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Cell Migrations: Causes and Functions pp 13–29Cite as

Contour Models of Cellular Adhesion

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Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 1146))

Abstract

The development of traction-force microscopy, in the past two decades, has created the unprecedented opportunity of performing direct mechanical measurements on living cells as they adhere or crawl on uniform or micro-patterned substrates. Simultaneously, this has created the demand for a theoretical framework able to decipher the experimental observations, shed light on the complex biomechanical processes that govern the interaction between the cell and the extracellular matrix and offer testable predictions. Contour models of cellular adhesion, represent one of the simplest and yet most insightful approach in this problem. Rooted in the paradigm of active matter, these models allow to explicitly determine the shape of the cell edge and calculate the traction forces experienced by the substrate, starting from the internal and peripheral contractile stresses as well as the passive restoring forces and bending moments arising within the actin cortex and the plasma membrane. In this chapter I provide a general overview of contour models of cellular adhesion and review the specific cases of cells equipped with isotropic and anisotropic actin cytoskeleton as well as the role of bending elasticity.

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References

  • Arreaga G, Capovilla R, Chryssomalakos C, Guven J (2002) Area-constrained planar elastica. Phys Rev E 65:031801

    Article  Google Scholar 

  • Banerjee S, Giomi L (2013) Polymorphism and bistability in adherent cells. Soft Matter 9:5251–5260

    Article  CAS  Google Scholar 

  • Barry NP, Bretscher MS (2010) Dictyostelium amoebae and neutrophils can swim. Proc Natl Acad Sci U S A 107:11376–11380

    Article  CAS  Google Scholar 

  • Bar-Ziv R, Tlusty T, Moses E, Safran SA, Bershadsky AD (1999) Pearling in cells: a clue to understanding cell shape. Proc Natl Acad Sci USA 96:10140–10145

    Article  CAS  Google Scholar 

  • Bischofs IB, Klein F, Lehnert D, Bastmeyer M, Schwarz US (2008) Filamentous network mechanics and active contractility determine cell and tissue shape. Biophys J 95:3488–3496

    Article  CAS  Google Scholar 

  • Bischofs IB, Schmidt SS, Schwarz US (2009) Effect of adhesion geometry and rigidity on cellular force distributions. Phys Rev Lett 103:048101

    Article  Google Scholar 

  • Burridge K, Chrzanowska-Wodnicka M (1996) Focal adhesions, contractility and signalling. Annu Rev Cell Dev Biol 12:463–519

    Article  CAS  Google Scholar 

  • Burridge K, Wittchen ES (2013) The tension mounts: stress fibers as force-generating mechanotransducers. J Cell Biol 200:9–19

    Article  CAS  Google Scholar 

  • Chopra A, Tabdanov E, Patel H, Janmey PA, Kresh JY (2011) Cardiac myocyte remodeling mediated by N-cadherin-dependent mechanosensing. Am J Physiol Heart Circ Physiol 300:H1252-H1266

    Article  CAS  Google Scholar 

  • Danen EHJ, Sonneveld P, Brakebusch C, Fässler R, Sonnenberg A (2002) The fibronectin-binding integrins α5β1 and αvβ3 differentially modulate RhoA-GTP loading, organization of cell matrix adhesions, and fibronectin fibrillogenesis. J Cell Biol 159:1071–1086

    Article  CAS  Google Scholar 

  • DeTurck D, Gluck H, Pomerleano D, Vick DS (2007) The four vertex theorem and its converse. Not Am Math Soc 54:192–207

    Google Scholar 

  • Discher DE, Janmey PA, Wang YL (2005) Tissue cells feel and respond to the stiffness of their substrate. Science 310:1139–1143

    Article  CAS  Google Scholar 

  • Djondjorov P, Vassilev V, Mladenov I (2011) Analytic description and explicit parametrisation of the equilibrium shapes of elastic rings and tubes under uniform hydrostatic pressure. Int J Mech Sci 53:355–364

    Article  Google Scholar 

  • do Carmo MP (1976) Differential geometry of curves and surfaces. Prentice-Hall, Upper Saddle River

    Google Scholar 

  • Engler A, Bacakova L, Newman C, Hategan A, Griffin M, Discher D (2004) Substrate compliance versus ligand density in cell on gel responses. Biophys J 86:617–628

    Article  CAS  Google Scholar 

  • Engler AJ, Sen S, Sweeney HL, Discher DE (2006) Matrix elasticity directs stem cell lineage specification. Cell 126:677–689

    Article  CAS  Google Scholar 

  • Flaherty J, Keller J, Rubinow S (1972) Post buckling behavior of elastic tubes and rings with opposite sides in contact. SIAM J Appl Math 23:446–455

    Article  Google Scholar 

  • Geiger B, Spatz JP, Bershadsky AD (2009) Environmental sensing through focal adhesions. Nat Rev Mol Cell Biol 10:21–33

    Article  CAS  Google Scholar 

  • Ghibaudo M, Saez A, Trichet L, Xayaphoummine A, Browaeys J, Silberzan P, Buguin A, Ladoux B (2008) Traction forces and rigidity sensing regulate cell functions. Soft Matter 4:1836–1843

    Article  CAS  Google Scholar 

  • Ghibaudo M, Trichet L, Le Digabel J, Richert A, Hersen P, Ladoux B (2009) Substrate topography induces a crossover from 2D to 3D behavior in fibroblast migration. Biophys J 97:357–368

    Article  CAS  Google Scholar 

  • Giomi L (2013) Softly constrained films. Soft Matter 9:8121–8139

    Article  CAS  Google Scholar 

  • Giomi L, Mahadevan L (2012) Minimal surfaces bounded by elastic lines. Proc R Soc A 468:1851–1864

    Article  Google Scholar 

  • Gray A (1997) Modern differential geometry of curves and surfaces with mathematica. CRC-Press, Boca Raton

    Google Scholar 

  • Janmey PA, McCulloch CA (2007) Cell mechanics: integrating cell responses to mechanical stimuli. Annu Rev Biomed Eng 9:134

    Article  Google Scholar 

  • Jülicher F, Kruse K, Prost J, Joanny JF (2007) Active behavior of the cytoskeleton. Phys Rep 449:3–28

    Article  Google Scholar 

  • Landau LD, Lifshitz EM (1970) Theory of elasticity. A course of theoretical physics, vol 7. Pergamon Press, Oxford

    Google Scholar 

  • Lévy M (1884) Mémoire sur un nouveau cas intégrable du problème de lélastique et l’une des ses applications. J Math Pure Appl 10:5–42

    Google Scholar 

  • Lo CM, Wang HB, Dembo M, Wang YL (2000) Cell movement is guided by the rigidity of the substrate. Biophys J 79:144–152

    Article  CAS  Google Scholar 

  • Mendez MG, Janmey PA (2012) Transcription factor regulation by mechanical stress. Int J Biochem Cell Biol 44:728–732

    Article  CAS  Google Scholar 

  • Mertz AF, Banerjee S, Che Y, German GK, Xu Y, Hyland C, Marchetti MC, Horsley V, Dufresne ER (2012) Scaling of traction forces with the size of cohesive cell colonies. Phys Rev Lett 108:198101

    Article  Google Scholar 

  • Midwood KS, Williams LV, Schwarzbauer JE (2004) Tissue repair and the dynamics of the extracellular matrix. Int J Biochem Cell Biol 36:1031–1037

    Article  CAS  Google Scholar 

  • Mitrossilis D, Fouchard J, Guiroy A, Desprat N, Rodriguez N, Fabry B, Asnacios A (2009) Single-cell response to stiffness exhibits muscle-like behavior. Proc Natl Acad Sci USA 106:18243–18248

    Article  CAS  Google Scholar 

  • Mora S, Phou T, Fromental JM, Audoly B, Pomeau Y (2012) Shape of an elastic loop strongly bent by surface tension: experiments and comparison with theory. Phys Rev E 86:026119

    Article  Google Scholar 

  • Pedley TJ, Kessler JO (1992) Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu Rev Fluid Mech 24:313–358

    Article  Google Scholar 

  • Pellegrin S, Mellor H (2007) Actin stress fibres. J Cell Sci 120:3491–3499

    Article  CAS  Google Scholar 

  • Pomp W, Schakenraad K, Balcıoğlu HE, van Hoorn H, Danen EHJ, Merks RMH, Schmidt T, Giomi L (2018) Cytoskeletal anisotropy controls geometry and forces of adherent cells. Phys Rev Lett 121:178101

    Article  CAS  Google Scholar 

  • Reinhart-King CA, Dembo M, Hammer DA (2008) Cell-cell mechanical communication through compliant substrates. Biophys J 95:6044–6051

    Article  CAS  Google Scholar 

  • Sabass B, Gardel ML, Waterman CM, Schwarz US (2008) High resolution traction force microscopy based on experimental and computational advances. Biophys J 94:207–220

    Article  CAS  Google Scholar 

  • Sawada Y, Tamada M, Dubin-Thaler BJ, Cherniavskaya O, Sakai R, Tanaka S, Sheetz MP (2006) Force sensing by mechanical extension of the Src family kinase substrate p130Cas. Cell 127:1015–1026

    Article  CAS  Google Scholar 

  • Schwarz US, Safran SA (2013) Physics of adherent cells. Rev Mod Phys 85:1327

    Article  CAS  Google Scholar 

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

    Google Scholar 

  • Sochol RD, Higa AT, Janairo RRR, Li S, Lin L (2011) Unidirectional mechanical cellular stimuli via micropost array gradients. Soft Matter 7:4606–4609

    Article  CAS  Google Scholar 

  • Tadjbakhsh I, Odeh F (1967) Equilibrium states of elastic rings. J Appl Math Anal Appl 18:59–74

    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 100:1484–1489

    Article  CAS  Google Scholar 

  • Tanimoto H, Sano M (2012) Dynamics of traction stress field during cell division. Phys Rev Lett 109:248110

    Article  Google Scholar 

  • Torres PG, Bischofs I, Schwarz U (2012) Contractile network models for adherent cells. Phys Rev E 85:011913

    Article  Google Scholar 

  • Trappmann B, Gautrot JE, Connelly JT, Strange DGT, Li Y, Oyen ML, Cohen Stuart MA, Boehm H, Li B, Vogel V, Spatz JP, Watt FM, Huck WTS (2012) Extracellular-matrix tethering regulates stem-cell fate. Nat Mater 11:642–649

    Article  CAS  Google Scholar 

  • Vassilev V, Djondjorov P, Mladenov I (2008) Cylindrical equilibrium shapes of fluid membranes. J Phys A: Math Gen 41:435201

    Article  Google Scholar 

  • Wakatsuki T, Wysolmerski R, Elson E (2003) Mechanics of cell spreading: role of myosin II. J Cell Sci 116:1617–1625

    Article  CAS  Google Scholar 

  • Yeung T, Georges PC, Flanagan LA, Marg B, Ortiz M, Funaki M, Zahir N, Ming W, Weaver V, Janmey PA (2005) Effects of substrate stiffness on cell morphology, cytoskeletal structure, and adhesion. Cell Motil Cytoskeleton 60:24–34

    Article  Google Scholar 

Download references

Acknowledgements

I am indebted with Koen Schakenraad, Thomas Schmidt, Wim Pomp and Shiladitya Banerjee for contributing to the work reviewed here. This work is partially supported by the Netherlands Organisation for Scientific Research (NWO/OCW), as part of the Frontiers of Nanoscience program and the Vidi scheme.

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Authors and Affiliations

  1. Instituut-Lorentz, Universiteit Leiden, Leiden, The Netherlands

    Luca Giomi

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  1. Luca Giomi
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Correspondence to Luca Giomi .

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Editors and Affiliations

  1. Department of Environmental Science and Policy, Center for Complexity and Biosystems University of Milan, Milan, Italy

    Caterina A. M. La Porta

  2. Department of Physics, Center for Complexity and Biosystems University of Milan, Milan, Italy

    Stefano Zapperi

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Giomi, L. (2019). Contour Models of Cellular Adhesion. In: La Porta, C., Zapperi, S. (eds) Cell Migrations: Causes and Functions. Advances in Experimental Medicine and Biology, vol 1146. Springer, Cham. https://doi.org/10.1007/978-3-030-17593-1_2

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