Skip to main content
SpringerLink
Log in

Review and perspective on soft matter modeling in cellular mechanobiology: cell contact, adhesion, mechanosensing, and motility

  • Review and Perspective in Mechanics
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Mechanical interactions between cells and extracellular matrix are known to regulate cellular processes ranging from cell signaling, spreading, migration, tissue morphogenesis, to cell differentiation, which may even alter cell phenotype and change physical properties of cells. Moreover, understanding cell contact, adhesion, and cellular mechanotransduction has great significance to cell cultures, muscle growth, and wound healing, and some related diseases such as cancer and fibrosis. For these reasons, cell mechanobiology research has become a focal point in the field of molecular and cell biology research receiving much attention from both biologists and biophysicists in recent years. In fact, cellular mechanobiology is an emerging multidisciplinary field that encompasses molecular cell biology, cell developmental biology, bioengineering and biophysics, and soft matter physics and mechanics. In this document, we would like to present an overview on the recent research developments on mechanics of cells and cellular mechanotransduction through the viewpoint of soft matter physics and biophysics, particularly from the perspective of mechanics of soft materials. Specifically, we review the recent research activities in mechanics of soft matter contact and cell behaviors involving experimental observations, mathematical modeling, and computational methods. Finally, the paper provides author’s perspectives on future issues and challenges on modeling and computational aspects.

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

Similar content being viewed by others

References

  1. Morin, S.A., Shepherd, R.F., Kwok, S.W., Stokes, A.A., Nemiroski, A., Whitesides, G.M.: Camouflage and display for soft machines. Science 337, 828–832 (2012)

    Article  Google Scholar 

  2. Shepherd, R.F., Ilievski, F., Choi, W., Morin, S.A., Stokes, A.A., Mazzeo, A.D., Chen, X., Wang, M., Whitesides, G.M.: Multigait soft robot. Proc. Nat. Acad. Sci. 108(51), 20400–20403 (2011)

    Article  Google Scholar 

  3. Suo, Z., Ma, E.Y., Gleskova, H., Wagner, S.: Mechanics of rollable and foldable film-on-foil electronics. Appl. Phys. Lett. 74(8), 1177–1179 (1999)

    Article  Google Scholar 

  4. Wood, R., Walsh, C.: Smaller, softer, safer, smarter robots 5, 210ed19 (2013). www.ScienceTranslationalMedicine.org

  5. Sun, J.Y., Keplinger, C., Whitesides, G.M., Suo, Z.: Ionic skin. Adv. Mater. 26(45), 7608–7614 (2014)

    Article  Google Scholar 

  6. Shin, H., Jo, S., Mikos, A.G.: Biomimetic materials for tissue engineering. Biomaterials 24, 4353–4364 (2003)

    Article  Google Scholar 

  7. Zeng, X., Li, S., Ren, B.: Soft matter modeling of biological cells. In: Li, S., Sun, B. (eds.) Advances in Soft Matter Mechanics, pp. 95–117. Higher Education Press, Beijing (2012)

    Chapter  Google Scholar 

  8. Lindner, R.A., Ralson, G.B.: Macromolecular crowding: effects on actin polymerisation. Biophys. Chem. 66, 57–66 (1997)

    Article  Google Scholar 

  9. Yang, Y., Tobias, I., Olson, W.: Finite element analysis of DNA supercoiling. J. Chem. Phys. 98, 1673–1686 (1993)

    Article  Google Scholar 

  10. Style, R.W., Jagota, A., Hui, C.-Y., Dufresne, E.R.: Elastocapillarity: surface tension and the mechanics of soft solids. Ann. Rev. Condens. Matter Phys. 8, 99–118 (2016)

    Article  Google Scholar 

  11. Gao, H., Qian, J., Chen, B.: Probing mechanical principles of focal contacts in cell-matrix adhesion with a coupled stochastic-elastic modeling framework. J. R. Soc. Interface 8, 1217–1232 (2011)

    Article  Google Scholar 

  12. Friedl, P., Zanker, K.S., Brocker, E.B.: Cell migration strategies in 3-D extracellular matrix: differences in morphology, cell matrix interactions, and integrin function. Microsc. Res. Tech. 43(5), 369–378 (1998)

    Article  Google Scholar 

  13. Aman, A., Piotrowski, T.: Cell migration during morphogenesis. Dev. Biol. 341(1), 20–33 (2010)

    Article  Google Scholar 

  14. Friedl, P., Gilmour, D.: Collective cell migration in morphogenesis, regeneration and cancer. Nat. Rev. Mol. Cell Biol. 10(7), 445–457 (2009)

    Article  Google Scholar 

  15. Li, L., He, Y., Zhao, M., Jiang, J.: Collective cell migration: implications for wound healing and cancer invasion. Burns Trauma 1, 21–26 (2013)

    Article  Google Scholar 

  16. Fong, E., Tzlil, S., Tirrellb, D.A.: Boundary crossing in epithelial wound healing. Proc. Nat. Acad. Sci. U.S.A. 107, 19302–19307 (2010)

    Article  Google Scholar 

  17. Poujade, M., Grasland-Mongrain, E., Hertzog, A., Jouanneau, J., Chavrier, P., Ladoux, B., Buguin, A., Silberzan, P.: Collective migration of an epithelial monolayer in response to a model wound. Proc. Nat. Acad. Sci. 104(41), 15988–15993 (2007)

    Article  Google Scholar 

  18. Kopp, F., Hermawan, A., Oak, P.S., Herrmann, A., Wagner, E., Roidl, A.: Salinomycin treatment reduces metastatic tumor burden by hampering cancer cell migration. Mol. Cancer 13(1), 16 (2014)

    Article  Google Scholar 

  19. Kamata, H., Hirata, H.: Redox regulation of cellular signaling. Cell. Signal. 24(5), 981–990 (1999)

    Google Scholar 

  20. Huttenlocher, A., Sandborg, R.R., Horwitz, A.F.: Adhesion in cell migration. Curr. Opin. Cell Biol. 7(5), 697–706 (1995)

    Article  Google Scholar 

  21. Kong, D., Ji, B., Dai, L.: Stability of adhesion clusters and cell reorientation under lateral cyclic tension. Biophys. J. 95, 4034–4044 (2008)

    Article  Google Scholar 

  22. Chen, B., Ji, B., Gao, H.: Modeling active mechanosensing in cell-matrix interactions. Ann. Rev Biophys. 44, 1–32 (2015)

    Article  Google Scholar 

  23. He, S., Su, Y., Ji, B., Gao, H.: Some basic questions on mechanosensing in cell-substrate interaction. J. Mech. Phys. Solids 70, 116–135 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  24. Deng, L., Trepat, X., Butler, J.P., Millet, E., Morgan, K.G., Weitz, D.A., Fredberg, J.J.: Fast and slow dynamics of the cytoskeleton. Nat. Mater. 5, 636–640 (2006)

    Article  Google Scholar 

  25. Hochmuth, R.M., Waugh, R.E.: Erythrocyte membrane elasticity and viscosity. Annu. Rev. Physiol. 49(1), 209–219 (1987)

    Article  Google Scholar 

  26. Kim, T., Hwang, W., Lee, H., Kamm, R.D.: Computational analysis of viscoelastic properties of crosslinked actin networks. PLoS Comput. Biol. 5, e1000439 (2009)

    Article  Google Scholar 

  27. Lieleg, O., Claessens, M.M., Bausch, A.R.: Structure and dynamics of cross-linked actin networks. Soft Matter 6(2), 218–225 (2010)

    Article  Google Scholar 

  28. Singer, S.J., Nicolson, G.L.: The fluid mosaic model of the structure of cell membranes. Science 175(4023), 720–731 (1972)

    Article  Google Scholar 

  29. Helfrich, W.: Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28, 693–703 (1973)

    Article  Google Scholar 

  30. Ramaswamy, S., Toner, J., Prost, J.: Nonequilibrium fluctuations, traveling waves, and instabilities in active membranes. Phys. Rev. Lett. 84(15), 3494 (2000)

    Article  Google Scholar 

  31. Chen, H.-Y.: Internal states of active inclusions and the dynamics of an active membrane. Phys. Rev. Lett. 92(16), 168101 (2004)

    Article  Google Scholar 

  32. Gov, N.S.: Membrane undulations driven by force fluctuations of active proteins. Phys. Rev. Lett. 93(26), 268104 (2004)

    Article  Google Scholar 

  33. Berthoumieux, H., Maitre, J.-L., Heisenberg, C.-P., Paluch, E.K., Julicher, F., Salbreux, G.: Active elastic thin shell theory for cellular deformations. New J. Phys. 16(6), 065005 (2014)

    Article  Google Scholar 

  34. Salbreux, G., Jülicher, F.: Mechanics of active surfaces (2017). arXiv preprint: arXiv:1701.09095

  35. Sauer, R.A.: Stabilized finite element formulations for liquid membranes and their application to droplet contact. Int. J. Numer. Methods Fluids 75, 519–545 (2014)

    Article  MathSciNet  Google Scholar 

  36. Ma, L., Klug, W.S.: Viscous regularization and r-adaptive meshing for finite element analysis of lipid membrane mechanics. J. Comput. Phys. 227, 5816–5835 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  37. Arroyo, M., DeSimone, A.: Relaxation dynamics of fluid membranes. Phys. Rev. E 79, 031915 (2008)

    Article  MathSciNet  Google Scholar 

  38. Rahimi, M., Arroyo, M.: Shape dynamics, lipid hydrodynamics, and the complex viscoelasticity of bilayer membranes. Phys. Rev. E 86(1), 011932 (2012)

    Article  Google Scholar 

  39. Sauer, R.A., Duong, T.X., Corbett, C.J.: A computational formulation for constrained solid and liquid membranes considering isogeometric finite elements. Comput. Methods Appl. Mech. Eng. 271, 48–68 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  40. Sauer, R.A., Duong, T.X.: On the theoretical foundations of thin solid and liquid shells. Math. Mech. Solids 22(3), 343–371 (2017)

    Article  MATH  Google Scholar 

  41. Sauer, A., Duong, T.X., Mandadadapu, K.K., Steigmann, D.J.: A stabilized finite element formulation for liquid shells and its application to lipid bilayers. J. Comput. Phys. 330, 436–466 (2017)

    Article  MathSciNet  Google Scholar 

  42. Steigmann, D., Baesu, E., Rudd, R.E., Belak, J., McElfresh, M.: On the variational theory of cell-membrane equilibria. Interfaces Free Bound. 5(4), 357–366 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  43. Agrawal, A., Steigmann, D.J.: Boundary-value problems in the theory of lipid membranes. Continuum Mech. Thermodyn. 21(1), 57–82 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  44. Agrawal, A., Steigmann, D.J.: Modeling protein-mediated morphology in biomembranes. Biomech. Model. Mechanobiol. 8(5), 371–379 (2009)

    Article  Google Scholar 

  45. Weikl, T.R., Hu, J., Xu, G.-K., Lipowsky, R.: Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: insights from computational model systems and theory. Cell Adhes. Migr. 10, 576–589 (2016)

    Article  Google Scholar 

  46. Hu, J., Lipowsky, R., Weikl, T.R.: Binding constants of membrane-anchored receptors and ligands depend strongly on the nanoscale roughness of membranes. Proc. Nat. Acad. Sci. U.S.A. 110, 15283–15288 (2015)

    Article  Google Scholar 

  47. Hu, J., Xu, G.K., Lipowsky, R., Weikl, T.R.: Binding kinetics of membrane-anchored receptors and ligands: molecular dynamics simulations and theory. J. Chem. Phys. 143(24), 12B612_1 (2015)

  48. Xu, G.-K., Hu, J., Lipowsky, R., Weikl, T.R.: Binding constants of membrane-anchored receptors and ligands: a general theory corroborated Monte Carlo simulations. J. Chem. Phys. 143, 243136 (2015)

    Article  Google Scholar 

  49. Li, D., Ji, B.: Predicted rupture force of a single molecular bond becomes rate independent at ultralow loading rates. Phys. Rev. Lett. 112, 078302 (2014)

    Article  Google Scholar 

  50. Erdmann, T., Schwarz, U.S.: Bistability of cell-matrix adhesions resulting from non-linear receptorligand dynamics. Biophys. J. 91, L60–62 (2006)

    Article  Google Scholar 

  51. Erdmann, T., Schwarz, U.S.: Impact of receptor-ligand distance on adhesion cluster stability. Eur. Phys. J. E 22, 123–137 (2007)

    Article  Google Scholar 

  52. Thomas, W., Forero, M., Yakovenko, O., Nilsson, L., Vicini, P.: Catch-bond model derived from allostery explains force-activated bacterial adhesion. Biophys. J. 90, 753–764 (2006)

    Article  Google Scholar 

  53. Pereverzev, Y.V., Prezhdo, O.V., Forero, M., Sokurenko, E.V., Thomas, W.E.: The two-pathway model for the catch-slip transition in biological adhesion. Biophys. J. 89, 1446–1454 (2005)

    Article  Google Scholar 

  54. Kruse, K., Joanny, J.F., Jlicher, J., Prost, J., Sekimoto, K.: Asters, vortices, and rotating spirals in active gels of polar filaments. Phys. Rev. Lett. 92, 078101 (2004)

    Article  Google Scholar 

  55. Kruse, K., Joanny, J.F., Jlicher, J., Prost, J., Sekimoto, K.: Generic theory of active polar gels: a paradigm for cytoskeletal dynamics. Eur. Phys. J. E 16, 5–16 (2005)

    Article  Google Scholar 

  56. Marchetti, M.C., Joanny, J.F., Ramaswamy, S., Liverpool, T.B., Prost, J., Rao, M., Simha, R.: Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013)

    Article  Google Scholar 

  57. Ramaswamy, S.: The mechanics and statistics of active matter. Ann. Rev. Condens. Matter Phys. 1, 323–345 (2010)

    Article  Google Scholar 

  58. Sanchez, T., Chen, D.T.N., DeCamp, S.J., Heymann, M., Dogic, Z.: Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012)

    Article  Google Scholar 

  59. Sokolov, I., Kievsky, Y.Y., Kaszpurenko, J.M.: Self-assembly of ultrabright fluorescent silica particles. Small 3, 419–423 (2007)

    Article  Google Scholar 

  60. Silva, M.S., Depken, M., Stuhrmann, B., Korsten, M., MacKintosh, F.C., Koenderink, G.H.: Active multistage coarsening of actin networks driven by myosin motors. Proc. Natl. Acad. Sci. Am. USA 108, 9408–9413 (2011)

    Article  Google Scholar 

  61. Prost, J., Jlicher, F., Joanny, J.F.: Active gel physics. Nat. Phys. 11, 111–117 (2015)

    Article  Google Scholar 

  62. Kreis, T., Vale, R.: Cytoskeletal and Motor Proteins. Oxford University Press, New York (1993)

    Google Scholar 

  63. Dogterom, M., Yurke, B.: Measurement of the force-velocity relation for growing microtubules. Science 278, 856 (1997)

    Article  Google Scholar 

  64. Simha, R.A., Ramaswamy, S.: Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys. Rev. Lett. 89, 058101 (2002)

    Article  MATH  Google Scholar 

  65. Hatwalne, Y., Ramaswamy, S., Rao, M., Simha, R.A.: Rheology of active-particle suspensions. Phys. Rev. Lett. 92, 118101 (2004)

    Article  Google Scholar 

  66. Kruse, K., Jülicher, J.: Actively contracting bundles of polar filaments. Phys. Rev. Lett. 85, 1778–1781 (2000)

    Article  Google Scholar 

  67. Liverpool, T.B., Marchetti, M.C.: Instabilities of isotropic solutions of active polar filaments. Phys. Rev. Lett. 90, 138102 (2003)

    Article  Google Scholar 

  68. Fialho, A.R., Blowa, M.L., Marenduzzoa, D.: Anchoring-driven spontaneous rotations in active gel droplets. Soft Matter 13, 5933–5941 (2017)

    Article  Google Scholar 

  69. Callan-Jones, A., Voituriez, R.: Active gel model of amoeboid cell motility. New J. Phys. 15, 025022 (2013)

    Article  Google Scholar 

  70. Blanch-Mercader, C., Casademunt, J.: Spontaneous motility of actin lamellar fragments. Phys. Rev. Lett. 110, 078102 (2013)

    Article  Google Scholar 

  71. Salbreux, G., Joanny, J.F., Prost, J., Pullarkat, P.: Shape oscillations of non-adhering fibroblast cells. Phys. Biol. 4, 268–284 (2007)

    Article  Google Scholar 

  72. Sedzinski, J., Biro, M., Oswald, A., Tinevez, J.-Y., Salbreux, G.: Polar actomyosin contractility destabilizes the position of the cytokinetic furrow. Nature 476, 462–466 (2011)

    Article  Google Scholar 

  73. Turlier, H., Audoly, B., Prost, J., Joanny, J.F.: Furrow constriction in animal cell cytokinesis. Biophys. J. 106, 114–123 (2014)

    Article  Google Scholar 

  74. Salbreux, G., Prost, J., Joanny, J.F.: Hydrodynamics of cellular cortical flows and the formation of contractile rings. Phys. Rev. Lett. 103, 058102 (2009)

    Article  Google Scholar 

  75. Tjhung, E., Marenduzzo, D., Cates, M.E.: Spontaneous symmetry breaking in active droplets provides a generic route to motility. Proc. Natl. Acad. Sci. Am. USA 109, 12381–12386 (2012)

    Article  Google Scholar 

  76. Hawkins, R.J., Renaud Poincloux, R., Bnichou, O., Piel, M., Chavrier, P., Voituriez, R.: Spontaneous contractility-mediated cortical flow generates cell migration in three-dimensional environments. Biophys. J. 101, 1041–1045 (2011)

    Article  Google Scholar 

  77. Ranft, J., Basan, M., Elgeti, J., Joanny, J.F., Prost, J., Jülicher, F.: Fluidization of tissues by cell division and apoptosis. Proc. Natl. Acad. Sci. Am. USA 107, 20863–20868 (2010)

    Article  Google Scholar 

  78. Delarue, M., Montel, F., Vignjevic, D., Prost, J., Joanny, J.F., Cappello, G.: Compressive stress inhibits proliferation in tumor spheroids through a volume limitation. Biophys. J. 107, 1821–1828 (2014)

    Article  Google Scholar 

  79. Broedersz, C.P., MacKintosh, F.C.: Modeling semiflexible polymer networks. Rev. Mod. Phys. 86, 995–1036 (2014)

    Article  Google Scholar 

  80. Sun, S.X., Walcott, S., Wolgemuth, C.W.: Cytoskeletal cross-linking and bundling in motor-independent contraction. Curr. Biol. 20(15), R649–R654 (2010)

    Article  Google Scholar 

  81. Storm, C., Pastore, J.J., MacKintosh, F.C., Lubensky, T.C., Janmey, P.A.: Nonlinear elasticity in biological gels. Nature 435, 191 (2005)

    Article  Google Scholar 

  82. Yao, N.Y., Broedersz, C.P., Lin, Y.C., Kasza, K.E., MacKintosh, F.C., Weitz, D.A.: Elasticity in ionically cross-linked neurofilament networks. Biophys. J. 98(10), 2147–2153 (2010)

    Article  Google Scholar 

  83. Broedersz, C.P., MacKintosh, F.C.: Molecular motors stiffen non-affine semiflexible polymer networks. Soft Matter 7(7), 3186–3191 (2011)

    Article  Google Scholar 

  84. Basu, A., Wen, Q., Mao, X., Lubensky, T.C., Janmey, P.A., Yodh, A.G.: Nonaffine displacements in flexible polymer networks. Macromolecules 44(6), 1671–1679 (2011)

    Article  Google Scholar 

  85. Wen, Q., Basu, A., Janmey, P.A., Yodh, A.G.: Non-affine deformations in polymer hydrogels. Soft Matter 8(31), 8039–8049 (2012)

    Article  Google Scholar 

  86. Kroy, K., Frey, E.: Force-extension relation and plateau modulus for wormlike chains. Phys. Rev. Lett. 77(2), 306 (1996)

    Article  Google Scholar 

  87. DiDonna, B.A., Lubensky, T.C.: Nonaffine correlations in random elastic media. Phys. Rev. E 72(6), 066619 (2005)

    Article  Google Scholar 

  88. Heussinger, C., Frey, E.: Stiff polymers, foams, and fiber networks. Phys. Rev. Lett. 96(1), 017802 (2006)

    Article  Google Scholar 

  89. Carrillo, J.M.Y., MacKintosh, F.C., Dobrynin, A.V.: Nonlinear elasticity: from single chain to networks and gels. Macromolecules 46(9), 3679–3692 (2013)

    Article  Google Scholar 

  90. Head, D.A., Levine, A.J., MacKintosh, F.C.: Deformation of cross-linked semiflexible polymer networks. Phys. Rev. Lett. 91(10), 108102 (2003)

    Article  Google Scholar 

  91. Head, D.A., Levine, A.J., MacKintosh, F.C.: Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks. Phys. Rev. E 68(6), 061907 (2003)

    Article  Google Scholar 

  92. Wilhelm, J., Frey, E.: Elasticity of stiff polymer networks. Phys. Rev. Lett. 91(10), 108103 (2003)

    Article  Google Scholar 

  93. Heussinger, C., Frey, E.: Floppy modes and nonaffine deformations in random fiber networks. Phys. Rev. Lett. 97(10), 105501 (2006)

    Article  Google Scholar 

  94. Heussinger, C., Bathe, M., Frey, E.: Statistical mechanics of semiflexible bundles of wormlike polymer chains. Phys. Rev. Lett. 99(4), 048101 (2007)

    Article  Google Scholar 

  95. Heussinger, C., Schaefer, B., Frey, E.: Nonaffine rubber elasticity for stiff polymer networks. Phys. Rev. E 76(3), 03190 (2007)

    Article  Google Scholar 

  96. Liu, A.J., Nagel, S.R.: The jamming transition and the marginally jammed solid. Ann. Rev. Condens. Matter Phys. 1(1), 347–369 (2010)

    Article  Google Scholar 

  97. Onck, P.R., Koeman, T., Van Dillen, T., van der Giessen, E.: Alternative explanation of stiffening in cross-linked semiflexible networks. Phys. Rev. Lett. 95(17), 178102 (2005)

    Article  Google Scholar 

  98. Huisman, E.M., Storm, C., Barkema, G.T.: Monte Carlo study of multiply crosslinked semiflexible polymer networks. Phys. Rev. E 78(5), 051801 (2008)

    Article  Google Scholar 

  99. Huisman, E.M., Lubensky, T.C.: Internal stresses, normal modes, and nonaffinity in three-dimensional biopolymer networks. Phys. Rev. Lett. 106(8), 088301 (2011)

    Article  Google Scholar 

  100. Huisman, E.M., van Dillen, T., Onck, P.R., Van der Giessen, E.: Three-dimensional cross-linked F-actin networks: relation between network architecture and mechanical behavior. Phys. Rev. Lett. 99(20), 208103 (2007)

    Article  Google Scholar 

  101. Broedersz, C.P., Sheinman, M., MacKintosh, F.C.: Filament-length-controlled elasticity in 3D fiber networks. Phys. Rev. Lett. 108(7), 078102 (2012)

    Article  Google Scholar 

  102. Foucard, L., Vernerey, F.J.: A thermodynamical model for stress-fiber organization in contractile cells. Appl. Phys. Lett 100(1), 013702 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  107. Ingber, D.E., Wang, N., Stamenovic, D.: Tensegrity, cellular biophysics, and the mechanics of living systems. Rep. Prog. Phys. 77, 046603 (2014)

    Article  MathSciNet  Google Scholar 

  108. Ingber, D.E.: Cellular tensegrity: defining new rules of biological design that govern the cytoskeleton. J. Cell Sci. 104, 613–27 (1993)

    Google Scholar 

  109. Wang, N., Ingber, D.E.: Control of cytoskeletal mechanics by extracellular matrix, cell shape, and mechanical tension. Biophys. J. 66, 2181–2189 (1994)

    Article  Google Scholar 

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

    Article  Google Scholar 

  111. Deguchi, S., Ohashi, S., Sato, M.: Tensile properties of single stress fibers isolated from cultured vascular smooth muscle cells. J. Biomech. 39, 2603–2610 (2006)

    Article  Google Scholar 

  112. Wang, N., Naruse, K., Stamenovic, D., Fredberg, J.J., Mijailovich, S.M., Tolic-Norrelykke, I.M., Polte, T., Mannix, R., Ingber, D.E.: Mechanical behavior in living cells consistent with the tensegrity model. Proc. Nat. Acad. Sci. USA 98, 7765–7770 (2001)

    Article  Google Scholar 

  113. Wang, N., Tolic-Norrelykke, I.M., Chen, J., Mijailovich, S.M., Butler, J.P., Fredberg, J.J., Stamenovic, D.: Cell prestress: I. Stiffness and prestress are closely associated in adherent contractile cells. Am. J. Physiol. Cell Physiol. 282, C606–616 (2002)

    Article  Google Scholar 

  114. Ingber, D.E.: Tensegrity I. Cell structure and hierarchical systems. J. Cell Sci. 116, 1157–1173 (2003)

    Article  Google Scholar 

  115. Coughlin, M.F., Stamenovic, D.: A tensegrity structure with buckling compression elements: application to cell mechanics. J. Appl. Mech. 64, 480–486 (1997)

    Article  MATH  Google Scholar 

  116. Hu, S., Chen, J., Wang, N.: Cell spreading controls balance of prestress by microtubules and extracellular matrix. Frontier Biosci. 9, 2177–2182 (2004)

    Article  Google Scholar 

  117. Polte, T.R., Eichler, G.S., Wang, N., Ingber, D.E.: Extracellular matrix controls myosin light chain phosphorylation and cell contractility through modulation of cell shape and cytoskeletal prestress. Am. J. Physiol. Cell Physiol. 286, C518–528 (2004)

    Article  Google Scholar 

  118. Stamenovic, D., Coughlin, M.F.: 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, 63–74 (1999)

    Article  Google Scholar 

  119. Stamenovic, D., Coughlin, M.F.: A quantitative model of cellular elasticity based on tensegrity. ASME J. Biomech. Eng. 122, 39–43 (2000)

    Article  Google Scholar 

  120. Bonakdar, N., Gerum, R., Kuhn, M., Spörrer, M., Lippert, A., Schneider, W., Aifantis, K.E., Fabry, B.: Mechanical plasticity of cells. Nat. Mater. 15, 1090–1094 (2016)

    Article  Google Scholar 

  121. Vera, C., Skelton, R., Bossens, F., Sung, L.A.: 3-D nanomechanics of an erythrocyte junctional complex in equibiaxial and anisotropic deformations. Ann. Biomed. Eng. 33, 1387–1404 (2005)

    Article  Google Scholar 

  122. Pickett-Heaps, J.D., Forer, A., Spurck, T.: Traction fibre: toward a tensegral model of the spindle. Cell Motil. Cytoskelet. 37, 1–6 (1997)

    Article  Google Scholar 

  123. Xu, G.K., Li, B., Feng, X.-Q., Gao, H.: A tensegrity model of cell reorientation on cyclically stretched substrates. Biophys. J. 111, 1478–1486 (2016)

    Article  Google Scholar 

  124. Ingber, D.E.: The origin of cellular life. BioEssays 22, 1160–1170 (2000)

    Article  Google Scholar 

  125. Farrell Jr., H.M., Qi, P.X., Brown, E.M., Cooke, P.H., Tunick, M.H., Wickham, E.D., Unruh, J.J.: Molten globule structures in milk proteins: implications for potential new structure-function relationships. J. Dairy Sci. 85, 459–471 (2002)

    Article  Google Scholar 

  126. Zanotti, G., Guerra, C.: Is tensegrity a unifying concept of protein folds? FEBS Lett. 534, 7–10 (2003)

    Article  Google Scholar 

  127. Edwards, S.A., Wagner, J., Grater, F.: Dynamic prestress in a globular protein. PLoS ONE Comput. Biol. 8, e1002509 (2012)

    Article  Google Scholar 

  128. Shen, T., Wolynes, P.G.: Nonequilibrium statistical mechanical model for cytoskeletal assembly: towards understanding tensegrity in cells. Phys. Rev. E 72, 041927 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  130. Fabry, B., Maksym, G.N., Butler, J.P., Glogauer, M., Navajas, D., Taback, N.A., Millet, E.J., Fredberg, J.J.: Time scale and other invariants of integrative mechanical behavior in living cells. Phys. Rev. E 68, 041914 (2003)

    Article  Google Scholar 

  131. Fabry, B., Maksym, G.N., Butler, J.P., Glogauer, M., Navajas, D., Fredberg, J.J.: Scaling the microrheology of living cells. Phys. Rev. Lett. 87, 148102 (2001)

    Article  Google Scholar 

  132. Trepat, X., Deng, L., An, S.S., Navajas, D., Tschumperlin, D.J., Gerthoffer, W.T., Butler, J.P., Fredberg, J.J.: Universal physical response to stretch in living cells. Nature 441, 592–595 (2007)

    Article  Google Scholar 

  133. de Gennes, P.-G., Brochard-Wyart, F., Quere, D.: Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer, Berlin (2010)

    MATH  Google Scholar 

  134. Cammarata, R.C.: Surface and interface stress effects in thin films. Prog. Surf. Sci. 46(1), 1–38 (1994)

    Article  Google Scholar 

  135. Spaepen, F.: Interfaces and stresses in thin films. Acta Mater. 48(1), 31–42 (2000)

    Article  Google Scholar 

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

    Article  Google Scholar 

  137. Erdmann, T., Schwarz, U.S.: Stability of adhesion clusters under constant force. Phys. Rev. Lett. 92, 108102 (2004)

    Article  Google Scholar 

  138. Noy, A., Vezenov, D.V., Lieber, C.M.: Chemical force microscopy. Annu. Rev. Mater. Sci. 27(1), 381–421 (1997)

    Article  Google Scholar 

  139. Butt, H.-J., Cappella, B., Kappl, M.: Force measurements with the atomic force microscope: technique, interpretation and applications. Surf. Sci. Rep. 59(1), 1–152 (2005)

    Article  Google Scholar 

  140. Balland, M., Desprat, N., Icard, D., Frol, S., Asnacios, A., Browaeys, J., Hnon, S., Gallet, F.: Power laws in microrheology experiments on living cells: comparative analysis and modeling. Phys. Rev. E 74, 021911 (2006)

    Article  Google Scholar 

  141. Evans, E.: Probing the relation between force-lifetime-and chemistry in single molecular bonds. Ann. Rev. Biophys. Biomol. Struct. 30, 105–128 (2001)

    Article  Google Scholar 

  142. Pericet-Camara, R., Auernhammer, G.K., Koynov, K.R., Larenzoni, S., Raiteri, R., Bonaccurso, E.: Solid-supported thin elastomer films deformed by microdrops. Soft Matter 5, 3611–3617 (2009)

    Article  Google Scholar 

  143. Jerison, E.R., Xu, Y., Wilen, L.A., Dufresne, E.R.: Deformation of an elastic substrate by a three-phase contact line. Phys. Rev. Lett. 106, 186103 (2011)

    Article  Google Scholar 

  144. Style, R.W., Boltyanskiy, R., Che, Y., Wettlaufer, J.S., Wilen, L.A., Dufresne, E.R.: Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses. Phys. Rev. Lett. 110, 066103 (2013)

    Article  Google Scholar 

  145. Style, R.W., Boltyanskiy, R., Allen, B., Jensen, K.E., Foote, H.P., Wettlaufer, J.S., Dufresne, E.R.: Stiffening solids with liquid inclusions. Nat. Phys. 11, 82–87 (2015)

    Article  Google Scholar 

  146. Style, R.W., Hyland, C., Boltyanskiy, R., Wettlaufer, J.S., Dufresne, E.R.: Surface tension and contact with soft elastic solids. Nat. Commun. 4, 2728 (2013)

    Article  Google Scholar 

  147. Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A 241(1226), 376–396 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  148. Kumar, S., Maxwell, I.Z., Heisterkamp, A., Polte, T.R., Lele, T.P., Salanga, M., Mazur, E., Ingber, D.E.: Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics. Biophys. J. 90(10), 3762–3773 (2006)

    Article  Google Scholar 

  149. Kobayashi, T., Sokabe, M.: Sensing substrate rigidity by mechanosensitive ion channels with stress fibers and focal adhesions. Curr. Opin. Cell Biol. 22, 669–676 (2010)

    Article  Google Scholar 

  150. Oakes, P.W., Beckham, Y., Stricker, J., Gardel, M.L.: Tension is required but not sufficient for focal adhesion maturation without a stress fiber template. J. Cell Biol. 196, 363–374 (2012)

    Article  Google Scholar 

  151. Tondon, A., Hsu, H.-J., Kaunas, R.: Dependence of cyclic stretch-induced stress fiber reorientation on stretch waveform. J. Biomech. 45, 728–735 (2012)

    Article  Google Scholar 

  152. Geiger, B., Spatz, J.P., Bershadsky, A.D.: Environmental sensing through focal adhesions. Nat. Rev. Microbiol. 10, 21–33 (2009)

    Google Scholar 

  153. Chen, B., Kemkemer, R., Deibler, M., Spatz, J., Gao, H.: Cyclic stretch induces cell reorientation on substrates by destabilizing catch bonds in focal adhesions. PLoS ONE 7, e48346 (2012)

    Article  Google Scholar 

  154. Kong, D., Ji, B., Dai, L.: Stabilizing to disruptive transition of focal adhesion response to mechanical forces. J. Biomech. 43, 2524–2529 (2010)

    Article  Google Scholar 

  155. Qian, J., Gao, H.: Soft matrices suppress cooperative behaviors among receptor-ligand bonds in cell adhesion. PLoS ONE 23, e12342 (2010)

    Article  Google Scholar 

  156. Schwarz, U.: Forces and elasticity in cell adhesion, Doctoral dissertation, Tesis presentada a la Universidad de Potsdam, para optar al grado de Doctor of Philosophy (2004)

  157. Shemesh, T., Geiger, B., Bershadsky, A.D., Kozlov, M.M.: Focal adhesions as mechanosensors: a physical mechanism. Proc. Natl. Acad. Sci. USA 102, 12383–12388 (2005)

    Article  Google Scholar 

  158. Qian, J., Wang, J.Z., Gao, H.: Lifetime and strength of adhesive molecular bond clusters between elastic media. Langmuir 24, 1262–1270 (2008)

    Article  Google Scholar 

  159. Qian, J., Wang, J.Z., Lin, Y., Gao, H.: Lifetime and strength of periodic bond clusters between elastic media under inclined loading. Biophys. J. 97, 2438–2445 (2009)

    Article  Google Scholar 

  160. Cao, X., Bana, E., Baker, B.M., Lin, Y., Burdickd, J.A., Chen, C.S., Shenoy, V.B.: Multiscale model predicts increasing focal adhesion size with decreasing stiffness in fibrous matrices. Proc. Natl. Acad. Sci. USA 114, E4549–E4555 (2017)

    Article  Google Scholar 

  161. Baker, B.M., Trappmann, B., Wang, W.Y., Sakar, M.S., Iris, L., Kim, I.L., Shenoy, V.B., Burdick, J.A., Chen, C.S.: Cell-mediated fibre recruitment drives extracellular matrix mechanosensing in engineered fibrillar microenvironments. Nat. Mater. 14, 1262–1268 (2015)

    Article  Google Scholar 

  162. Rape, A.D., Guo, W.-H., Wang, Y.-L.: The regulation of traction force in relation to cell shape and focal adhesions. Biomaterials 32, 2043–2051 (2011)

    Article  Google Scholar 

  163. Chen, B., Gao, H.: Mechanical principle of enhancing cell-substrate adhesion via pre-tension in the cytoskeleton. Biophys. J. 98, 2154–2162 (2010)

    Article  Google Scholar 

  164. Zhong, Y., Kong, D., Dai, L., Ji, B.: Frequency-dependent focal adhesion instability and cell reorientation under cyclic substrate stretching. Cell. Mol. Bioeng. 4, 442–456 (2011)

    Article  Google Scholar 

  165. Besser, A., Schwarz, U.S.: Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction. New J. Phys. 9, 425 (2007)

    Article  Google Scholar 

  166. Chen, B., Gao, H.: Motor force homeostasis in skeletal muscle contraction. Biophys. J. 101, 396–403 (2001)

    Article  Google Scholar 

  167. Fan, H., Li, S.: Modeling microtubule cytoskeleton via an active liquid crystal elastomer model. Comput. Materi. Sci. 96(Part B), 559–566 (2014)

  168. Schwarz, U.S., Erdmann, T., Bischofs, I.B.: Focal adhesions as mechanosensors: the two-spring model. Biosystems 83, 225–232 (2006)

    Article  Google Scholar 

  169. Sauer, R.A., Li, S.: Contact mechanics model for quasi-continua. Int. J. Numer. Meth. Eng. 71, 931–962 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  170. Sauer, R.A., Li, S.: An atomic interaction based continuum mechanics model for adhesive contact mechanics. Finite Elem. Anal. Des. 43, 384–396 (2007)

    Article  MathSciNet  Google Scholar 

  171. Sauer, R.A., Li, S.: An atomistically enriched continuum model for nanoscale contact mechanics and its application to contact scaling. J. Nanosci. Nanotechnol 8(7), 3757–3773 (2008)

    Google Scholar 

  172. Sauer, R.A., Wriggers, P.: Formulation and analysis of a 3D finite element implementation for adhesive contact at the nanoscale. Comput. Methods Appl. Mech. Eng. 198, 3871–3883 (2009)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  175. Zeng, X., Li, S.: A three dimensional soft matter cell model for mechanotransduction. Soft Matter 8, 5765 (2012)

    Article  Google Scholar 

  176. Zeng, X., Li, S.: A biomechanical cell model by liquid crystal elastomers. ASCE. J. Eng. Mech. 140(4), 04013003 (2014)

    Article  Google Scholar 

  177. Erath, J., Schmidt, S., Fery, A.: Characterization of adhesion phenomena and contact of surfaces by soft colloidal probe AFM. Soft Matter 6, 1432–1437 (2010)

    Article  Google Scholar 

  178. Kollmannsberger, P., Mierke, C.T., Fabry, B.: Nonlinear viscoelasticity of adherent cells is controlled by cytoskeletal tension. Soft Matter 7, 3127–3132 (2011)

    Article  Google Scholar 

  179. Fu, J., Wang, Y.-K., Yang, M.T., Desai, R.A., Yu, X.: Mechanical regulation of cell function with geometrically modulated elastomeric substrates. Nat. Methods 7, 733–736 (2010)

    Article  Google Scholar 

  180. Saez, A., Buguin, A., Silberzan, P., Ladoux, B.: Is the mechanical activity of epithelial cells controlled by deformations or forces? Biophys. J. 89, L52–54 (2005)

    Article  Google Scholar 

  181. Rivas, G., Fernandez, J.A., Minton, A.P.: Direct observation of the self-association of dilute proteins in the presence of inert macromolecules at high concentration via tracer sedimentation equilibrium: theory, experiment, and biological significance. Biochemistry 38, 9379–9388 (1999)

    Article  Google Scholar 

  182. Bell, G.I.: Models for the specific adhesion of cells to cells. Science 200, 618–627 (1978)

    Article  Google Scholar 

  183. Boettiger, D.: Mechanical control of integrin-mediated adhesion and signaling. Curr. Opin. Cell Biol. 24, 592–599 (2012)

    Article  Google Scholar 

  184. Krishnan, R., Binu Oommen, B., Walton, E.B., Maloney, J.M., van Vliet, K.J.: Modeling and simulation of chemomechanics at the cell-matrix interface. Cell Adhes. Migr. 2, 83–94 (2008)

    Article  Google Scholar 

  185. Masuzzo, P., van Troys, M., Ampe, C., Martens, L.: Taking aim at moving targets in computational cell migration. Trends Cell Biol. 26, 88–110 (2016)

    Article  Google Scholar 

  186. Fan, H., Li, S.: Modeling universal dynamics of cell spreading on elastic substrates. Biomech. Model. Mechanobiol. (BMMB) 14, 1265–1280 (2015)

    Article  Google Scholar 

  187. Fan, H., Li, S.: A three-dimensional surface formulation for adhesive contact in finite deformation. Int. J. Numer. Meth. Eng. 107, 252–270 (2015)

    Article  MATH  Google Scholar 

  188. Li, S., Fan, H.: On multiscale moving contact line theory. Proc. R. Soc. Lond. A 471, 20150224 (2015). The Royal Society

  189. Minaki, H., Li, S.: Multiscale modeling and simulation of dynamic wetting. Comput. Methods Appl. Mech. Eng. 273, 273–302 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  190. Monroy, F., Langevin, D.: Direct experimental observation of the crossover from capillary to elastic surface waves on soft gels. Phys. Rev. Lett. 81, 3167 (1998)

    Article  Google Scholar 

  191. Mora, S., Phou, T., Fromental, J.-M., Pismen, L.M., Pomeau, Y.: Capillarity driven instability of a soft solid. Phys. Rev. Lett. 105, 214301 (2010)

    Article  Google Scholar 

  192. Mora, S., Abkarian, M., Tabuteau, H., Pomeau, Y.: Surface instability of soft solids under strain. Soft Matter 7, 10612–10619 (2011)

    Article  Google Scholar 

  193. Chen, D., Cai, S., Suo, Z., Hayward, R.C.: Surface energy as a barrier to creasing of elastomer films: an elastic analogy to classical nucleation. Phys. Rev. Lett. 109, 038001 (2012)

    Article  Google Scholar 

  194. Yoon, J., Kim, J., Hayward, R.C.: Nucleation, growth, and hysteresis of surface creases on swelled polymer gels. Soft Matter 6, 5807–5816 (2010)

    Article  Google Scholar 

  195. Lo, C.M., Wang, H.B., Dembo, M., Wang, Y.L.: Cell movement is guided by the rigidity of the substrate. Biophys. J. 79(1), 144–152 (2000)

    Article  Google Scholar 

  196. Peyton, S.R., Putnam, A.J.: Extracellular matrix rigidity governs smooth muscle cell motility in a biphasic fashion. J. Cell. Physiol. 204(1), 198–209 (2005)

    Article  Google Scholar 

  197. Tee, S.Y., Fu, J., Chen, C.S., Janmey, P.A.: Cell shape and substrate rigidity both regulate cell stiffness. Biophys. J. 100(5), L25–L27 (2011)

    Article  Google Scholar 

  198. Zhong, Y., Ji, B.: Impact of cell shape on cell migration behavior on elastic substrate. Biofabrication 5, 015011 (2013)

    Article  Google Scholar 

  199. Canovic, E.P., Seid, D.T., Barbone, P.E., Smith, M.L., Stamenovic, D.: Stiffness versus prestress relationship at subcellular length scale. J. Biomech. 47, 3222–3225 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  201. Gardel, M.L., Sabass, B., Ji, L., Danuser, G., Schwarz, U.S., Waterman, C.M.: Traction stress in focal adhesions correlates biphasically with actin retrograde flow speed. J. Cell Biol. 183(6), 999–1005 (2008)

    Article  Google Scholar 

  202. Mertz, A.F., Che, Y., Banerjee, S., Goldstein, J.M., Rosowski, K.A., Revilla, S.F., Niessen, C.M., Marchetti, M.C., Dufresne, E.R., Horsley, V.: Cadherin-based intercellular adhesions organize epithelial cell-matrix traction forces. Proc. Nat. Acad. Sci. 110(3), 842–847 (2013)

    Article  Google Scholar 

  203. Tan, J.L., Tien, J., Pirone, D.M., Gray, D.S., Bhadriraju, K., Chen, C.S.: Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proc. Natl. Acad. Sci. USA 100(4), 1484–1489 (2003)

    Article  Google Scholar 

  204. Jungbauer, S., Gao, H., Spatz, J.P., Kemkemer, R.: Two characteristic regimes in frequency-dependent dynamic reorientation of fibroblasts on cyclically stretched substrates. Biophys. J. 95(7), 3470–3478 (2008)

    Article  Google Scholar 

  205. Liu, B., Qu, M.J., Qin, K.R., Li, H., Li, Z.K., Shen, B.R., Jiang, Z.L.: Role of cyclic strain frequency in regulating the alignment of vascular smooth muscle cells in vitro. Biophys. J. 94(4), 1497–1507 (2008)

    Article  Google Scholar 

  206. Nicolas, A., Safran, S.A.: Limitation of cell adhesion by the elasticity of the extracellular matrix. Biophys. J. 91(1), 61–73 (2006)

    Article  Google Scholar 

  207. Chen, S., Gao, H.: Bio-inspired mechanics of reversible adhesion: orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials. J. Mech. Phys. Solids 55(5), 1001–1015 (2007)

    Article  MATH  Google Scholar 

  208. Deshpande, V.S., McMeeking, R.M., Evans, A.G.: A model for the contractility of the cytoskeleton including the effects of stress-fibre formation and dissociation. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 463(2079), 787–815 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  209. Lemmon, C.A., Romer, L.H.: A predictive model of cell traction forces based on cell geometry. Biophys. J. 99(9), L78–L80 (2010)

    Article  Google Scholar 

  210. Edwards, C.M., Schwarz, U.S.: Force localization in contracting cell layers. Phys. Rev. Lett. 107(12), 128101 (2011)

    Article  Google Scholar 

  211. Walcott, S., Sun, S.X.: A mechanical model of actin stress fiber formation and substrate elasticity sensing in adherent cells. Proc. Natl. Acad. Sci. Am. 107(17), 7757–7762 (2010)

    Article  Google Scholar 

  212. Zemel, A., Rehfeldt, F., Brown, A.E.X., Discher, D.E., Safran, S.A.: Optimal matrix rigidity for stress fiber polarization in stem cells. Nat. Phys. 6(6), 468 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  214. Schwarz, U.S., Safran, S.A.: Elastic interactions of cells. Phys. Rev. Lett. 88(4), 048102 (2002)

    Article  Google Scholar 

  215. Carlsson, A.E.: Contractile stress generation by actomyosin gels. Phys. Rev. E 74(5), 051912 (2006)

    Article  Google Scholar 

  216. Lin, S.Z., Li, B., Lan, L., Feng, X.Q.: Activation and synchronization of the oscillatory morphodynamics in multicellular monolayer. Proc. Nat. Acad. Sci. U.S.A. 114, 8157–8162 (2017)

    Article  Google Scholar 

  217. Lin, S.Z., Xue, S.L., Li, B., Feng, X.Q.: An oscillating dynamic model of collective cells in a monolayer. J. Mech. Phys. Solids. (2017). https://doi.org/10.1016/j.jmps.2017.09.013

  218. Lin, S.Z., Li, B., Xu, G.K., Feng, X.Q.: Collective dynamics of cancer cells confined in a confluent monolayer of normalcells. J. Biomech. 52, 140–147 (2017)

    Article  Google Scholar 

  219. Chen, B., Chen, X., Gao, H.: Dynamics of cellular reorientation on a substrate under biaxial cyclic stretches. Nano Lett. 15, 5525–5529 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  221. Charras, G., Sahai, E.: Physical influences of the extracellular environment on cell migration. Nat. Rev. Mol. Cell Biol. 15, 813–824 (2014)

    Article  Google Scholar 

  222. Trappmann, B., Gautro, J.E., Connelly, J.T.: Extracellular-matrix tethering regulates stem-cell fate. Nat. Mater. 11, 642–649 (2012)

    Article  Google Scholar 

  223. Ulrich, T.A., Lee, T.G., Shon, H.K., Moon, D., Kumar, S.: Microscale mechanisms of agarose-induced disruption of collagen remodeling. Biomaterials 32, 5633–5642 (2011)

    Article  Google Scholar 

  224. Zaman, M.H.: Multiscale modeling of tumor cell migration. AIP Conf. Proc. 851, 117 (2005)

    Article  Google Scholar 

  225. Kim, D.H., Provenzano, P.P., Smith, C.L., Levchenko, A.: Matrix nanotopography as a regulator of cell function. J. Cell Biol. 197, 351–360 (2012)

    Article  Google Scholar 

  226. Kardash, E., Reichman-Fried, M., Maître, J.L.: A role for Rho GTPases and cell-cell adhesion in single-cell motility in vivo. Nat. Cell Biol. 12, 47–53 (2010)

    Article  Google Scholar 

  227. Friedl, P., Locker, J., Sahai, E., Segall, J.E.: Classifying collective cancer cell invasion. Nat. Cell Biol. 14, 777–783 (2012)

    Article  Google Scholar 

  228. Friedl, P., Sahai, E., Weiss, S., Yamada, K.M.: New dimensions in cell migration. Nat. Rev. Mol. Cell Biol. 13, 743–747 (2012)

    Article  Google Scholar 

  229. Tambe, D.T., Hardin, C.C., Angelini, T.E.: Collective cell guidance by cooperative intercellular forces. Nat. Mater. 10, 469–475 (2011)

    Article  Google Scholar 

  230. Ummadi, J.G., Vrushali, S., Joshi, V.S., Gupta, P.R., Indrabcdef, A.K., Koley, D.: Single-cell migration as studied by scanning electrochemical microscopy. Anal. Methods 7, 8826–8831 (2015)

    Article  Google Scholar 

  231. Ziebert, F., Löber, J. and Aranson, I.S.: Macroscopic model of substrate-based cell motility, In: Physical Models of Cell Motility, pp. 1–67. Springer, Berlin (2016)

  232. Zaman, M.H., Kamm, R.D., Matsudaira, P., Lauffenburger, D.A.: Computational model for cell migration in three-dimensional matrices. Biophys. J. 89, 1389–1397 (2005)

    Article  Google Scholar 

  233. Schlüter, D.K., Ramis-Conde, I., Chaplain, M.A.J.: Computational modeling of single-cell migration: the leading role of extracellular matrix fibers. Biophys. J. 103, 1141–1151 (2012)

    Article  Google Scholar 

  234. Friedl, P., Wolf, K.: Plasticity of cell migration: a multiscale tuning model. J. Cell Biol. 188, 11–19 (2010)

    Article  Google Scholar 

  235. Hatami-Marbin, H., Picu, R.C.: Heterogeneous long-range correlated deformation of semiflexible random fiber networks. Phys. Rev. E 80, 046703 (2009)

    Article  Google Scholar 

  236. Qi, S.Y., Groves, J.T., Chakraborty, A.K.: Synaptic pattern formation during cellular recognition. Proc. Nat. Acad. Sci. U.S.A. 98, 6548–6553 (2001)

    Article  Google Scholar 

  237. Weikl, T.R., Lipowsky, R.: Pattern formation during T-cell adhesion. Biophys. J. 87, 3665–3678 (2004)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  239. Vernerey, F.J., Farsad, M.: An Eulerian/XFEM formulation for the large deformation of cortical cell membrane. Comput. Methods Biomechan. Biomed. Eng. 14(05), 433–445 (2011)

    Article  Google Scholar 

  240. Vernerey, F.J., Farsad, M.: A mathematical model of the coupled mechanisms of cell adhesion, contraction and spreading. J. Math. Biol. 68(4), 989–1022 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  241. Peng, X., Huang, J., Xiong, C., Fang, J.: Cell adhesion nucleation regulated by substrate stiffness: a Monte Carlo study. J. Biomech. 45, 116–122 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Aerospace Engineering, Chongqing University, Chongqing, 400030, China

    Liang Zhang

  2. Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, CA, 74720, USA

    Liang Zhang & Shaofan Li

  3. Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Xiqiao Feng

Authors
  1. Liang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiqiao Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shaofan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaofan Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Feng, X. & Li, S. Review and perspective on soft matter modeling in cellular mechanobiology: cell contact, adhesion, mechanosensing, and motility. Acta Mech 228, 4095–4122 (2017). https://doi.org/10.1007/s00707-017-2057-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-017-2057-3

Search

Navigation