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Divided medium-based model for analyzing the dynamic reorganization of the cytoskeleton during cell deformation

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Abstract

Cell deformability and mechanical responses of living cells depend closely on the dynamic changes in the structural architecture of the cytoskeleton (CSK). To describe the dynamic reorganization and the heterogeneity of the prestressed multi-modular CSK, we developed a two-dimensional model for the CSK which was taken to be a system of tension and compression interactions between the nodes in a divided medium. The model gives the dynamic reorganization of the CSK consisting of fast changes in connectivity between nodes during medium deformation and the resulting mechanical behavior is consistent with the strain-hardening and prestress-induced stiffening observed in cells in vitro. In addition, the interaction force networks which occur and balance to each other in the model can serve to identify the main CSK substructures: cortex, stress fibers, intermediate filaments, microfilaments, microtubules and focal adhesions. Removing any of these substructures results in a loss of integrity in the model and a decrease in the prestress and stiffness, and suggests that the CSK substructures are highly interdependent. The present model may therefore provide a useful tool for understanding the cellular processes involving CSK reorganization, such as mechanotransduction, migration and adhesion processes.

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References

  • Alcaraz J, Buscemi L, Grabulosa M, Trepat X, Fabry B, Farré R, Navajas D (2003) Microrheology of human lung epithelial cells measured by atomic force microscopy. Biophys J 84(3):2071–2079

    Google Scholar 

  • Balaban NQ, Schwarz US, Riveline D, Goichberg P, Tzur G, Sabanay I, Mahalu D, Safran S, Bershadsky A, Addadi L, Geiger B (2001) Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. Nat Cell Biol 3(5):466–472

    Article  Google Scholar 

  • Bershadsky AD, Balaban NQ, Geiger B (2003) Adhesion- dependent cell mechanosensitivity. Annu Rev Cell Dev Biol 19:677–695

    Article  Google Scholar 

  • Cambou J, Jean M (2001) Micromécanique des matériaux granulaires. Hermes Sciences, Paris

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Chen CS, Alonso JL, Ostuni E, Whitesides GM, Ingber DE (2003) Cell shape provides global control of focal adhesion assembly. Biochem Biophys Res Commun 307(2):355–361

    Article  Google Scholar 

  • Chicurel ME, Chen CS, Ingber DE (1998) Cellular control lies in the balance of forces. Curr Opin Cell Biol 10(2):232–239

    Article  Google Scholar 

  • Collinsworth AM, Zhang S, Kraus WE, Truskey GA (2002) Apparent elastic modulus and hysteresis of skeletal muscle cells throughout differentiation. Am J Physiol Cell Physiol 283(4):C1219–C1227

    Google Scholar 

  • Coughlin MF, Stamenović D (1997) A tensegrity structure with buckling compression elements: applications to cell mechanics. J Appl Mech 64:480–486

    MATH  Google Scholar 

  • Coughlin MF, Stamenović D (1998) A tensegrity model of the cytoskeleton in spread and round cells. J Biomech Eng 120(6):770–777

    Google Scholar 

  • Coughlin MF, Stamenović D (2003) A prestressed cable network model of the adherent cell cytoskeleton. Biophys J 84(2 Pt 1):1328–1336

    Google Scholar 

  • Coulombe PA, Bousquet O, Ma L, Yamada S, Wirtz D (2000) The ‘ins’ and ‘outs’ of intermediate filament organization. Trends Cell Biol 10(10):420–428

    Article  Google Scholar 

  • Davies PF, Robotewskyj A, Griem ML (1994) Quantitative studies of endothelial cell adhesion. Directional remodeling of focal adhesion sites in response to flow forces. J Clin Invest 93(5):2031–2038

    Article  Google Scholar 

  • Deguchi S, Ohashi T, Sato M (2005) Tensile properties of single stress fibers isolated from cultured vascular smooth muscle cells. J Biomech 38:1751–1759

    Article  Google Scholar 

  • Desprat N, Richert A, Simeon J, Asnacios A (2005) Creep function of a single living cell. Biophys J 88(3):2224–2233

    Article  Google Scholar 

  • Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas D, Taback NA, Millet EJ, Fredberg JJ (2003) Time scale and other invariants of intergrative mechanical behavior in living cells. Phys Rev E 68:041914-32

    Article  Google Scholar 

  • Forgacs G, Yook SH, Janmey PA, Jeong H, Burd CG (2004) Role of the cytoskeleton in signaling networks. J Cell Sci 117(Pt 13):2769–2775

    Article  Google Scholar 

  • Fudge DS, Gardner KH, Forsyth VT, Riekel C, Gosline JM (2003) The mechanical properties of hydrated intermediate filaments: insights from hagfish slime threads. Biophys J 85(3):2015– 2027

    Google Scholar 

  • Gittes F, Mickey B, Nettleton J, Howard J (1993) Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape. J Cell Biol 120(4):923– 934

    Article  Google Scholar 

  • Griffin MA, Engler AJ, Barber TA, Healy KE, Sweeney HL, Discher DE (2004) Patterning, prestress, peeling dynamics of myocytes. Biophys J 86(2):1209–1222

    Google Scholar 

  • Harris AK, Wild P, Stopak D (1980) Silicone rubber substrata: a new wrinkle in the study of cell locomotion. Science 208(4440):177–179

    Article  Google Scholar 

  • Heidemann SR, Wirtz D (2004) Towards a regional approach to cell mechanics. Trends Cell Biol 14(4):160–166

    Article  Google Scholar 

  • Heidemann SR, Kaech S, Buxbaum RE, Matus A (1999) Direct observations of the mechanical behaviors of the cytoskeleton in living fibroblasts. J Cell Biol 145(1):109–122

    Article  Google Scholar 

  • Hubmayr RD, Shore SA, Fredberg JJ, Planus E, Panettieri RA, Moller W, Heyder J, Wang N (1996) Pharmacological activation changes stiffness of cultured human airway smooth muscle cells. Am J Physiol 271(5 Pt 1):C1660–C1668

    Google Scholar 

  • Hughes-Fulford M (2004) Signal transduction and mechanical stress. Sci STKE 2004(249):RE12

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

    Article  Google Scholar 

  • Ingber DE (2000) Opposing views on tensegrity as a structural framework for understanding cell mechanics. J Appl Physiol 89(4):1663–1670

    Google Scholar 

  • Ingber DE (2003) Tensegrity I. cell structure and hierarchical systems biology. J Cell Sci 116(Pt 7):1157–1173

    Article  Google Scholar 

  • Janson ME, de~Dood ME, Dogterom M (2003) Dynamic instability of microtubules is regulated by force. J Cell Biol 161(6):1029–1034

    Article  Google Scholar 

  • Jean M (1999)The non-smooth contact dynamics method. Comput Methods Appl Mech Engng 177:235–257

    Article  MATH  MathSciNet  Google Scholar 

  • Jean M (2001) Non-smooth contact dynamics approach of cohesive materials. Philos Trans R Soc Lond A 359:2497–2518

    Article  MATH  MathSciNet  Google Scholar 

  • Katoh K, Kano Y, Masuda M, Onishi H, Fujiwara K (1998) Isolation and contraction of the stress fiber. Mol Biol Cell 9(7):1919–1938

    Google Scholar 

  • Kaverina I, Rottner K, Small JV (1998) Targeting, capture, and stabilization of microtubules at early focal adhesions. J Cell Biol 142(1):181–190

    Article  Google Scholar 

  • Kojima H, Ishijima A, Yanagida T (1994) Direct measurement of stiffness of single actin filaments with and without tropomyosin by in vitro nanomanipulation. Proc Natl Acad Sci USA 91(26):12962–12966

    Article  Google Scholar 

  • Kole TP, Tseng Y, Huang L, Katz JL, Wirtz D (2004) Rho kinase regulates the intracellular micromechanical response of adherent cells to rho activation. Mol Biol Cell 15(7):3475– 3484

    Article  Google Scholar 

  • Kole TP, Tseng Y, Jiang I, Katz JL, Wirtz D (2005) Intracellular mechanics of migrating fibroblasts. Mol Biol Cell 16(1):328–338

    Article  Google Scholar 

  • Kurachi M, Hoshi M, Tashiro H (1995) Buckling of a single microtubule by optical trapping forces: direct measurement of microtubule rigidity. Cell Motil Cytoskeleton 30(3):221– 228

    Article  Google Scholar 

  • Laurent VM, Canadas P, Fodil R, Planus E, Asnacios A, Wendling S, and Isabey D (2002) Tensegrity behaviour of cortical and cytosolic cytoskeletal components in twisted living adherent cells. Acta Biotheor 50(4):331–356

    Article  Google Scholar 

  • Laurent VM, Fodil R, Canadas P, Féréol S, Louis B, Planus E, Isabey D (2003) Partitioning of cortical and deep cytoskeleton responses from transient magnetic bead twisting. Ann Biomed Engng 31(10):1263–1278

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Marek LF, Kelley RO, Perdue BD (1982) Organization of the cytoskeleton in square fibroblasts. Cell Motil 2(2):115–130

    Article  Google Scholar 

  • McGarry JG, Prendergast PJ (2004) A three-dimensional finite element model of an adherent eukaryotic cell. Eur Cell Mater 7:27–33; discussion 33–4

    Google Scholar 

  • Meazzini MC, Toma CD, Schaffer JL, Gray ML, (1998) Osteoblast cytoskeletal modulation in response to mechanical strain in vitro. J Orthop Res 16(2):170–180

    Article  Google Scholar 

  • Micoulet A, Spatz JP, Ott A (2005) Mechanical response analysis and power generation by single-cell stretching. Chemphyschem 6(4):663–670

    Article  Google Scholar 

  • Mooney DJ, Langer R, Ingber DE (1995) Cytoskeletal filament assembly and the control of cell spreading and function by extracellular matrix. J Cell Sci 108(Pt 6):2311–2320

    Google Scholar 

  • Moreau JJ (1993) New computation methods in granular dynamics. Powder Grains 93:227–232

    Google Scholar 

  • Petersen NO, McConnaughey WB, Elson EL (1982) Dependence of locally measured cellular deformability on position on the cell, temperature, cytochalasin b. Proc Natl Acad Sci USA 79(17):5327–5331

    Article  Google Scholar 

  • Pienta KJ, Coffey DS (1991) Cellular harmonic information transfer through a tissue tensegrity-matrix system. Med Hypotheses 34(1):88–95

    Article  Google Scholar 

  • Planus E, Galiacy S, Matthay M, Laurent V, Gavrilovic J, Murphy G, Clérici C, Isabey D, Lafuma C, d’Ortho MP (1999) Role of collagenase in mediating in vitro alveolar epithelial wound repair. J Cell Sci 112(Pt 2):243–252

    Google Scholar 

  • Pourati J, Maniotis A, Spiegel D, Schaffer JL, Butler JP, Fredberg JJ, Ingber DE, Stamenovic D, Wang N (1998) Is cytoskeletal tension a major determinant of cell deformability in adherent endothelial cells?. Am J Physiol 274(5 Pt 1):C1283–C1289

    Google Scholar 

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

    Google Scholar 

  • Sato K, Adachi T, Matsuo M, Tomita Y (2005) Quantitative evaluation of threshold fiber strain that induces reorganization of cytoskeletal actin fiber structure in osteoblastic cells. J Biomech 38(9):1895–1901

    Article  Google Scholar 

  • Smith PG, Deng L, Fredberg JJ, Maksym GN (2003) Mechanical strain increases cell stiffness through cytoskeletal filament reorganization. Am J Physiol Lung Cell Mol Physiol 285(2):L456–L463

    Google Scholar 

  • Stamenovic D, Coughlin MF (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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Stamenovic D, Mijailovich SM, Tolic-Nørrelykke IM, Chen J, Wang N (2002) Cell prestress. II. contribution of microtubules. Am J Physiol Cell Physiol 282(3):C617–C624

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Thoumine O, Ott A (1996) Influence of adhesion and cytoskeletal integrity on fibroblast traction. Cell Motil Cytoskeleton 35(3):269–280

    Article  Google Scholar 

  • Thoumine O, Ott A (1997) Time scale dependent viscoelastic and contractile regimes in fibroblasts probed by microplate manipulation. J Cell Sci 110(Pt 17):2109–2116

    Google Scholar 

  • Thoumine O, Cardoso O, Meister JJ (1999) Changes in the mechanical properties of fibroblasts during spreading: a micromanipulation study. Eur Biophys J 28(3):222–234

    Article  Google Scholar 

  • Tseng Y, An KM, Esue O, Wirtz D (2004) The bimodal role of filamin in controlling the architecture and mechanics of f-actin networks. J Biol Chem 279(3):1819–1826

    Article  Google Scholar 

  • Volokh KY, Vilnay O, Belsky M (2000) Tensegrity architecture explains linear stiffening and predicts softening of living cells. J Biomech 33(12):1543–1549

    Article  Google Scholar 

  • Wakatsuki T, Kolodney MS, Zahalak GI, Elson EL (2000) Cell mechanics studied by a reconstituted model tissue. Biophys J 79(5):2353–2368

    Google Scholar 

  • Wang N (1998) Mechanical interactions among cytoskeletal filaments. Hypertension 32(1):162–165

    Google Scholar 

  • Wang N, Ingber DE (1994) Control of cytoskeletal mechanics by extracellular matrix, cell shape, mechanical tension. Biophys J 66(6):2181–2189

    Article  Google Scholar 

  • Wang N, Stamenovic D (2000) Contribution of intermediate filaments to cell stiffness, stiffening, and growth. Am J Physiol Cell Physiol 279(1):C188–C194

    Google Scholar 

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

    Article  Google Scholar 

  • Wang N, Naruse K, Stamenovic D, Fredberg JJ, Mijailovich SM, Tolic-Nørrelykke IM, Polte T, Mannix R, Ingber DE (2001) Mechanical behavior in living cells consistent with the tensegrity model. Proc Natl Acad Sci USA 98(14):7765–7770

    Article  Google Scholar 

  • Wang N, Tolic-Nørrelykke IM, Chen J, Mijailovich SM, Butler JP, Fredberg JJ, Stamenovic D (2002) Cell prestress. I. stiffness and prestress are closely associated in adherent contractile cells. Am J Physiol Cell Physiol 282(3):C606–C616

    Google Scholar 

  • Wendling S, Oddou C, Isabey D (1999) Stiffening response of a cellular tensegrity model. J Theor Biol 196(3):309–325

    Article  Google Scholar 

  • Wendling S, Planus E, Laurent VM, Barbe L, Mary A, Oddou C, Isabey D (2000) Role of cellular tone and microenvironmental conditions on cytoskeleton stiffness assessed by tensegrity model. Eur Phys J Appl Physiol 9:51–62

    Article  Google Scholar 

  • Wendling S, Canadas P, Chabrand P (2003) Toward a generalised tensegrity model describing the mechanical behaviour of the cytoskeleton structure. Comput Methods Biomech Biomed Engng 6(1):45–52

    Article  Google Scholar 

  • Zhen Y-Y, Libotte T, Munck M, Noegel AA, Korenbaum E (2002) Nuance, a giant protein connecting the nucleus and actin cytoskeleton. J Cell Sci 115(Pt 15):3207–3222

    Google Scholar 

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Milan, J.L., Wendling-Mansuy, S., Jean, M. et al. Divided medium-based model for analyzing the dynamic reorganization of the cytoskeleton during cell deformation. Biomech Model Mechanobiol 6, 373–390 (2007). https://doi.org/10.1007/s10237-006-0057-7

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