Nanobiomechanics of living cells: A review

Interface Focus

Volumn 4, Issue 2, 2014, Pages

  Chen, Jinju ^a,b  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

^b NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

Cell mechanics; Modelling; Nanobiomechanics; Nanoindentation

Indexed keywords

EID: 84894326871     PISSN: 20428898     EISSN: 20428901     Source Type: Journal    
DOI: 10.1098/rsfs.2013.0055     Document Type: Review

References (126)

1. Lee DA, Knight MM, Campbell JJ, Bader DL. 2011 Stem cell mechanobiology. J. Cell. Biochem. 112, 1-9. (doi:10.1002/jcb.22758)
2. Chen J, Irianto J, Inamdar S, Pravincumar P, Lee DA, Bader DL, Knight MM. 2012 Cell mechanics, structure, and function are regulated by the stiffness of the three-dimensional microenvironment. Biophys. J. 103, 1188-1197. (doi:10.1016/j.bpj. 2012.07.054)
3. Ingber DE. 1994 Cellular tensegrity and mechanochemical transduction. In Cell mechanics and cellular engineering (VC Mow, F Guilak, R Tran-Son-Tay eds), pp. 329-342. New York, NY, Springer.
4. Ingber DE. 2006 Cellular mechanotransduction: putting all the pieces together again. FASEB J. 20, 811-827. (doi:10.1096/fj.05-5424rev)
5. Liedert A, Kaspar D, Claes L, Ignatius A. 2006 Signal transduction pathways involved in mechanical regulation of HB-GAM expression in osteoblastic cells. Biochem. Biophys. Res. Commun. 342, 1070-1076. (doi:10.1016/j.bbrc. 2006.02.063)
6. Robling AG, Bellido T, Turner CH. 2006 Mechanical stimulation in vivo reduces osteocyte expression of selerostin. J. Musculoskelet. Neuronal Interact. 6, 354-354.
7. Setton LA, Chen J. 2006 Mechanobiology of the intervertebral disc and relevance to disc degeneration. J. Bone Joint Surg. Am. A 88, 52-57. (doi:10.2106/jbjs.f.00001)
8. Trickey WR, Baaijens FPT, Laursen TA, Alexopoulos LG, Guilak F. 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)
9. Xu J et al. 2011 Effects of micropatterned curvature on the motility and mechanical properties of airway smooth muscle cells. Biochem. Biophys. Res. Commun. 415, 591-596. (doi:10.1016/j.bbrc.2011.10.111)
10. Kim Y, Hong JW, Kim J, Shin JH. 2013 Comparative study on the differential mechanical properties of human liver cancer and normal cells. Anim. Cells Syst. 17, 170-178. (doi:10.1080/19768354. 2013.789452)
11. Ekpenyong AE et al. 2012 Viscoelastic properties of differentiating blood cells are fate-and functiondependent. PLoS ONE 7, 0045237. (doi:10.1371/journal.pone.0045237)
12. Lee GYH, Lim CT. 2007 Biomechanics approaches to studying human diseases. Trends Biotechnol. 25, 111-118. (doi:10.1016/j.tibtech.2007.01.005)
13. Tan SJ, Li Q, Lim CT. 2010 Manipulation and isolation of single cells and nuclei. Methods Cell Biol 98, pp. 79-96. (doi:10.1016/S0091-679X(10) 98004-7)
14. Puig-De-Morales-Marinkovic M, Turner KT, Butler JP, Fredberg JJ, Suresh S. 2007 Viscoelasticity of the human red blood cell. Am. J. Physiol. Cell Physiol. 293, C597-C605. (doi:10.1152/ajpcell.00562.2006)
15. Suresh S, Spatz J, Mills JP, Micoulet A, Dao M, Lim CT, Beil M, Seufferlein T. 2005 Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria. Acta Biomater. 1, 15-30. (doi:10.1016/j.actbio.2004.09.001)
16. Dao M, Lim CT, Suresh S. 2003 Mechanics of the human red blood cell deformed by optical tweezers. J. Mech. Phys. Solids 51, 2259-2280. (doi:10.1016/j.jmps.2003.09.019)
17. Liu Y-P, Li C, Liu K-K, Lai ACK. 2006 The deformation of an erythrocyte under the radiation pressure by optical stretch. J. Biomech. Eng. Trans. ASME 128, 830-836. (doi:10.1115/1.2354204)
18. Li QS, Lee GYH, Ong CN, Lim CT. 2008 AFM indentation study of breast cancer cells. Biochem. Biophys. Res. Commun. 374, 609-613. (doi:10. 1016/j.bbrc.2008.07.078)
19. Shin D, Athanasiou K. 1999 Cytoindentation for obtaining cell biomechanical properties. J. Orthop. Res. 17, 880-890. (doi:10.1002/jor.1100170613)
20. Han S-K, Colarusso P, Herzog W. 2009 Confocal microscopy indentation system for studying in situ chondrocyte mechanics. Med. Eng. Phys. 31, 1038-1042. (doi:10.1016/j.medengphy.2009. 05.013)
21. Lim CT, Zhou EH, Quek ST. 2006 Mechanical models for living cells: a review. J. Biomech. 39, 195-216. (doi:10.1016/j.jbiomech.2004.12.008)
22. Hochmuth RM. 2000 Micropipette aspiration of living cells. J. Biomech. 33, 15-22. (doi:10.1016/s0021-9290(99)00175-x)
23. Trickey WR, Lee GM, Guilak F. 2000 Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage. J. Orthop. Res. 18, 891-898. (doi:10.1002/jor.1100180607)
24. Leipzig ND, Athanasiou KA. 2005 Unconfined creep compression of chondrocytes. J. Biomech. 38, 77-85. (doi:10.1016/j.jbiomech.2004.03.013)
25. Darling EM, Zauscher S, Guilak F. 2006 Viscoelastic properties of zonal articular chondrocytes measured by atomic force microscopy. Osteoarthritis Cartilage 14, 571-579. (doi:10.1016/j.joca.2005.12.003)
26. Pravincumar P, Bader DL, Knight MM. 2012 Viscoelastic cell mechanics and actin remodelling are dependent on the rate of applied pressure. PLoS ONE 7, e43938. (doi:10.1371/journal.pone.0043938)
27. Ohashi T, Hagiwara M, Bader DL, Knight MM. 2006 Intracellular mechanics and mechanotransduction associated with chondrocyte deformation during pipette aspiration. Biorheology 43, 201-214.
28. Kamm R, Lammerding J, Mofrad M. 2010 Cellular nanomechanics. New York, NY: Springer.
29. Dalby MJ, Gadegaard N, Curtis ASG, Oreffo ROC. 2007 Nanotopographical control of human osteoprogenitor differentiation. Curr. Stem Cell Res. Ther. 2, 129-138. (doi:10.2174/157488807780599220)
30. Bidan CM, Kommareddy KP, Rumpler M, Kollmannsberger P, Fratzl P, Dunlop JWC. 2013 Geometry as a factor for tissue growth: towards shape optimization of tissue engineering scaffolds. Adv. Healthcare Mater. 2, 186-194. (doi:10.1002/adhm.201200159)
31. Salinas CN, Anseth KS. 2008 The enhancement of chondrogenic differentiation of human mesenchymal stem cells by enzymatically regulated RGD functionalities. Biomaterials 29, 2370-2377. (doi:10. 1016/j.biomaterials.2008.01.035)
32. 2 nanotube diameter directs cell fate. Nano Lett. 7, 1686-1691. (doi:10.1021/nl070678d)
33. 2 and ZnO nanoparticles and modulation of the degranulation process in human neutrophils. Toxicol. Lett. 221, 57-63. (doi:10.1016/j.toxlet. 2013.05.010)
34. Lo Schiavo V, Robert P, Mishal Z, Puech P-H, Gentile F, Decuzzi P, Bongrand P, Limozin L. 2013 Transient adhesion mediated by ligand-receptor interaction on surfaces of variable nanotopography. Int. J. Nanotechnol. 10, 404-418. (doi:10.1504/ijnt. 2013.053512)
35. Thomas G, Burnham NA, Camesano TA, Wen Q. 2013 Measuring the mechanical properties of living cells using atomic force microscopy. J. Visual. Exp. 76, e50497. (doi:10.3791/50497)
36. Chen J, Birch MA, Bull SJ. 2010 Nanomechanical characterization of tissue engineered bone grown on titanium alloy in vitro. J. Mater. Sci. Mater. Med. 21, 277-282. (doi:10.1007/s10856-009-3843-9)
37. Mahaffy RE, Park S, Gerde E, Kas J, Shih CK. 2004 Quantitative analysis of the viscoelastic properties of thin regions of fibroblasts using atomic force microscopy. Biophys. J. 86, 1777-1793. (doi:10. 1016/s0006-3495(04)74245-9)
38. Young R, Lovell P. 1991 Introduction to polymers, 2nd edn. Cambridge, UK: Cambridge University Press.
39. Portoles JF, Cumpson PJ. 2013 A compact torsional reference device for easy, accurate and traceable AFM piconewton calibration. Nanotechnology 24, 335706. (doi:10.1088/0957-4484/24/33/335706)
40. Hansma HG, Hoh JH. 1994 Biomolecular imaging with the atomic-force microscope. Annu. Rev. Biophys. Biomol. Struct. 23, 115-139. (doi:10.1146/annurev.bb.23.060194.000555)
41. Atkins A, Tabor D. 1965 Plastic indentation in metals with cones. J. Mech. Phys. Solids 13, 149-164. (doi:10.1016/0022-5096(65)90018-9)
42. Chen J, Bull SJ. 2006 On the relationship between plastic zone radius and maximum depth during nanoindentation. Surface Coatings Technol. 201, 4289-4293. (doi:10.1016/j.surfcoat.2006.08.099)
43. Chen J, Bull SJ. 2006 A critical examination of the relationship between plastic deformation zone size and Young's modulus to hardness ratio in indentation testing. J. Mater. Res. 21, 2617-2627. (doi:10.1557/jmr.2006.0323)
44. Chen J, Bull SJ. 2009 On the factors affecting the critical indenter penetration for measurement of coating hardness. Vacuum 83, 911-920. (doi:10. 1016/j.vacuum.2008.11.007)
45. Ofek G, Willard VP, Koay EJ, Hu JC, Lin P, Athanasiou KA. 2009 Mechanical characterization of differentiated human embryonic stem cells. J. Biomech Eng. Trans. ASME 131, 061011. (doi:10. 1115/1.3127262)
46. Shieh AC, Athanasiou KA. 2006 Biomechanics of single zonal chondrocytes. J. Biomech. 39, 1595-1602. (doi:10.1016/j.jbiomech.2005.05.002)
47. Turunen SM, Han SK, Herzog W, Korhonen RK. 2013 Cell deformation behavior in mechanically loaded rabbit articular cartilage 4 weeks after anterior cruciate ligament transection. Osteoarthritis Cartilage 21, 505-513. (doi:10.1016/j.joca. 2012.12.001)
48. Ingber DE. 1993 Cellular tensegrity: defining new rules of biological design that govern the cytoskeleton. J. Clin. Ultrasound 21, 613-627.
49. Ingber DE. 1997 Tensegrity: the architectural basis of cellular mechanotransduction. Annu. Rev. Physiol. 59, 575-599. (doi:10.1146/annurev. physiol.59.1.575)
50. Forgacs G. 1995 On the possible role of cytoskeletal filamentous networks in intracellular signaling: an approach based on percolation. J. Cell Sci. 108, 2131-2143.
51. Ofek G, Natoli RM, Athanasiou KA. 2009 In situ mechanical properties of the chondrocyte cytoplasm and nucleus. J. Biomech. 42, 873-877. (doi:10. 1016/j.jbiomech.2009.01.024)
52. Freeman PM, Natarajan RN, Kimura JH, Andriacchi TP. 1994 Chondrocyte cells respond mechanically to compressive loads. J. Orthop. Res. 12, 311-320. (doi:10.1002/jor.1100120303)
53. Rao CS, Reddy CE. 2008 An FEM approach into nanoindentation on linear elastic and viscoelastic characterization of soft living cells. Int. J. Nanotechnol. Appl. 2, 55-68.
54. Caille N, Thoumine O, Tardy Y, Meister JJ. 2002 Contribution of the nucleus to the mechanical properties of endothelial cells. J. Biomech. 35, 177-187. (doi:10.1016/s0021-9290(01)00201-9)
55. Nair K, Yan K, Sun W. 2007 A multi level numerical model for quantifying cell deformation in encapsulated alginate structures. J. Mech. Mater. Struct. 2, 1121-1139. (doi:10.2140/jomms.2007. 2.1121)
56. Kang I, Panneerselvam D, Panoskaltsis VP, Eppell SJ, Marchant RE, Doerschuk CM. 2008 Changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor-alpha. Biophys. J. 94, 3273-3285. (doi:10.1529/biophysj.106.099333)
57. Guilak F, Mow VC. 2000 The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage. J. Biomech. 33, 1663-1673. (doi:10.1016/s0021-9290(00)00105-6)
58. Chen J, Lu G. 2012 Finite element modelling of nanoindentation based methods for mechanical properties of cells. J. Biomech. 45, 2810-2816. (doi:10.1016/j.jbiomech.2012.08.037)
59. Calladine CR. 1978 Fuller, Buckminster tensegrity structures and Maxwell, Clerk rules for construction of stiff frames. Int. J. Solids Struct. 14, 161-172. (doi:10.1016/0020-7683(78)90052-5)
60. Stamenovic D, Fredberg JJ, Wang N, Butler JP, Ingber DE. 1996 A microstructural approach to cytoskeletal mechanics based on tensegrity. J. Theor. Biol. 181, 125-136. (doi:10.1006/jtbi. 1996.0120)
61. Ingber DE, Prusty D, Sun ZQ, Betensky H, Wang N. 1995 Cell shape, cytoskeletal mechanics, and cell cycle control in angiogenesis. J. Biomech. 28, 1471-1484. (doi:10.1016/0021-9290(95) 00095-x)
62. Ingber DE, Bojanowski K, Chen C, Huang S, Maniotis A. 1996 Cellular tensegrity: an architectural basis for control of cell shape and morphogenesis. Mol. Biol. Cell 7, 1975-1975.
63. Ingber DE et al. 1994 Cellular tensegrity: Exploring how mechanical changes in the cytoskeleton regulate cell growth, migration, and tissue pattern during morphogenesis. Int. Rev. Cytol. 150, 173-224.
64. McGarry JG, Prendergast PJ. 2004 A threedimensional finite element model of an adherent eukaryotic cell. Eur. Cells Mater. 7, 27-33. discussion 33-24.
65. De Santis G, Lennon AB, Boschetti F, Verhegghe B, Verdonck P, Prendergast PJ. 2011 How can cells sense the elasticity of a substrate? an analysis using a cell tensegrity model. Eur. Cells Mater. 22, 202-213.
66. Nguyen BV, Wang QG, Kuiper NJ, El Haj AJ, Thomas CR, Zhang Z. 2001 Biomechanical properties of single chondrocytes and chondrons determined by micromanipulation and finite-element modelling. J. R. Soc. Interface 7, 1723-1733. (doi:10.1098/rsif. 2010.0207)
67. Rivlin RS, Saunders DW. 1951 Large elastic deformations of isotropic materials VIII. Experiments on the deformation of rubber. Phil. Trans. R. Soc. Lond. A 328, 565-584. (doi:10.1098/rsta. 1951.0004)
68. Ogden RW. 1998 Nonlinear elastic deformations. New York, NY: Dover.
69. Ogden RW. 1972 Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. A 326, 565-584. (doi:10.1098/rspa.1972.0026)
70. Biot M. 1941 General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155-164. (doi:10. 1063/1.1712886)
71. Strange DGT, Fletcher TL, Tonsomboon K, Brawn H, Zhao X, Oyen ML. 2013 Separating poroviscoelastic deformation mechanisms in hydrogels. Appl. Phys. Lett. 102, 031913. (doi:10.1063/1.4789368)
72. Oyen ML. 2013 Nanoindentation of biological and biomimetic materials. Exp. Tech. 37, 73-87. (doi:10.1111/j.1747-1567.2011.00716.x)
73. Wu JZ, Herzog W, Epstein M. 1998 Evaluation of the finite element software ABAQUS for biomechanical modelling of biphasic tissues. J. Biomech. 31, 165-169. (doi:10.1016/S0021-9290(97)00117-6)
74. Hu Y, Zhao X, Vlassak JJ, Suo Z. 2010 Using indentation to characterize the poroelasticity of gels. Appl. Phys. Lett. 96 121904. (doi:10.1063/1. 3370354)
75. Mow VC, Kuei SC, Lai WM, Armstrong CG. 1980 Biphasic creep and stress-relaxation of articularcartilage in compression: theory and experiments. J. Biomech. Eng. Trans. ASME 102, 73-84. (doi:10. 1115/1.3138202)
76. Bowen RM. 1980 Incompressible porous-media models by use of the theory of mixtures. Int. Eng. Sci. 18, 1129-1148. (doi:10.1016/0020-7225(80) 90114-7)
77. Setton LA, Zhu WB, Mow VC. 1993 The biphasic poroviscoelastic behavior of articular-cartilage: role of the surface zone in governing the compressive behavior. J. Biomech. 26, 581-592. (doi:10.1016/0021-9290(93)90019-b)
78. Gu WY, Lai WM, Mow VC. 1998 A mixture theory for charged-hydrated soft tissues containing multielectrolytes: passive transport and swelling behaviors. J. Biomech. Eng. Trans. ASME 120, 169-180. (doi:10.1115/1.2798299)
79. Manual ASUs. 2012 Hibbitt, Karlsson and Sorensen, Inc.
80. Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas D, Fredberg JJ. 2001 Scaling the microrheology of living cells. Phys. Rev. Lett. 87, 148102. (doi:10.1103/PhysRevLett.87.148102)
81. Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas D, Taback NA, Millet EJ, Fredberg JJ. 2003 Time scale and other invariants of integrative mechanical behavior in living cells. Phys. Rev. E 68, 041914. (doi:10.1103/PhysRevE.68.041914)
82. Doerner M, Nix W. 1986 A method for interpreting the data from depth-sensing indentation instruments. J. Mater Res. 1, 601-609. (doi:10. 1557/JMR.1986.0601)
83. Johnson KL. 1985 Contact mechanics. Cambridge, UK: Cambridge University Press.
84. Sneddon I. 1965 The relationship between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47-57. (doi:10.1016/0020-7225(65)90019-4)
85. Charras GT, Williams BA, Sims SM, Horton MA. 2004 Estimating the sensitivity of mechanosensitive ion channels to membrane strain and tension. Biophys. J. 87, 2870-2884. (doi:10.1529/biophysj. 104.040436)
86. Charras GT, Yarrow JC, Horton MA, Mahadevan L, Mitchison TJ. 2005 Non-equilibration of hydrostatic pressure in blebbing cells. Nature 435, 365-369. (doi:10.1038/nature03550)
87. Cheng L, Xia X, Yu W, Scriven LE, Gerberich WW. 2000 Flat-punch indentation of viscoelastic material. J. Polym. Sci. B Polym. Phys. 38, 10-22. (doi:10. 1002/(sici)1099-0488(20000101)38:1<10::aidpolb2>3.0. co;2-6)
88. Cheng L, Xia X, Scriven LE, Gerberich WW. 2005 Spherical-tip indentation of viscoelastic material. Mech. Mater. 37, 213-226. (doi:10.1016/j. mechmat.2004.03.002)
89. Cheng YT, Ni WY, Cheng CM. 2005 Determining the instantaneous modulus of viscoelastic solids using instrumented indentation measurements. J. Mater. Res. 20, 3061-3071. (doi:10.1557/jmr.2005.0389)
90. Cheng YT, Cheng CM. 2006 Relationship between contact stiffness, contact depth, and mechanical properties for indentation in linear viscoelastic solids using axisymmetric indenters. Struct. Control Health Monit. 13, 561-569. (doi:10.1002/stc.127)
91. Oyen ML. 2006 Analytical techniques for indentation of viscoelastic materials. Phil. Mag. 86, 5625-5641. (doi:10.1080/14786430600740666)
92. Ward KA, Li WI, Zimmer S, Davis T. 1991 Viscoelastic properties of transformed cells: role in tumor cell progression and metastasis formation. Biorheology 28, 301-313.
93. Rosenbluth MJ, Crow A, Shaevitz JW, Fletcher DA. 2008 Slow stress propagation in adherent cells. Biophys. J. 95, 6052-6059. (doi:10.1529/biophysj. 108.139139)
94. Baaijens FPT, Trickey WR, Laursen TA, Guilak F. 2005 Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte. Ann. Biomed. Eng. 33, 494-501. (doi:10.1007/s10439-005-2506-3)
95. Moeendarbary E, Valon L, Fritzsche M, Harris AR, Moulding DA, Thrasher AJ, Stride E, Mahadevan L, Charras GT. 2013 The cytoplasm of living cells behaves as a poroelastic material. Nat. Mater. 12, 253-261. (doi:10.1038/nmat3517)
96. Kalyanam S, Yapp RD, Insana MF. 2009 Poroviscoelastic behavior of gelatin hydrogels under compression-implications for bioelasticity imaging. J. Biomech. Eng. Trans. ASME 131, 081005. (doi:10. 1115/1.3127250)
97. Cui YH, Wang X, Zhang YX, He FJ. 2010 Poroviscoelastic properties of anisotropic cylindrical composite materials. Phil. Mag. 90, 1197-1212. (doi:10.1080/14786430903317253)
98. Liu K, Ovaert TC. 2011 Poro-viscoelastic constitutive modeling of unconfined creep of hydrogels using finite element analysis with integrated optimization method. J. Mech. Behav. Biomed. Mater. 4, 440-450. (doi:10.1016/j.jmbbm.2010.12.005)
99. Guilak F, Haider MA, Setton LA, Laursen TA, Baaijens FPT. 2006 Multiphasic models of cell mechanics. Cambridge, UK: Cambridge University Press.
100. Alcaraz J, Buscemi L, Grabulosa M, Trepat X, Fabry B, Farre R, Navajas D. 2003 Microrheology of human lung epithelial cells measured by atomic force microscopy. Biophys. J. 84, 2071-2079. (doi:10. 1016/S0006-3495(03)75014-0)
101. Rotsch C, Jacobson K, Radmacher M. 1999 Dimensional and mechanical dynamics of active and stable edges in motile fibroblasts investigated by using atomic force microscopy. Proc. Natl Acad. Sci. USA 96, 921-926. (doi:10.1073/pnas.96.3.921)
102. Charras GT, Horton MA. 2002 Determination of cellular strains by combined atomic force microscopy and finite element modeling. Biophys. J. 83, 858-879. (doi:10.1016/S0006-3495(02) 75214-4)
103. Charras GT, Horton MA. 2002 Single cell mechanotransduction and its modulation analyzed by atomic force microscope indentation. Biophys. J. 82, 2970-2981. (doi:10.1016/S0006-3495 (02)75638-5)
104. Hoh JH, Schoenenberger CA. 1994 Surfacemorphology and mechanical-properties of mdck monolayers by atomic-force microscopy. J. Cell Sci. 107, 1105-1114.
105. Acerbi I, Luque T, Gimenez A, Puig M, Reguart N, Farre R, Navajas D, Alcaraz J. 2012 Integrin-specific mechanoresponses to compression and extension probed by cylindrical flat-ended AFM tips in lung cells. PLoS ONE 7, e32261. (doi:10.1371/journal. pone.0032261)
106. Koay EJ, Shieh AC, Athanasiou KA. 2003 Creep indentation of single cells. J. Biomech. Eng. Trans. ASME 125, 334-341. (doi:10.1115/1.1572517)
107. Darling EM, Topel M, Zauscher S, Vail TP, Guilak F. 2008 Viscoelastic properties of human mesenchymally-derived stem cells and primary osteoblasts, chondrocytes, and adipocytes. J. Biomech. 41, 454-464. (doi:10.1016/j.jbiomech. 2007.06.019)
108. 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, 1784-1791. (doi:10.1529/biophysj.106. 083097)
109. Chan EP, Hu Y, Johnson PM, Suo Z, Stafford CM. 2012 Spherical indentation testing of poroelastic relaxations in thin hydrogel layers. Soft Matter 8, 1492-1498. (doi:10.1039/c1sm06514a)
110. Tu Y, Gazis D. 1964 The contact problem of a plate pressed between two spheres. J. Appl. Mech. 31, 659-666. (doi:10.1115/1.3629728)
111. Chen WT. 1971 Computation of stresses and displacements in a layered elastic medium. Int. J. Eng. Sci. 9, 775-800. (doi:10.1016/0020-7225(71)90072-3)
112. Chen W, Engel P. 1972 Impact and contact stress analysis in multilayer media. Int. J. Solids Struct. 8, 1257-1281. (doi:10.1016/0020-7683(72) 90079-0)
113. Rosenbluth MJ, Lam WA, Fletcher DA. 2006 Force microscopy of nonadherent cells: A comparison of leukemia cell deformability. Biophys. J. 90, 2994-3003. (doi:10.1529/biophysj.105.067496)
114. Ng L, Hung H-H, Sprunt A, Chubinskaya S, Ortiz C, Grodzinsky A. 2007 Nanomechanical properties of individual chondrocytes and their developing growth factor-stimulated pericellular matrix. J. Biomech. 40, 1011-1023. (doi:10.1016/j. jbiomech.2006.04.004)
115. Kailas L, Ratcliffe EC, Hayhurst EJ, Walker MG, Foster SJ, Hobbs JK. 2009 Immobilizing live bacteria for AFM imaging of cellular processes. Ultramicroscopy 109, 775-780. (doi:10.1016/j.ultramic.2009. 01.012)
116. Chen J. 2013 Understanding the nanoindentation mechanisms of a microsphere for biomedical applications. J. Phys. D, Appl. Phys. 46, 495303. (doi:10.1088/0022-3727/46/49/495303)
117. Jaasma MJ, Jackson WM, Keaveny TM. 2006 Measurement and characterization of whole-cell mechanical behavior. Ann. Biomed. Eng. 34, 748-758. (doi:10.1007/s10439-006-9081-0)
118. Johnson KL, Kendall K, Roberts AD. 1971 Surface energy and contact of elastic solids. Proc. R. Soc. Lond. A 324, 301-313. (doi:10.1098/rspa.1971.0141)
119. Derjaguin BV, Muller VM, Toporov YP. 1975 Effect of contact deformations on adhesion of particles. J. Colloid Interface Sci. 53, 314-326. (doi:10.1016/0021-9797(75)90018-1)
120. Maugis D. 1996 On the contact and adhesion of rough surfaces. J. Adhesion Sci. Technol. 10, 161-175. (doi:10.1163/156856196_00832)
121. Sen S, Subramanian S, Discher DE. 2005 Indentation and adhesive probing of a cell membrane with AFM: theoretical model and experiments. Biophys. J. 89, 3203-3213. (doi:10.1529/biophysj.105.063826)
122. Lin DC, Horkay F. 2008 Nanomechanics of polymer gels and biological tissues: a critical review of analytical approaches in the Hertzian regime and beyond. Soft Matter 4, 669-682. (doi:10.1039/b714637j)
123. Martins RP, Finan JD, Guilak F, Lee DA. 2012 Mechanical regulation of nuclear structure and function. Annu. Rev. Biomed. Eng. 14, pp. 431-455. (doi:10.1146/annurevbioeng-071910-124638)
124. Vichare S, Inamdar MM, Sen S. 2012 Influence of cell spreading and contractility on stiffness measurements using AFM. Soft Matter 8, 10 464-10 471. (doi:10.1039/c2sm26348c)
125. Lai WM, Hou JS, Mow VC. 1991 A triphasic theory for the swelling and deformation behaviors of articular-cartilage. J. Biomech. Eng. Trans. ASME 113, 245-258. (doi:10.1115/1.2894880)
126. Harris AK, Wild P, Stopak D. 1980 Silicone-rubber substrata: new wrinkle in the study of cell locomotion. Science 208, 177-179. (doi:10.1126/science.6987736)