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A model for the contractility of the cytoskeleton including the effects of stress-fibre formation and dissociation. (English) Zbl 1131.92025
Summary: A model for the contractility of cells is presented that accounts for the dynamic reorganization of the cytoskeleton. It is motivated by three key biochemical processes: (i) an activation signal that triggers actin polymerization and myosin phosphorylation, (ii) the tension-dependent assembly of the actin and myosin into stress fibres, and (iii) the cross-bridge cycling between the actin and the myosin filaments that generates the tension. Simple relations are proposed to model these coupled phenomena and a constitutive law is developed for the activation and response of a single stress fibre. This law is generalized to two- and three-dimensional cytoskeletal networks by employing a homogenization analysis and a finite strain continuum model is developed.
The key features of the model are illustrated by considering: (i) a single stress fibre on a series of supports and (ii) a two-dimensional square cell on four supports. The model is shown to be capable of predicting a variety of key experimentally established characteristics including: (i) the decrease of the forces generated by the cell with increasing support compliance, (ii) the influence of cell shape and boundary conditions on the development of structural anisotropy, and (iii) the high concentration of the stress fibres both at the focal adhesions and at the sites of localized applied tension. Moreover, consistent with the experimental findings, the model predicts that multiple activation signals are more effective at developing stress fibres than a single prolonged signal.

MSC:
92C37 Cell biology
92C40 Biochemistry, molecular biology
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[1] Balaban, N.Q. <i>et al.</i> 2001 Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. <i>Nat. Mater.</i>&nbsp;<b>3</b>, 466–472.
[2] Bao, G. & Suresh, S. 2003 Cell and molecular mechanics of biological materials. <i>Nat. Mater.</i>&nbsp;<b>2</b>, 715–725, (doi:10.1038/nmat1001).
[3] Burridge, K. & Chrzanowska-Wodnicka, M. 1996 Focal adhesions, contractility and signaling. <i>Annu. Rev. Cell Dev. Biol.</i>&nbsp;<b>12</b>, 463–469, (doi:10.1146/annurev.cellbio.12.1.463).
[4] Burton, K. & Taylor, D.L. 1997 Traction forces of cytokinesis measured with optically modified elastic substrata. <i>Nature</i>&nbsp;<b>385</b>, 450–454, (doi:10.1038/385450a0).
[5] Choquet, D., Felsenfeld, D.P. & Sheetz, M.P. 1997 Extracellular matrix rigidity causes strengthening of integrin cytoskeleton linkage. <i>Cell</i>&nbsp;<b>88</b>, 39–48, (doi:10.1016/S0092-8674(00)81856-5).
[6] Deshpande, V.S., McMeeking, R.M. & Evans, A.G. 2006 A bio-chemo-mechanical model for cell contractility. <i>Proc. Natl Acad. Sci. USA</i>&nbsp;<b>103</b>, 14015–14020, (doi:10.1073/pnas.0605837103).
[7] Discher, D.E., Janmey, P. & Wang, Y.-L. 2005 Tissue cells feel and respond to the stiffness of their substrate. <i>Science</i>&nbsp;<b>310</b>, 1139–1143, (doi:10.1126/science.1116995).
[8] Franke, R.P., Grafe, M., Schnittler, H., Seiffge, D., Mittermayer, C. & Drenckhahn, D. 1984 Induction of human vascular endothelial stress fibers by fluid shear stress. <i>Nature</i>&nbsp;<b>307</b>, 648–649, (doi:10.1038/307648a0).
[9] Grinnell, F. 1994 Fibroblasts, myofibroblasts, and wound contraction. <i>J. Cell Biol.</i>&nbsp;<b>124</b>, 401–404, (doi:10.1083/jcb.124.4.401).
[10] Harris, A.K., Stopak, D. & Wild, P. 1981 Fibroblast traction as a mechanism for collagen morphogenesis. <i>Nature</i>&nbsp;<b>290</b>, 249–251, (doi:10.1038/290249a0).
[11] Hill, A.V. 1938 The heat of shortening and the dynamic constants of muscle. <i>Proc. R. Soc. B</i>&nbsp;<b>126</b>, 136–195.
[12] Hill, R. 1963 Elastic properties of reinforced solids: some theoretical principles. <i>J. Mech. Phys. Solids</i>&nbsp;<b>11</b>, 357–372, (doi:10.1016/0022-5096(63)90036-X).
[13] Hochmuth, R.M. 1987 <i>Handbook of bioengineering</i> (eds. Skalak, R. & Chien, S.), pp. 12.1–12.7, New York, NY: McGraw-Hill
[14] Ingber, D.E. 1997 Tensegrity: the architectural basis of cellular mechanotransduction. <i>Annu. Rev. Physiol.</i>&nbsp;<b>57</b>, 575–599, (doi:10.1146/annurev.physiol.59.1.575).
[15] Kolega, J. 1986 Effects of mechanical tension on protrusive activity and microfilament and intermediate filament organization in an epidermal epithelium moving in culture. <i>J. Cell Biol.</i>&nbsp;<b>102</b>, 1400–1411, (doi:10.1083/jcb.102.4.1400).
[16] Lo, C.-M., Wang, H.-B., Dembo, M. & Wang, Y.-L. 2000 Cell movement is guided by the rigidity of the substrate. <i>Biophys. J.</i>&nbsp;<b>79</b>, 144–152.
[17] Mochitate, K., Pawelek, P. & Grinnell, F. 1991 Stress relaxation of contracted collagen gels: disruption of actin filament bundles, release of cell surface fibronectin, and down-regulation of DNA and protein synthesis. <i>Exp. Cell Res.</i>&nbsp;<b>193</b>, 198–207, (doi:10.1016/0014-4827(91)90556-A).
[18] Mohrdieck, C., Wanner, A., Roos, W., Roth, A., Sackmann, E., Spatz, J.P. & Arzt, E. 2005 A theoretical description of elastic pillar substrates in biophysical experiments. <i>Chem. Phys. Chem.</i>&nbsp;<b>6</b>, 1492–1498.
[19] Nelson, C.M., Jean, R.P., Tan, J.L., Liu, W.F., Sniadecki, N.J., Spector, A.A. & Chen, C.S. 2005 Emergent patterns of growth controlled by multicellular form and mechanics. <i>Proc. Natl Acad. Sci. USA</i>&nbsp;<b>102</b>, 11594–11599, (doi:10.1073/pnas.0502575102).
[20] Parker, K.K. <i>et al.</i> 2002 Directional control of lamellipodia extension by constraining cell shape and orienting cell tractional forces. <i>FASEB J.</i>&nbsp;<b>16</b>, 1195–1204, (doi:10.1096/fj.02-0038com).
[21] Rice, J.J., Winslow, R.L. & Hunter, W.C. 1999 Comparison of putative cooperative mechanisms in cardiac muscle: length dependence and dynamic responses. <i>Am. J. Physiol. Heart Circ. Physiol.</i>&nbsp;<b>276</b>, H1734–H1754.
[22] Robling, A.G., Burr, D.B. & Turner, C.H. 2001 Recovery periods restore mechanosensitivity to dynamically loaded bone. <i>J. Exp. Biol.</i>&nbsp;<b>204</b>, 3389–3399.
[23] Roure, O.D., Saez, A., Buguin, A., Austin, R.H., Chavrier, P., Silberza, P. & Ladoux, B. 2005 Force mapping in epithelial cell migration. <i>Proc. Natl Acad. Sci. USA</i>&nbsp;<b>102</b>, 2390–2395, (doi:10.1073/pnas.0408482102).
[24] Rudy, Y. 2000 From genome to physiome: integrative models of cardiac excitation. <i>Ann. Biomed. Eng.</i>&nbsp;<b>28</b>, 945–950, (doi:10.1114/1.1308484).
[25] Satcher, R.L.J. & Dewey, C.F.J. 1996 Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. <i>Biophys. J.</i>&nbsp;<b>71</b>, 109–118.
[26] Storm, C., Pastore, J.J., MacKintosh, F.C., Lubensky, T.C. & Janmey, P.A. 2005 Nonlinear elasticity in biological gels. <i>Nature</i>&nbsp;<b>435</b>, 191–194, (doi:10.1038/nature03521).
[27] Tan, J.L., Tien, J., Pirone, D.M., Gray, D.S., Bhadriraju, K. & Chen, C.S. 2003 Cells lying on a bed of microneedles: an approach to isolate mechanical force. <i>Proc. Natl Acad. Sci. USA</i>&nbsp;<b>100</b>, 1484–1489, (doi:10.1073/pnas.0235407100).
[28] Thomopoulos, S., Fomovsky, G.M. & Holmes, J.W. 2005 The development of structural and mechanical anisotropy in fibroblast populated collagen gels. <i>J. Biomech. Eng. Trans. ASME</i>&nbsp;<b>127</b>, 742–750, (doi:10.1115/1.1992525).
[29] Wang, N., Butler, J.P. & Ingber, D.E. 1993 Mechanotransduction across the cell surface through the cytoskeleton. <i>Science</i>&nbsp;<b>260</b>, 1124–1127, (doi:10.1126/science.7684161).
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