  Google Scholar 

  • Koay EJ, Shieh AC, Athanasiou KA (2003) Creep indentation of single cells. J Biomech Eng 125:334–41. doi:10.1115/1.1572517

    Article  Google Scholar 

  • Korhonen RK, Laasanen MS, Töyräs J et al (2002) Comparison of the equilibrium response of articular cartilage in unconfined compression, confined compression and indentation. J Biomech 35:903–9

    Article  Google Scholar 

  • Korhonen RK, Han SK, Herzog W (2010) Osmotic loading of in situ chondrocytes in their native environment. Mol Cell Biomech 7:125–34

    Google Scholar 

  • Ladjal H, Hanus JL, Pillarisetti A, et al (2009) Atomic force microscopy-based single-cell indentation: Experimentation and finite element simulation. In: 2009 IEEE/RSJ international conference on intelligent robots and systems. IEEE, 1326–1332. doi:10.1109/IROS.2009.5354351

  • Leipzig ND, Athanasiou KA (2005) Unconfined creep compression of chondrocytes. J Biomech 38:77–85. doi:10.1016/j.jbiomech.2004.03.013

    Article  Google Scholar 

  • Li LP, Herzog W (2006) Arthroscopic evaluation of cartilage degeneration using indentation testing-influence of indenter geometry. Clin Biomech (Bristol, Avon) 21:420–426. doi:10.1016/j.clinbiomech.2005.12.010

    Article  Google Scholar 

  • Mäkelä JTA, Korhonen RK (2016) Highly nonlinear stress relaxation response of articular cartilage in indentation—importance of collagen nonlinearity. J Biomech. doi:10.1016/j.jbiomech.2016.04.002

  • Moeendarbary E, Valon L, Fritzsche M et al (2013) The cytoplasm of living cells behaves as a poroelastic material. Nat Mater 12:253–261. doi:10.1038/nmat3517

    Article  Google Scholar 

  • Mow VC, Kuei SC, Lai WM, Armstrong CG (1980) Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J Biomech Eng 102:73–84. doi:10.1115/1.3138202

    Article  Google Scholar 

  • Mustata M, Ritchie K, McNally HA (2010) Neuronal elasticity as measured by atomic force microscopy. J Neurosci Methods 186:35–41. doi:10.1016/j.jneumeth.2009.10.021

    Article  Google Scholar 

  • Ng L, Hung H-H, Sprunt A et al (2007) Nanomechanical properties of individual chondrocytes and their developing growth factor-stimulated pericellular matrix. J Biomech 40:1011–23. doi:10.1016/j.jbiomech.2006.04.004

    Article  Google Scholar 

  • Nguyen TD, Oloyede A, Gu YT (2015b) A poroviscohyperelastic model for numerical analysis of mechanical behavior of single chondrocyte. Comput Methods Biomech Biomed Eng 1–11. doi:10.1080/10255842.2014.996875

  • Nguyen BV, Wang QG, Kuiper NJ et al (2010) Biomechanical properties of single chondrocytes and chondrons determined by micromanipulation and finite-element modelling. J R Soc Interface 7:1723–33. doi:10.1098/rsif.2010.0207

    Article  Google Scholar 

  • Nguyen TD, Gu YT, Oloyede A, Senadeera W (2014) Analysis of strain-rate dependent mechanical behavior of single chondrocyte: a finite element study. Int J Comput Methods 11:1–20. doi:10.1142/S0219876213440052

    MathSciNet  Google Scholar 

  • Nguyen TD, Oloyede A, Singh S, Gu YT (2015a) Microscale consolidation analysis of relaxation behavior of single living chondrocytes subjected to varying strain-rates. J Mech Behav Biomed Mater 49:343–354. doi:10.1016/j.jmbbm.2015.05.003

  • Nguyen TD, Gu YT (2014) Determination of strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes using atomic force microscopy and inverse finite element analysis. J Biomech Eng 136:101004. doi:10.1115/1.4028098

    Article  Google Scholar 

  • Nguyen TD, Gu YT (2014) Exploration of mechanisms underlying the strain-rate-dependent mechanical property of single chondrocytes. Appl Phys Lett 104:183701. doi:10.1063/1.4876056

    Article  Google Scholar 

  • Nia HT, Han L, Li Y et al (2011) Poroelasticity of cartilage at the nanoscale. Biophys J 101:2304–13. doi:10.1016/j.bpj.2011.09.011

    Article  Google Scholar 

  • Ofek G, Natoli RM, Athanasiou KA (2009) In situ mechanical properties of the chondrocyte cytoplasm and nucleus. J Biomech 42:873–7. doi:10.1016/j.jbiomech.2009.01.024

    Article  Google Scholar 

  • Oswald ES, Chao P-HG, Bulinski JC et al (2008) Dependence of zonal chondrocyte water transport properties on osmotic environment. Cell Mol Bioeng 1:339–348. doi:10.1007/s12195-008-0026-6

    Article  Google Scholar 

  • Park S, Costa KD, Ateshian GA (2004) Microscale frictional response of bovine articular cartilage from atomic force microscopy. J Biomech 37:1679–87. doi:10.1016/j.jbiomech.2004.02.017

    Article  Google Scholar 

  • Pogoda K, Jaczewska J, Wiltowska-Zuber J et al (2012) Depth-sensing analysis of cytoskeleton organization based on AFM data. Eur Biophys J 41:79–87. doi:10.1007/s00249-011-0761-9

    Article  Google Scholar 

  • Qu CJ, Karjalainen HM, Helminen HJ, Lammi MJ (2006) The lack of effect of glucosamine sulphate on aggrecan mRNA expression and (35)S-sulphate incorporation in bovine primary chondrocytes. Biochim Biophys Acta 1762:453–9. doi:10.1016/j.bbadis.2006.01.005

    Article  Google Scholar 

  • Rico F, Roca-Cusachs P, Gavara N et al (2005) Probing mechanical properties of living cells by atomic force microscopy with blunted pyramidal cantilever tips. Phys Rev E 72:021914. doi:10.1103/PhysRevE.72.021914

    Article  Google Scholar 

  • Rivlin RS (1948) Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Philos Trans R Soc A Math Phys Eng Sci 241:379–397. doi:10.1098/rsta.1948.0024

    Article  MathSciNet  MATH  Google Scholar 

  • Sader JE, Chon JWM, Mulvaney P (1999) Calibration of rectangular atomic force microscope cantilevers. Rev Sci Instrum 70:3967. doi:10.1063/1.1150021

    Article  Google Scholar 

  • Seifzadeh A, Wang J, Oguamanam DCD, Papini M (2011) A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion. J Biomech Eng 133:081004. doi:10.1115/1.4004832

    Article  Google Scholar 

  • Shieh AC, Athanasiou KA (2006) Biomechanics of single zonal chondrocytes. J Biomech 39:1595–602. doi:10.1016/j.jbiomech.2005.05.002

    Article  Google Scholar 

  • Shin D, Athanasiou K (1999) Cytoindentation for obtaining cell biomechanical properties. J Orthop Res 17:880–90. doi:10.1002/jor.1100170613

    Article  Google Scholar 

  • Simeonova M, Wachner D, Gimsa J (2002) Cellular absorption of electric field energy: influence of molecular properties of the cytoplasm. Bioelectrochemistry 56:215–218. doi:10.1016/S1567-5394(02)00010-5

    Article  Google Scholar 

  • Spilker RL, Suh JK, Mow VC (1992) A finite element analysis of the indentation stress relaxation response of linear biphasic articular cartilage. J Biomech Eng 114:191–201. doi:10.1115/1.2891371

    Article  Google Scholar 

  • Steklov N, Srivastava A, Sung KLP et al (2009) Aging-related differences in chondrocyte viscoelastic properties. Mol Cell Biomech 6:113–9

    Google Scholar 

  • Stolz M, Raiteri R, Daniels AU et al (2004) Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy. Biophys J 86:3269–83. doi:10.1016/S0006-3495(04)74375-1

    Article  Google Scholar 

  • Stossel TP (1993) On the crawling of animal cells. Science 260:1086–94. doi:10.1126/science.8493552

    Article  Google Scholar 

  • Suh JK, DiSilvestro MR (1999) Biphasic poroviscoelastic behavior of hydrated biological soft tissue. J Appl Mech 66:528. doi:10.1115/1.2791079

    Article  Google Scholar 

  • Tanska P, Turunen SM, Han SK et al (2013) Superficial collagen fibril modulus and pericellular fixed charge density modulate chondrocyte volumetric behaviour in early osteoarthritis. Comput Math Methods Med 2013:164146. doi:10.1155/2013/164146

    Article  Google Scholar 

  • Tee SY, Fu J, Chen CS, Janmey PA (2011) Cell shape and substrate rigidity both regulate cell stiffness. Biophys J 100:L25–7. doi:10.1016/j.bpj.2010.12.3744

    Article  Google Scholar 

  • Trickey WR, Lee GM, Guilak F (2000) Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage. J Orthop Res 18:891–8. doi:10.1002/jor.1100180607

  • Trickey WR, Vail TP, Guilak F (2004) The role of the cytoskeleton in the viscoelastic properties of human articular chondrocytes. J Orthop Res 22:131–9. doi:10.1016/S0736-0266(03)00150-5

    Article  Google Scholar 

  • Trickey WR, Baaijens FPT, Laursen TA et al (2006) Determination of the Poisson’s ratio of the cell: recovery properties of chondrocytes after release from complete micropipette aspiration. J Biomech 39:78–87. doi:10.1016/j.jbiomech.2004.11.006

  • Turi A, Lu RC, Lin P-S (1981) Effect of heat on the microtubule disassembly and its relationship to body temperatures. Biochem Biophys Res Commun 100:584–590. doi:10.1016/S0006-291X(81)80216-1

    Article  Google Scholar 

  • Vargas-Pinto R, Gong H, Vahabikashi A, Johnson M (2013) The effect of the endothelial cell cortex on atomic force microscopy measurements. Biophys J 105:300–9. doi:10.1016/j.bpj.2013.05.034

    Article  Google Scholar 

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Acknowledgments

The authors gratefully acknowledge support from the Academy of Finland (Grant No. 286526), Sigrid Juselius Foundation, Finland, European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013) ERC Grant Agreement No. 281180, Doctoral Programme in Medical Physics and Engineering and CSC-IT Center for Science for providing computational resources and technical support. Authors thank Atria Lihakunta Oyj for supplying fresh bovine joints. Janne Ylärinne, M.Sc., is acknowledged for the cell culturing, Janne Mäkelä, M.Sc., and Jarkko Iivarinen, Ph.D., for technical assistance with the optimization code and Ari Halvari, M.Sc., for technical assistance with AFM measurements.

Funding   The funding sources had no involvement in the study design, collection, analysis or interpretation of data, writing of the manuscript or in the decision to submit the manuscript for publication

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Authors and Affiliations

  1. Department of Applied Physics, University of Eastern Finland, POB 1627, 70211, Kuopio, Finland

    Cristina Florea, Petri Tanska, Mika E. Mononen & Rami K. Korhonen

  2. Department of Integrative Medical Biology, Umeå University, POB 843, 90187, Umeå, Sweden

    Chengjuan Qu & Mikko J. Lammi

  3. School of Public Health, Health Science Center of Xi’an Jiaotong University, Key Laboratory of Trace Elements and Endemic Diseases, National Health and Family Planning Commission, Xi’an, China

    Mikko J. Lammi

  4. School of Engineering and Technology, Savonia University of Applied Sciences, POB 1188, 70201, Kuopio, Finland

    Mikko S. Laasanen

  5. Diagnostic Imaging Center, Kuopio University Hospital, Kuopio, Finland

    Rami K. Korhonen

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  1. Cristina Florea
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Florea, C., Tanska, P., Mononen, M.E. et al. A combined experimental atomic force microscopy-based nanoindentation and computational modeling approach to unravel the key contributors to the time-dependent mechanical behavior of single cells. Biomech Model Mechanobiol 16, 297–311 (2017). https://doi.org/10.1007/s10237-016-0817-y

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