Skip to main content
SpringerLink
Log in

Bio-chemo-mechanical models for nuclear deformation in adherent eukaryotic cells

  • Review Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

Adherent eukaryotic cells are subjected to a broad variety of extracellular and intracellular stimuli regulating their behaviour. These stimuli can be either purely chemical, for example soluble factors binding to the cell membrane, or mechano-chemical, for example integrin-based adhesion complexes stretching the cell cytoskeleton. Here, we focus on mechano-chemical stimuli such as extracellular forces (interstitial flow, pressurization) and intracellular forces (due to cell adhesion), which may combine generating stress–strain states in the cytoskeleton. These states are transferred to the nucleus to influence the transcription of specific genes, likely by changing the chromatin organization and by altering the permeability of the nuclear membrane. While there exists increasing experimental evidence of the mechanosensing role of the cell nucleus, both the underlying molecular mechanisms involved, and the nuclear structural behaviour in response to forces, are still poorly understood. Here, we review the existing literature on computational models developed to investigate the chemo-mechanical behaviour of adherent eukaryotic cells. We analyse two main classes of models of single-cell mechanics, based either on the discrete or on the continuum approaches. We focus on the bio-chemo-mechanical model and modelling techniques accounting for the nuclear body. The modelling techniques are discussed highlighting their ability in predicting cytoskeletal contractility states and nuclear stress–strain states.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Affonce D, Lutchen K (2006) New perspectives on the mechanical basis for airway hyperreactivity and airway hypersensitivity in asthma. J Appl Physiol 101(6):1710–1719

    Google Scholar 

  • Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2007) Molecular biology of the cell, 5th edn. Garland Science, New York

    Google Scholar 

  • Anderson AE, Ellis BJ, Weiss JA (2007) Verification, validation and sensitivity studies in computational biomechanics. Comput Methods Biomech Biomed Eng 10(3):171-1844

    Google Scholar 

  • Baaijens F, Trickey W, Laursen T, Guilak F (2005) Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte. Ann Biomed Eng 33(4):494–501

    Google Scholar 

  • Badique F, Stamov D, Davidson P, Veuillet M, Reiter G, Freund J, Franz C, Anselme K (2013) Directing nuclear deformation on micropillared surfaces by substrate geometry and cytoskeleton organization. Biomaterials 34(12):2991–3001

    Google Scholar 

  • Banerjee S, Marchetti M (2013) Controlling cell matrix traction forces by extracellular geometry. New J Phys 15:035015

    Google Scholar 

  • Bao G, Suresh S (2003) Cell and molecular mechanics of biological materials. Nat Mater 2(11):715–725

    Google Scholar 

  • Baudriller H, Maurin B, Canadas P, Montcourrier P, Parmeggiani A, Bettache N (2006) Form-finding of complex tensegrity structures: application to cell cytoskeleton modelling. C. R. Mech. 334(11): 662–668

    Google Scholar 

  • Boey S, Boal D, Discher D (1998) Simulations of the erythrocyte cytoskeleton at large deformation. I. Microscopic models. Biophys J 75(3):1573–1583

    Google Scholar 

  • Burns L, Wente S (2012) Trafficking to uncharted territory of the nuclear envelope. Curr Opin Cell Biol 24(3):341–349

    Google Scholar 

  • Bursa J, Lebis R, Holata J (2012) Tensegrity finite element models of mechanical tests of individual cells. Technol Health Care 20(2): 135–150

    Google Scholar 

  • Buxboim A, Ivanovska I, Discher D (2010) Matrix elasticity, cytoskeletal forces and physics of the nucleus: how deeply do cells ‘feel’ outside and in? J Cell Sci 123(3):297–308

    Google Scholar 

  • Caille N, Thoumine O, Tardy Y, Meister J (2002) Contribution of the nucleus to the mechanical properties of endothelial cells. J Biomech 35(2):177–187

    Google Scholar 

  • Canadas P, Laurent V, Oddou C, Isabey D, Wendling S (2002) Cellular tensegrity model to analyse the structural viscoelasticity of the cytoskeleton. J Theor Biol 218(2):155–173

    MathSciNet  Google Scholar 

  • Canadas P, Wendling-Mansuy S, Isabey D (2006) Frequency response of a viscoelastic tensegrity model: structural rearrangement contribution to cell dynamics. ASME J Biomech Eng 128(4):487–495

    Google Scholar 

  • Cao Y, Bly R, Moore W, Gao Z, Cuitino A, Soboyejo W (2007) On the measurement of human osteosarcoma cell elastic modulus using shear assay experiment. J Mater Sci 18(1):103–109

    Google Scholar 

  • Cao L, Guilak F, Setton L (2009) Pericellular matrix mechanics in the anulus fibrosus predicted by a three-dimensional finite element model and in situ morphology. Cell Mol Bioeng 2(3):306–319

    Google Scholar 

  • Chalut K, Kulangara K, Giacomelli M, Wax A, Leong K (2010) Deformation of stem cell nuclei by nanotopographical cues. Soft Matter 6(8):1675–1681

    Google Scholar 

  • Chambliss A, Khatau S, Erdenberger N, Robinson D, Hodzic D, Longmore G, Wirtz D (2013) The LINC-anchored actin cap connects the extracellular milieu to the nucleus for ultrafast mechanotransduction. Sci Rep 3(8):1087

    Google Scholar 

  • Charras G, Horton M (2002) Determination of cellular strains by combined atomic force microscopy and finite element modeling. Biophys J 83(2):858–879

    Google Scholar 

  • Chen C, Mrksich M, Huang S, Whitesides GM, Ingber DE (1997) Geometric control of cell life and death. Science 276(5317):1425–1428

    Google Scholar 

  • Chen K, Li Y, Kim M, Li S, Yuan S, Chien S, Shyy J (1999) Mechanotransduction in response to shear stress: roles of receptor tyrosine kinases, integrins, and Shc. J Biol Chem 274(26):18393–18400

    Google Scholar 

  • Chen CS, Tan JL, Tien J, Pirone DM, Gray DS, Bhadriraju K (2003) Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proc Natl Acad Sci USA 100(4):1484–1489

    Google Scholar 

  • Chen T, Wu C, Tang M, Huang J, Su F (2010) Complexity of the tensegrity structure for dynamic energy and force distribution of cytoskeleton during cell spreading. PLoS One 5(12):e14392

    Google Scholar 

  • Correa-Meyer E, Pesce L, Guerrero C, Sznajder J (2002) Cyclic stretch activates ERK1/2 via G proteins and EGFR in alveolar epithelial cells. Am J Physiol Lung Cell Mol Physiol 282(5):L883–L891

    Google Scholar 

  • Costa K, Yin F (1999) Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy. J Biomech Eng (Trans. ASME) 121:462–471

    Google Scholar 

  • Coughlin MF, Stamenovic D (2003) A prestressed cable network model of the adherent cell cytoskeleton. Biophys J 84:1328–1336

    Google Scholar 

  • Cusachs P, Alcaraz J, Sunyer R, Samitier J, Farré R, Navajas D (2008) Micropatterning of single endothelial cell shape reveals a tight coupling between nuclear volume in g1 and proliferation. Biophys J 94(12):4984–4995

    Google Scholar 

  • Dahl K, Scaffidi P, Islam M, Yodh A, Wilson K, Misteli T (2006) Distinct structural and mechanical properties of the nuclear lamina in Hutchinson–Gilford progeria syndrome. Proc Natl Acad Sci USA 103(27):10271–10276

    Google Scholar 

  • Dahl K, Ribeiro A, Lammerding J (2008) Nuclear shape, mechanics, and mechanotransduction. Circ Res 102(11):1307–1318

    Google Scholar 

  • Dao M, Lim C, Suresh S (2003) Mechanics of the human red blood cell deformed by optical tweezers. J Mech Phys Solids 51(11–12): 2259–2280

    Google Scholar 

  • De Santis G, Lennon A, Boschetti F, Verhegghe B, Verdonck P, Prendergast P (2011) How can cells sense the elasticity of a substrate? An analysis using a cell tensegrity model. Eur Cell Mater 22:202–213

    Google Scholar 

  • Dechat T, Adam S, Goldman R (2009) Nuclear lamins and chromatin: when structure meets function. Adv Enzym Regul 49(1):157–166

    Google Scholar 

  • Deguchi S, Yano M, Hashimoto K, Fukamachi H, Washio S, Tsujioka K (2011) Assessment of the mechanical properties of the nucleus inside a spherical endothelial cell based on microtensile test. J Mech Mater Struct 2(6):1087–1102

    Google Scholar 

  • Deshpande V, McMeeking R, Evans A (2006) A bio-chemo-mechanical model for cell contractility. Proc Natl Acad Sci USA 103(38):14015–14020

    Google Scholar 

  • Deshpande V, McMeeking R, Evans A (2007) A model for the contractility of the cytoskeleton including the effects of stress-fibre formation and dissociation. Proc R Soc A 463(2079):787–815

    MATH  MathSciNet  Google Scholar 

  • Deshpande V, Mrksich M, McMeeking R, Evans A (2008) A bio-mechanical model for coupling cell contractility with focal adhesion formation. J Mech Phys Solids 56(4):1484–1510

    MATH  Google Scholar 

  • Ding S, Schultz P (2004) A role for chemistry in stem cell biology. Nat Biotechnol 22(7):833–840

    Google Scholar 

  • Discher D, Janmey P, Wang Y-L (2005) Tissue cells feel and respond to the stiffness of their substrate. Science 310(5751):1139–1143

    Google Scholar 

  • Discher D, Mooney D, Zandstra P (2009) Growth factors, matrices, and forces combine and control stem cells. Science 324(5935): 1673–1677

    Google Scholar 

  • Dowling E, Ronan W, McGarry J (2013) Computational investigation of in situ chondrocyte deformation and actin cytoskeleton remodelling under physiological loading. Acta Biomater 9(4):5943–5955

    Google Scholar 

  • Dupont S, Morsut L, Aragona M, Enzo E, Giulitti S, Cordenonsi M, Zanconato F, Le Digabel J, Forcato M, Bicciato S, Elvassore N, Piccolo S (2011) Role of YAP/TAZ in mechanotransduction. Nature 474(7350):179–183

    Google Scholar 

  • Engler A, Sen S, Sweeney H, Discher D (2006) Matrix elasticity directs stem cell lineage specification. Cell 126(4):677–689

    Google Scholar 

  • Engler A, Carag-Krieger C, Johnson C, Raab M, Tang H, Speicher D, Sanger J, Sanger J, Discher D (2008) Embryonic cardiomyocytes beat best on a matrix with heart-like elasticity: scar-like rigidity inhibits beating. J Cell Sci 121(22):3794–3802

    Google Scholar 

  • Ferko M, Bhatnagar A, Garcia M, Butler P (2007) Finite-element stress analysis of a multicomponent model of sheared and focally-adhered endothelial cells. Ann Biomed Eng 35(2):858–859

    Google Scholar 

  • Fletcher D, Mullins R (2010) Cell mechanics and the cytoskeleton. Nature 463(7280):485–492

    Google Scholar 

  • Friedman M, Li S, Li X (2009) Activation of gene transcription by heat shock protein 27 may contribute to its neuronal protection. J Biol Chem 284:27944–27951

    Google Scholar 

  • Gimbrone M, Topper J, Nagel T, Anderson K, Garcia-Cardena G (2000) Endothelial dysfunction, hemodynamic forces, and atherogenesis. Ann NY Acad Sci 902:230–239

    Google Scholar 

  • Guharay F, Sachs F (1984) Stretch-activated single ion channel currents in tissue-cultured embryonic chick skeletal muscle. J Physiol 352:685–701

    Google Scholar 

  • Guilak F (1995) Compression-induced changes in the shape and volume of the chondrocyte nucleus. J Biomech 28(12):1529–1541

    Google Scholar 

  • Guilak F, Tedrow J, Burgkart R (2000) Viscoelastic properties of the cell nucleus. Biochem Biophys Res Commun 269(3):781–786

    Google Scholar 

  • Guilak F, Erickson G, Ting-Beall H (2002) The effects of osmotic stress on the viscoelastic and physical properties of articular chondrocytes. Biophys J 82(2):720–727

    Google Scholar 

  • Guilak F, Cohen D, Estes B, Gimble J, Liedtke W, Chen C (2009) Control of stem cell fate by physical interactions with the extracellular matrix. Cell Stem Cell 5(1):17–26

    Google Scholar 

  • Gundersen G, Worman H (2013) Nuclear positioning. Cell 152: 1376–1389

    Google Scholar 

  • Gunther U, Schuppan D, Bauer M, Matthes H, Stallmach A, Schmitt-Graff A, Riecken E, Herbst H (1999) Fibrogenesis and fibrolysis in collagenous colitis-patterns of procollagen types I and IV, matrix-metalloproteinase-1 and -13, and TIMP-I gene expression. Am J Pathol 155(2):493–503

    Google Scholar 

  • Gupta S, Marcel N, Sarin A, Shivashankar G (2012) Role of actin dependent nuclear deformation in regulating early gene expression. PLoS One 7(12):e53031

    Google Scholar 

  • Hadjipanayi E, Mudera V, Brown R (2009a) Close dependence of fibroblast proliferation on collagen scaffold matrix stiffness. J Tissue Eng Regen Med 3:77–84

    Google Scholar 

  • Hadjipanayi E, Mudera V, Brown R (2009b) Guiding cell migration in 3D:a collagen matrix with graded directional stiffness. Cell Motil Cytoskelet 66:121–128

    Google Scholar 

  • Haider M, Guilak F (2000) An axisymmetric boundary integral model for incompressible linear viscoelasticity: application to the micropipette aspiration contact problem. J Biomech Eng (Trans. ASME) 122(3):236–244

    Google Scholar 

  • Haider M, Guilak F (2002) An axisymmetric boundary integral model for assessing elastic cell properties in the micropipette aspiration contact problem. J Biomech Eng 124(5):586–595

    Google Scholar 

  • Han S, Sniadecki N (2011) Simulations of the contractile cycle in cell migration using a bio-chemical-mechanical model. Comput Methods Biomech Biomed Eng 14(5):459–468

    Google Scholar 

  • Heo S, Nerurkar N, Baker B, Shin J, Elliott D, Mauck R (2011) Fiber stretch and reorientation modulates mesenchymal stem cell morphology and fibrous gene expression on oriented nanofibrous microenvironments. Ann Biomed Eng 39(11):2780–2790

    Google Scholar 

  • Heydemann A, McNally E (2007) Consequences of disrupting the dystrophin-sarcoglycan complex in cardiac and skeletal myopathy. Trends Cardiovasc Med 17(2):55–59

    Google Scholar 

  • Huang C, Soltz M, Kopacz M, Mow V, Ateshian G (2003) Experimental verification of the roles of intrinsic matrix viscoelasticity and tension-compression nonlinearity in the biphasic response of cartilage. ASME J Biomech Eng 125(1):84–93

    Google Scholar 

  • Huang H, Kamm R, Lee R (2004) Cell mechanics and mechanotransduction: pathways, probes, and physiology. Stem Cells 287(1): C1–11

    Google Scholar 

  • Ingber D (1993) Cellular tensegrity: defining new rules of biological design that govern the cytoskeleton. J Cell Sci 104(Pt. 3): 613–627

    Google Scholar 

  • Ingber D (1997) Tensegrity: the architectural basis of cellular mechanotransduction. Annu Rev Physiol 59:575–599

    Google Scholar 

  • Ingber D (2003a) Tensegrity I: cell structure and hierarchical systems biology. J Cell Sci 116:1157–1173

    Google Scholar 

  • Ingber D (2003b) Tensegrity II: how structural networks influence cellula information processing networks. J Cell Sci 116:1397–1408

    Google Scholar 

  • Ingber D (2006) Cellular mechanotransduction: putting all the pieces together again. FASEB 20(7):811–827

    Google Scholar 

  • Ingber D (2008) Mechanobiology and diseases of mechanotransduction. Ann. Med. 35(8):564–577

    Google Scholar 

  • Isermann P, Lammerding J (2013) Nuclear mechanics and mechanotransduction in health and disease. Curr Biol 23(24):R1113–R1121

    Google Scholar 

  • Iyer K, Pulford S, Mogilner A, Shivashankar G (2012) Mechanical activation of cells induces chromatin remodeling preceding MKL nuclear transport. Biophys J 103(7):1416–1428

    Google Scholar 

  • Jaalouk D, Lammerding J (2009) Mechanobiology gone awry. Nat Rev Mol Cell Biol 10(1):63–73

    Google Scholar 

  • Jacot J, Kita-Matsuo H, Wei K, Chen H, Omens J, Mercola M, McCulloch A (2010) Cardiac myocyte force development during differentiation and maturation. Ann NY Acad Sci 1188:121–127

    Google Scholar 

  • Jadhav S, Eggleton C, Konstantopoulos K (2005) A 3-D computational model predicts that cell deformation affects selectin-mediated leukocyte rolling. Biophys J 88(1):96–104

    Google Scholar 

  • Jean R, Gray D, Spector A, Chen C (2004) Characterization of the nuclear deformation caused by changes in endothelial cell shape. J Biomech Eng 126(5):552–558

    Google Scholar 

  • Jean R, Chen C, Spector A (2005) Finite-element analysis of the adhesion-cytoskeleton-nucleus mechanotransduction pathway during endothelial cell rounding: axisymmetric model. J Biomech Eng 127(4):594–600

    Google Scholar 

  • Jerabek H, Heermann D (2014) How chromatin looping and nuclear envelope attachment affect genome organization in eukaryotic cell nuclei. Int Rev Cell Mol Biol 307:351–381

    Google Scholar 

  • Judex S, Gross T, Bray R, Zernicke R (1997) Adaptation of bone to physiological stimuli. J Biomech 30(5):421–429

    Google Scholar 

  • Julkunen P, Wilson W, Jurvelin J, Korhonen R (2009) Composition of the pericellular matrix modulates the deformation behaviour of chondrocytes in articular cartilage under static loading. Med Biol Eng Comput 47(12):1281–1290

    Google Scholar 

  • Kardas D, Nackenhorst U, Balzani D (2013) Computational model for the cell mechanical response of the osteocyte cytoskeleton based on self-stabilizing tensegrity structures. Biomech Model Mechanobiol 12(1):167–183

    Google Scholar 

  • Kaunas R, Nguyen P, Usami S, Chien S (2005) Cooperative effects of rho and mechanical stretch on stress fiber organization. Stem Cells 102(44):15895–15900

    Google Scholar 

  • Khatau S, Hale C, Stewart-Hutchinson P, Patel M, Stewart C, Searson P, Hodzic D, Wirtz D (2009) A perinuclear actin cap regulates nuclear shape. Proc Natl Acad Sci USA 106(45):19017–19022

    Google Scholar 

  • Khatau S, Kim D, Hale C, Bloom R, Wirtz D (2010) The perinuclear actin cap in health and disease. Nucleus 1(4):337–342

    Google Scholar 

  • Khatau SB, Bloom R, Bajpai S, Razafsky D, Zang S, Giri A, Wu P, Marchand J, Celedon A, Hale C, Sun SX, Hodzic D, Wirtz D (2012) The distinct roles of the nucleus and nucleus-cytoskeleton connections in three-dimensional cell migration. Sci Rep 2:488

    Google Scholar 

  • Kim D, Chambliss A, Wirtz D (2013a) The multi-faceted role of the actin cap in cellular mechanosensation and mechanotransduction. Soft Matter 9(23):5516–5523

    Google Scholar 

  • Kim D, Khatau S, Feng Y, Walcott S, Sun S, Longmore GA (2013b) Actin cap associated focal adhesions and their distinct role in cellular mechanosensing. Sci Rep 2:5516–5523

    Google Scholar 

  • Klein-Nulend J, Bacabac R, Veldhuijzen J, Van Loon J (2003) Microgravity and bone cell mechanosensitivity. Adv Space Res 32(8):1551–1559

    Google Scholar 

  • Kress S, Neumann A, Weyand B, Kasper C (2012) Stem cell differentiation depending on different surfaces. Adv Biochem Eng Biotechnol 126:263–283

    Google Scholar 

  • Lammerding J, Schulze P, Takahashi T, Kozlov S, Sullivan T, Kamm R, Stewart C, Lee R (2004) Lamin A/C deficiency causes defective nuclear mechanics and mechanotransduction. J Clin Investig 113(3):370–378

    Google Scholar 

  • Lammerding J, Fong L, Ji J, Reue K, Stewart C, Young S, Lee R (2006) Lamins A and C but not lamin B1 regulate nuclear mechanics. J Biol Chem 281(35):25768–25780

    Google Scholar 

  • Lammerding J (2011) Mechanics of the nucleus. Compr Physiol 1(2):783–807

    Google Scholar 

  • Lee J, Hale C, Panorchan P, Khatau S, George J, Tseng Y, Stewart C, Hodzic D, Wirtz D (2007) Nuclear lamin a/c deficiency induces defects in cell mechanics, polarization, and migration. Biophys J 93(7):2542–2552

    Google Scholar 

  • Leipzig N, Athanasiou K (2005) Unconfined creep compression of chondrocytes. J Biomech 38(1):77–85

    Google Scholar 

  • Li J, Dao M, Lim C, Suresh S (2005) Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. J Biomech 88(5):3707–3719

    Google Scholar 

  • Lim C, Zhou E, Quek S (2006) Mechanical models for living cells—a review. J Biomech 39(2):195–216

    Google Scholar 

  • Liu Z, Zhuge Y, Velazquez O (2009) Trafficking and differentiation of mesenchymal stem cells. J Cell Biochem 106(6):984–991

    Google Scholar 

  • Loh O, Vaziri A, Espinosa H (2009) The potential of MEMS for advancing experiments and modeling in cell mechanics. Exp Mech 49(1):105–124

    Google Scholar 

  • Lombardi M, Jaalouk D, Shanahan C, Burke B, Roux K, Lammerding J (2011) The interaction between nesprins and SUN proteins at the nuclear envelope is critical for force transmission between the nucleus and cytoskeleton. J Biol Chem 286(1):26473–26753124

    Google Scholar 

  • Lutolf M, Hubbell J (2005) Synthetic biomaterials as instructive extracellular microenvironments for morphogenesis in tissue engineering. Nat Biotechnol 23(1):47–55

    Google Scholar 

  • Luxton G, Gomes E, Folker E, Vintinner E, Gundersen G (2010) Linear arrays of nuclear envelope proteins harness retrograde actin flow for nuclear movement. Science 329(5994):956–959

    Google Scholar 

  • Luxton G, Gomes E, Folker E, Worman H, Gundersen G (2011) TAN lines: a novel nuclear envelope structure involved in nuclear positioning. Nucleus 2(3):173–181

    Google Scholar 

  • Maniotis A, Chen C, Ingber DE (1997) Demonstration of mechanical connections between integrins, cytoskeletal filaments, and nucleoplasm that stabilize nuclear structure. Proc Natl Acad Sci USA 94(3):849–854

    Google Scholar 

  • McElfresh M, Baesu E, Balhorn R, Belak J, Allen M, Rudd R (2002) Combining constitutive materials modeling with atomic force microscopy to understand the mechanical properties of living cells. Proc Natl Acad Sci USA 99(2):6493–6497

    Google Scholar 

  • McGarry J, Klein-Nulend J, Mullender M, Prendergast P (2004) A comparison of strain and fluid shear stress in stimulating bone cell responses–a computational and experimental study. FASEB J 19(3):482–484

    Google Scholar 

  • McGarry J, Prendergast P (2004) A three-dimensional finite element model of an adherent eukaryotic cell. Eur Cell Mater 7:27–33

    Google Scholar 

  • McGarry J, Murphy B, McHugh P (2005) Computational mechanics modelling of cell-substrate contact during cyclic substrate deformation. J Mech Phys Solids 53(12):2597–2637

    MATH  Google Scholar 

  • Mcgarry J, McHugh P (2008) Modelling of in vitro chondrocyte detachment. J Mech Phys Solids 56(4):1554–1565

    Google Scholar 

  • McGarry J (2009) Characterization of cell mechanical properties by computational modeling of parallel plate compression. Ann Biomed Eng 37(11):2317–2325

    Google Scholar 

  • Mehrbod M, Mofrad M (2011) On the significance of microtubule flexural behavior in cytoskeletal mechanics. PLoS One 6(10):e25627

    Google Scholar 

  • Mejat A, Misteli T (2010) LINC complexes in health and disease. Nucleus 1(1):40–52

    Google Scholar 

  • Meyer C, Alenghat F, Rim P, Fong J, Fabry B, Ingber D (2000) Mechanical control of cyclic AMP signalling and gene transcription through integrins. Nat Cell Biol 2(9):666–668

    Google Scholar 

  • Mills J, Qie L, Dao M, Lim C, Suresh S (2004) Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mech Chem Biosyst 1(3):169–180

    Google Scholar 

  • Milner J, Grol M, Beaucage K, Dixon S, Holdsworth DW (2012) Finite-element modeling of viscoelastic cells during high- frequency cyclic strain. J Funct Biomater 3(1):209–224

    Google Scholar 

  • Mofrad M (2009) Rheology of the cytoskeleton. Annu Rev Fluid Mech 41:433–453

    Google Scholar 

  • Nava M, Raimondi M, Pietrabissa R (2012) Controlling self-renewal and differentiation of stem cells via mechanical cues. J Biomed Biotechnol 2012:797410

  • Nelson C, Jean R, Tan J, Liu W, Sniadecki N, Spector A, Chen C (2005) Emergent patterns of growth controlled by multicellular form and mechanics. Proc Natl Acad Sci USA 102(33):11594–11599

    Google Scholar 

  • Ng L, Hung H, Sprunt A, Chubinskaya S, Ortiz C, Grodzinsky A (2007) Nanomechanical properties of individual chondrocytes and their developing growth factor-stimulated pericellular matrix. Biomaterials 40(5):1011–1123

    Google Scholar 

  • Nikkhah M, Edalat F, Manoucheri S, Khademhosseini A (2012) Engineering microscale topographies to control the cell-substrate interface. Biomaterials 33(21):5230–5246

    Google Scholar 

  • Ohashi T, Ishii Y, Ishikawa Y, Matsumoto T, Sato M (2002) Experimental and numerical analyses of local mechanical properties measured by atomic force microscopy for sheared endothelial cells. Biomed Mater Eng 12(3):319–327

    Google Scholar 

  • Pajerowski J, Dahl K, Zhong F, Sammak P, Discher D (2007) Physical plasticity of the nucleus in stem cell differentiation. Proc Natl Acad Sci USA 104(40):15619–15624

    Google Scholar 

  • Paszek M, Zahir N, Johnson K, Lakins J, Rozenberg G, Gefen A, Reinhart-King C, Margulies S, Dembo M, Boettiger D, Hammer D, Weaver V (2005) Tensional homeostasis and the malignant phenotype. Cancer Cells 8(3):241–254

    Google Scholar 

  • Pathak A, Deshpande V, McMeeking R, Evans A (2008) The simulation of stress fibre and focal adhesion development in cells on patterned substrates. J R Soc Interface 5(22):507–524

    Google Scholar 

  • Paul R, Heil P, Spatz J, Schwarz U (2008) Propagation of mechanical stress through the actin cytoskeleton toward focal adhesions: model and experiment. Biophys J 94(4):1470–1482

    Google Scholar 

  • Prager-Khoutorsky M, Lichtenstein A, Krishnan R, Rajendran K, Mayo A, Kam Z, Geiger B, Bershadsky A (2011) Fibroblast polarization is a matrix-rigidity-dependent process controlled by focal adhesion mechanosensing. Nat Cell Biol 13(12):1457–1465

    Google Scholar 

  • Qian J, Liu H, Lin Y, Chen W, Gao H (2013) A mechanochemical model of cell reorientation on substrates under cyclic stretch. PLoS ONE 8(6):e65864

    Google Scholar 

  • Radmacher M (2002) Measuring the elastic properties of living cells by the atomic force microscope in atomic force microscopy in cell biology. Methods Cell Biol 68:67–90

    Google Scholar 

  • Raimondi M, Eaton S, Laganà M, Aprile V, Nava M, Cerullo G, Osellame R (2013) 3D structural niches engineered via two-photon laser polymerization promote stem cell homing. Acta Biomater 9(1):4579–4584

    Google Scholar 

  • Rodriguez M, McGarry P, Sniadecki N (2013) Review on cell mechanics: experimental and modeling approaches. Appl Mech Rev 65(6):060801

    Google Scholar 

  • Ronan W, Deshpande V, McMeeking R, McGarry J (2012) Numerical investigation of the active role of the actin cytoskeleton in the compression resistance of cells. J Mech Behav Biomed Mater 14: 143–157

    Google Scholar 

  • Ronan W, Pathak A, Deshpande V, McMeeking R, McGarry P (2013) Simulation of the mechanical response of cells on micro-post substrates. J Biomech Eng 135(10):101012

    Google Scholar 

  • Satcher J, Dewey C (1996) Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. Biophys J 71(1):109–118

    Google Scholar 

  • Satcher R, Dewey C, Hartwig J (1997) Mechanical remodeling of endothelial surface and actin cytoskeleton induced by fluid flow. Microcirculation 4(4):439–453

    Google Scholar 

  • Sato M, Theret D, Wheeler L, Ohshima N, Nerem R (1990) Application of the micropipette technique to the measurement of cultured porcine aortic endothelial cell viscoelastic properties. ASME J Biomech Eng 112:263–268

    Google Scholar 

  • Schachter T, Shen T, Liu Y, Schneider M (2012) Kinetics of nuclear-cytoplasmic translocation of Foxo1 and Foxo3A in adult skeletal muscle fibers. Am J Physiol Cell Physiol 303(9):C977–C990

    Google Scholar 

  • Schreiber K, Kennedy B (2013) When lamins go bad: nuclear structure and disease. Cell 152(6):1365–1375

    Google Scholar 

  • Schwartz M (2010) Integrins and extracellular matrix in mechanotransduction. Cold Spring Harb Perspect Biol 2(12):a005066

    Google Scholar 

  • Shin D, Athanasiou K (1999) Cytoindentation for obtaining cell biomechanical properties. J Orthop Res 17(6):880–890

    Google Scholar 

  • Shivashankar G (2011) Mechanosignaling to the cell nucleus and gene regulation. Annu Rev Biophys 40:361–378

    Google Scholar 

  • Slomka N, Gefen A (2010) Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics. J Biomech 43(9):1806–1816

    Google Scholar 

  • Stamenovic D (2005) Effects of cytoskeletal prestress on cell rheological behavior. Acta Biomater, 1(3):255–262

    Google Scholar 

  • Stamenovic D, Fredberg J, Wang N, Butler J, Ingber D (1996) A microstructural approach to cytoskeletal mechanics based on tensegrity. J Theor Biol 181(2):125–136

    Google Scholar 

  • Stamenovic D, Coughlin M (1999) The role of prestress and architecture of the cytoskeleton and deformability of cytoskeletal filaments in mechanics of adherent cells: a quantitative analysis. J Theor Biol 201(1):63–74

    Google Scholar 

  • Stamenovic D, Wang N (2000) Invited review: engineering approaches to cytoskeletal mechanics. J Appl Physiol 89(5):2085–2090

    Google Scholar 

  • Stamenovic D, Ingber D (2002) Models of cytoskeletal mechanics of adherent cells. Biomech Model Mechanobiol 1(1):95–108

    Google Scholar 

  • Stamenovic D, Mijailovich SM, Tolic-Norrelykke IM, Wang N (2003) Experimental tests of the cellular tensegrity hypothesis. Biorheology 40(1–3):221–225

    Google Scholar 

  • Sugimoto H, Mundel T, Sund M, Xie L, Cosgrove D, Kalluri R (2006) Bone-marrow-derived stem cells repair basement membrane collagen defects and reverse genetic kidney disease. Proc Natl Acad Sci USA 103(19):7321–7326

    Google Scholar 

  • Sultan C, Stamenovic D, Ingber D (2004) A computational tensegrity model predicts dynamic rheological behaviors in living cells. Ann Biomed Eng 32(4):520–530

    Google Scholar 

  • Suresh S, Spatz J, Mills J, Micoulet A, Dao M, Lim C, Beil M, Seufferlein T (2005) Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria. Acta Biomater 1(1):15–30

    Google Scholar 

  • Tan J, Kalapesi F, Coroneo M (2006) Mechanosensitivity and the eye: cells coping with the pressure. Br J Ophthalmol 90(3):383–388

    Google Scholar 

  • Theret D, Levesque M, Sato M, Nerem R, Wheeler L (1988) The application of a homogeneous half-space model in the analysis of endothelial-cell micropipette measurements. ASME J Biomech Eng 110:190–199

    Google Scholar 

  • Thomas C, Collier J, Sfeir C, Healy K (1998) Engineering gene expression and protein synthesis by modulation of nuclear shape. Proc Natl Acad Sci USA 99(4):1972–1977

    Google Scholar 

  • Tibbitt M, Anseth K (2009) Hydrogels as extracellular matrix mimics for 3D cell culture. Biotechnol Bioeng 103(4):655–663

    Google Scholar 

  • Trickey W, Lee G, Guilak F (2000) Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage. J Orthop Res 18(6):891–898

    Google Scholar 

  • Trickey W, Baaijens F, Laursen T, Alexopoulos L, 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(1):78–87

    Google Scholar 

  • Tsai M, Wang S, Heidinger J, Shumaker D, Adam S, Goldman R, Zheng Y (2006) A mitotic lamin B matrix induced by RanGTP required for spindle assembly. Science 311(5769):1887–1893

    Google Scholar 

  • Vaziri A, Lee H, Mofrad M (2006) Deformation of the cell nucleus under indentation: mechanics and mechanisms. J Mater Res 21(8): 2126–2135

    Google Scholar 

  • Vaziri A, Mofrad M (2007) Mechanics and deformation of the nucleus in micropipette aspiration experiment. J Biomech 40(9):2053–2062

    Google Scholar 

  • Vaziri A, Gopinath A, Deshpande V (2007a) Continuum-based computational models in cell and nuclear mechanics. J Mech Mater Struct 2(6):1169–1191

    Google Scholar 

  • Vaziri A, Xue Z, Kamm RD, Kaazempur-Mofrad MR (2007b) A computational study on power-law rheology of soft glassy materials with application to cell mechanics. Comput Methods Appl Mech Eng 196(31–32):2965–2971

    Google Scholar 

  • Vaziri A, Gopinath A (2008) Cell and biomolecular mechanics in silico. Nat Mater 7(1):15–23

    Google Scholar 

  • Vollrath M, Kwan K, Corey D (2007) The micromachinery of mechanotransduction in hair cells. Ann Rev Neurosci 30:339–365

    Google Scholar 

  • Wang N, Butler J, Ingber D (1993) Mechanotransduction across the cell surface and through the cytoskeleton. Science 260(5111):1124–1127

    Google Scholar 

  • Wang H, Ip W, Boissy R, Grood ES (1995) Cell orientation response to cyclically deformed substrates: experimental validation of a cell model. J Biomech 28(12):1543–1552

    Google Scholar 

  • Wang J, Thampatty B (2006) An introductory review of cell mechanobiology. Biomech Model Mechanobiol 5(1):1–16

    Google Scholar 

  • Wang J, Thampatty B (2008) Mechanobiology of adult and stem cells. Int Rev Cell Mol Biol 271:301–346

    Google Scholar 

  • Wang N, Tytell J, Ingber D (2009) Mechanotransduction at a distance: mechanically coupling the extracellular matrix with the nucleus. Nat Rev Mol Cell Biol 10(1):75–82

    Google Scholar 

  • Wang S, Wolynes P (2012) Tensegrity and motor-driven effective interactions in a model cytoskeleton. J Chem Phys 136(14):145102

    Google Scholar 

  • Webster M, Witkin K, Cohen-Fix O (2009) Sizing up the nucleus: nuclear shape, size and nuclear-envelope assembly. J Cell Sci 122(10):1477–1486

    Google Scholar 

  • Wei Z, Deshpande V, McMeeking R, Evans A (2008) Analysis and interpretation of stress fiber organization in cells subjected to cyclic stretch. J Biomech Eng 130(3):031009

    Google Scholar 

  • Wiche G (1998) Role of plectin in cytoskeleton organization and dynamics. J Cell Sci 111(Pt 17):2477–2486

    Google Scholar 

  • Wojciak-Stothard B, Ridley A (2003) Shear stress-induced endothelial cell polarization is mediated by Rho and Rac but not Cdc42 or PI 3-kinases. J Cell Biol 161(2):429–439

    Google Scholar 

  • Yang MT, Sniadecki NJ, Chen CS (2007) Geometric considerations of micro- to nanoscale elastomeric post arrays to study cellular traction forces. Adv Mater 19(20):3119–3123

    Google Scholar 

  • Zeng X, Li S (2011a) Modelling and simulation of substrate elasticity sensing in stem cells. Comput Methods Biomech Biomed Eng 14(5):447–458

    Google Scholar 

  • Zeng X, Li S (2011b) Multiscale modeling and simulation of soft adhesion and contact of stem cells. J Mech Behav Biomed Mater 4(2):180–189

    Google Scholar 

  • Zhou E, Lim C, Quek S (2005) Finite element simulation of the micropipette aspiration of a living cell undergoing large viscoelastic deformation. Mech Adv Mater Struct 12(6):501–512

    Google Scholar 

Download references

Acknowledgments

This project is funded by the Cariplo Foundation (Milano), under grant 2010 “3D Micro structuring and Functionalisation of Polymeric Materials for Scaffolds in Regenerative Medicine”.

Author information

Authors and Affiliations

  1. LaBS - Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Piazza L. da Vinci, 32, 20133 , Milano, Italy

    Michele M. Nava, Manuela T. Raimondi & Riccardo Pietrabissa

Authors
  1. Michele M. Nava
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuela T. Raimondi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Riccardo Pietrabissa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michele M. Nava.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nava, M.M., Raimondi, M.T. & Pietrabissa, R. Bio-chemo-mechanical models for nuclear deformation in adherent eukaryotic cells. Biomech Model Mechanobiol 13, 929–943 (2014). https://doi.org/10.1007/s10237-014-0558-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-014-0558-8

Keywords

Search

Navigation