Abstract
Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key biological question is how cells integrate molecular activities for force generation on multicellular scales. In this review we discuss recent advances in modeling collective cell migration using quantitative tools and approaches rooted in soft matter physics. We focus on theoretical models of cell aggregates as continuous active media, where the feedback between mechanical forces and regulatory biochemistry gives rise to rich collective dynamical behavior. This class of models provides a powerful predictive framework for the physiological dynamics that underlies many developmental processes, where cells need to collectively migrate like a viscous fluid to reach a target region, and then stiffen to support mechanical stresses and maintain tissue cohesion.
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References
Ahmadi A, Marchetti MC, Liverpool TB (2006) Hydrodynamics of isotropic and liquid crystalline active polymer solutions. Phys Rev E 74(6):061913
Ajeti V, Tabatabai AP, Fleszar AJ, Staddon MF, Seara DS, Suarez C, Yousafzai MS, Bi D, Kovar DR, Banerjee S, Murrell MP (2019) Wound healing coordinates actin architectures to regulate mechanical work. Nat Phys 5:696
Albert PJ, Schwarz US (2016) Dynamics of cell ensembles on adhesive micropatterns: bridging the gap between single cell spreading and collective cell migration. PLoS Comput Biol 12(4):e1004863
Angelini TE, Hannezo E, Trepat X, Fredberg JJ, Weitz DA (2010) Cell migration driven by cooperative substrate deformation patterns. Phys Rev Lett 104(16):168104
Angelini TE, Hannezo E, Trepat X, Marquez M, Fredberg JJ, Weitz DA (2011) Glass-like dynamics of collective cell migration. Proc Nat Acad Sci 108(12):4714
Anon E, Serra-Picamal X, Hersen P, Gauthier NC, Sheetz MP, Trepat X, Ladoux B (2012) Cell crawling mediates collective cell migration to close undamaged epithelial gaps. Proc Nat Acad Sci 109(27):10891
Arciero J, Mi Q, Branca MF, Hackam DJ, Swigon D (2011) Continuum model of collective cell migration in wound healing and colony expansion. Biophys J 100:535
Banerjee S, Marchetti MC (2011a) Substrate rigidity deforms and polarizes active gels. Europhys Lett 96(2):28003
Banerjee S, Marchetti MC (2011b) Instabilities and oscillations in isotropic active gels. Soft Matter 7(2):463
Banerjee S, Marchetti MC (2012) Contractile stresses in cohesive cell layers on finite-thickness substrates. Phys Rev Lett 109(10):108101
Banerjee S, Marchetti MC (2013) Controlling cell-matrix traction forces by extracellular geometry. New J Phys 15(3):035015
Banerjee S, Liverpool TB, Marchetti MC (2011) Generic phases of cross-linked active gels: relaxation, oscillation and contractility. Europhys Lett 96(5):58004
Banerjee S, Utuje KJ, Marchetti MC (2015) Propagating stress waves during epithelial expansion. Phys Rev Lett 114(22):228101
Banerjee DS, Munjal A, Lecuit T, Rao M (2017) Actomyosin pulsation and flows in an active elastomer with turnover and network remodeling. Nat Commun 8(1):1121
Barton DL, Henkes S, Weijer CJ, Sknepnek R (2017) Active vertex model for cell-resolution description of epithelial tissue mechanics. PLoS Comput Biol 13(6):e1005569
Basan M, Risler T, Joanny JF, Sastre-Garau X, Prost J (2009) Homeostatic competition drives tumor growth and metastasis nucleation. HFSP J 3(4):265
Basan M, Elgeti J, Hannezo E, Rappel WJ, Levine H (2013) Alignment of cellular motility forces with tissue flow as a mechanism for efficient wound healing. Proc Nat Acad Sci 110(7):2452
Begnaud S, Chen T, Delacour D, Mège RM, Ladoux B (2016) Mechanics of epithelial tissues during gap closure. Curr Opin Cell Biol 42:52
Bement WM, Forscher P, Mooseker MS (1993) A novel cytoskeletal structure involved in purse string wound closure and cell polarity maintenance. J Cell Biol 121(3):565
Bi D, Lopez J, Schwarz J, Manning ML (2015) A density-independent rigidity transition in biological tissues. Nat Phys 11(12):1074
Bi D, Yang X, Marchetti MC, Manning ML (2016) Motility-driven glass and jamming transitions in biological tissues. Phys Rev X 6(2):021011
Bischofs IB, Schmidt SS, Schwarz US (2009) Effect of adhesion geometry and rigidity on cellular force distributions. Phys Rev Lett 103(4):048101
Blanch-Mercader C, Casademunt J (2017) Hydrodynamic instabilities, waves and turbulence in spreading epithelia. Soft Matter 13(38):6913
Blanch-Mercader C, Vincent R, Bazellières E, Serra-Picamal X, Trepat X, Casademunt J (2017) Effective viscosity and dynamics of spreading epithelia: a solvable model. Soft Matter 13(6):1235
Bois JS, Jülicher F, Grill SW (2011) Pattern formation in active fluids. Phys Rev Lett 106(2):028103
Bove A, Gradeci D, Fujita Y, Banerjee S, Charras G, Lowe AR (2017) Local cellular neighborhood controls proliferation in cell competition. Mol Biol Cell 28(23):3215
Brugués A, Anon E, Conte V, Veldhuis JH, Gupta M, Colombelli J, Muñoz JJ, Brodland GW, Ladoux B, Trepat X (2014) Forces driving epithelial wound healing. Nat Phys 10(9):683
Camley BA, Rappel WJ (2017) Physical models of collective cell motility: from cell to tissue. J Phys D Appl Phys 50(11):113002
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(4):H1252
Cochet-Escartin O, Ranft J, Silberzan P, Marcq P (2014) Border forces and friction control epithelial closure dynamics. Biophys J 106(1):65
D’Amico LA, Cooper MS (2001) Morphogenetic domains in the yolk syncytial layer of axiating zebrafish embryos. Dev Dyn 222(4):611
Deforet M, Hakim V, Yevick HG, Duclos G, Silberzan P (2014) Emergence of collective modes and tri-dimensional structures from epithelial confinement. Nat Commun 5:3747
Delanoë-Ayari H, Rieu J, Sano M (2010) 4D traction force microscopy reveals asymmetric cortical forces in migrating Dictyostelium cells. Phys Rev Lett 105(24):248103
Discher DE, Janmey P, Wang Yl (2005) Tissue cells feel and respond to the stiffness of their substrate. Science 310(5751):1139
Doxzen K, Vedula SRK, Leong MC, Hirata H, Gov NS, Kabla AJ, Ladoux B, Lim CT (2013) Guidance of collective cell migration by substrate geometry. Integr Biol 5(8):1026
Duclos G, Garcia S, Yevick H, Silberzan P (2014) Perfect nematic order in confined monolayers of spindle-shaped cells. Soft Matter 10(14):2346
Duclos G, Erlenkämper C, Joanny JF, Silberzan P (2017) Topological defects in confined populations of spindle-shaped cells. Nat Phys 13(1):58
Du Roure O, Saez A, Buguin A, Austin RH, Chavrier P, Siberzan P, Ladoux B (2005) Force mapping in epithelial cell migration. Proc Nat Acad Sci 102(7):2390
Edwards CM, Schwarz US (2011) Force localization in contracting cell layers. Phys Rev Lett 107(12):128101
Farhadifar R, Röper JC, Aigouy B, Eaton S, Jülicher F (2007) The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Curr Biol 17(24):2095
Farooqui R, Fenteany G (2005) Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement. J Cell Sci 118(1):51
Fenteany G, Janmey PA, Stossel TP (2000) Signaling pathways and cell mechanics involved in wound closure by epithelial cell sheets. Curr Biol 10(14):831
Fletcher AG, Osterfield M, Baker RE, Shvartsman SY (2014) Vertex models of epithelial morphogenesis. Biophys J 106(11):2291
Foty RA, Forgacs G, Pfleger CM, Steinberg MS (1994) Surface tensions of embryonic tissues predict their mutual envelopment behavior. Phys Rev Lett 72(14): 2298
Friedl P, Gilmour D (2009) Collective cell migration in morphogenesis, regeneration and cancer. Nat Rev Mol Cell Biol 10(7):445
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(9):1836
Gonzalez-Rodriguez D, Bonnemay L, Elgeti J, Dufour S, Cuvelier D, Brochard-Wyart F (2013) Detachment and fracture of cellular aggregates. Soft Matter 9(7):2282
Graner F, Glazier JA (1992) Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys Rev Lett 69(13):2013
Gross P, Kumar KV, Grill SW (2017) How active mechanics and regulatory biochemistry combine to form patterns in development. Ann Rev Biophys 46:337
Guevorkian K, Colbert MJ, Durth M, Dufour S, Brochard-Wyart F (2010) Aspiration of biological viscoelastic drops. Phys Rev Lett 104(21):218101
Guillot C, Lecuit T (2013) Mechanics of epithelial tissue homeostasis and morphogenesis. Science 340(6137):1185
Harris AR, Peter L, Bellis J, Baum B, Kabla AJ, Charras GT (2012) Characterizing the mechanics of cultured cell monolayers. Proc Nat Acad Sci 109(41):16449
Heisenberg CP, Bellaïche Y (2013) Forces in tissue morphogenesis and patterning. Cell 153(5):948
Honda H, Eguchi G (1980) How much does the cell boundary contract in a monolayered cell sheet?. J Theor Biol 84(3):575
Howard J, Grill SW, Bois JS (2011) Turing’s next steps: the mechanochemical basis of morphogenesis. Nat Rev Mol Cell Biol 12(6):392
Jacinto A, Martinez-Arias A, Martin P (2001) Mechanisms of epithelial fusion and repair. Nat Cell Biol 3(5):E117
Kabla AJ (2012) Collective cell migration: leadership, invasion and segregation. J R Soc Interface p. rsif20120448
Khalilgharibi N, Fouchard J, Recho P, Charras G, Kabla A (2016) The dynamic mechanical properties of cellularised aggregates. Curr Opin Cell Biol 42:113
Khalilgharibi N, Fouchard J, Asadipour N, Yonis A, Harris A, Mosaffa P, Fujita Y, Kabla A, Baum B, Munoz JJ et al (2019) Stress relaxation in epithelial monolayers is controlled by the actomyosin cortex. Nat Phys 15:839
Köpf MH, Pismen LM (2013) A continuum model of epithelial spreading. Soft Matter 9(14):3727
Ladoux B, Mège RM (2017) Mechanobiology of collective cell behaviours. Nat Rev Mol Cell Biol 18(12):743
Latorre E, Kale S, Casares L, Gómez-González M, Uroz M, Valon L, Nair RV, Garreta E, Montserrat N, del Campo A, Ladoux B, Arroyo M, Trepat X (2018) Active superelasticity in three-dimensional epithelia of controlled shape. Nature 563(7730):203
Lecuit T, Lenne PF, Munro E (2011) Force generation, transmission, and integration during cell and tissue morphogenesis. Annu Rev Cell Dev Biol 27:157
Lee P, Wolgemuth CW (2011) Crawling cells can close wounds without purse strings or signaling. PLoS Comput Biol 7(3):e1002007
Legant WR, Choi CK, Miller JS, Shao L, Gao L, Betzig E, Chen CS (2013) Multidimensional traction force microscopy reveals out-of-plane rotational moments about focal adhesions. Proc Nat Acad Sci 110(3):881
Levayer R, Lecuit T (2012) Biomechanical regulation of contractility: spatial control and dynamics. Trends Cell Biol 22(2):61
Li B, Sun SX (2014) Coherent motions in confluent cell monolayer sheets. Biophys J 107(7):1532
Linsmeier I, Banerjee S, Oakes PW, Jung W, Kim T, Murrell MP (2016) Disordered actomyosin networks are sufficient to produce cooperative and telescopic contractility. Nat Commun 7:12615
Lomakin AJ, Lee KC, Han SJ, Bui DA, Davidson M, Mogilner A, Danuser G (2015) Competition for actin between two distinct F-actin networks defines a bistable switch for cell polarization. Nat Cell Biol 17(11):1435
Marchetti MC, Joanny JF, Ramaswamy S, Liverpool TB, Prost J, Rao M, Simha RA (2013) Hydrodynamics of soft active matter. Rev Mod Phys 85(3):1143
Martin P, Lewis J (1992) Actin cables and epidermal movement in embryonic wound healing. Nature 360(6400):179
Maruthamuthu V, Sabass B, Schwarz US, Gardel ML (2011) Cell-ECM traction force modulates endogenous tension at cell-cell contacts. Proc Nat Acad Sci 108(12):4708
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(19):198101
Mertz AF, Che Y, Banerjee S, Goldstein JM, Rosowski KA, Revilla SF, Niessen CM, Marchetti MC, Dufresne ER, Horsley V (2013) Cadherin-based intercellular adhesions organize epithelial cell-matrix traction forces. Proc Nat Acad Sci 110(3):842
Murray J, Oster G (1984) Cell traction models for generating pattern and form in morphogenesis. J Math Biol 19(3):265
Murrell M, Oakes PW, Lenz M, Gardel ML (2015) Forcing cells into shape: the mechanics of actomyosin contractility. Nat Rev Mol Cell Biol 16(8):486
Noll N, Mani M, Heemskerk I, Streichan SJ, Shraiman BI (2017) Active tension network model suggests an exotic mechanical state realized in epithelial tissues. Nat Phys 13(12):1221
Notbohm J, Banerjee S, Utuje KJ, Gweon B, Jang H, Park Y, Shin J, Butler JP, Fredberg JJ, Marchetti MC (2016) Cellular contraction and polarization drive collective cellular motion. Biophys J 110(12):2729
Oakes PW, Banerjee S, Marchetti MC, Gardel ML (2014) Geometry regulates traction stresses in adherent cells. Biophys J 107(4):825
Pérez-González C, Alert R, Blanch-Mercader C, Gómez-González M, Kolodziej T, Bazellieres E, Casademunt J, Trepat X (2018) Active wetting of epithelial tissues. Nat Phys 15(1): 79
Petitjean L, Reffay M, Grasland-Mongrain E, Poujade M, Ladoux B, Buguin A, Silberzan P (2010) Velocity fields in a collectively migrating epithelium. Biophys J 98(9):1790
Phillips H, Steinberg M (1978) Embryonic tissues as elasticoviscous liquids. I. Rapid and slow shape changes in centrifuged cell aggregates. J Cell Sci 30(1):1
Poujade M, Grasland-Mongrain E, Hertzog A, Jouanneau J, Chavrier P, Ladoux B, Buguin A, Silberzan P (2007) Collective migration of an epithelial monolayer in response to a model wound. Proc Nat Acad Sci 104(41):15988
Prost J (1995) The physics of liquid crystals, vol 83. Oxford university press, Oxford
Prost J, Jülicher F, Joanny JF (2015) Active gel physics. Nat Phys 11(2):111
Ranft J, Basan M, Elgeti J, Joanny JF, Prost J, Jülicher F (2010) Fluidization of tissues by cell division and apoptosis. Proc Nat Acad Sci 107(49):20863
Ravasio A, Le AP, Saw TB, Tarle V, Ong HT, Bertocchi C, Mège RM, Lim CT, Gov NS, Ladoux B (2015a) Regulation of epithelial cell organization by tuning cell-substrate adhesion. Integr Biol 7(10):1228
Ravasio A, Cheddadi I, Chen T, Pereira T, Ong HT, Bertocchi C, Brugues A, Jacinto A, Kabla AJ, Toyama Y, et al (2015b) Gap geometry dictates epithelial closure efficiency. Nat Commun 6:7683
Recho P, Ranft J, Marcq P (2016) Soft Matter 12:2381
Robin FB, Michaux JB, McFadden WM, Munro EM (2018) J Cell Biol, 217(12):4230
Roca-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
Roca-Cusachs P, Conte V, Trepat X (2017) Quantifying forces in cell biology. Nat Cell Biol 19(7):742
Rosenblatt J, Raff MC, Cramer LP (2001) An epithelial cell destined for apoptosis signals its neighbors to extrude it by an actin-and myosin-dependent mechanism. Curr Biol 11(23):1847
Saw TB, Doostmohammadi A, Nier V, Kocgozlu L, Thampi S, Toyama Y, Marcq P, Lim CT, Yeomans JM, Ladoux B (2017) Topological defects in epithelia govern cell death and extrusion. Nature 544(7649):212
Schaumann EN, Staddon MF, Gardel ML, Banerjee S (2018) Force localization modes in dynamic epithelial colonies. Mol Biol Cell 29(23):2835
Schwarz US, Safran SA (2013) Physics of adherent cells. Rev Mod Phys 85(3):1327
Segerer FJ, Thüroff F, Alberola AP, Frey E, Rädler JO (2015) Emergence and persistence of collective cell migration on small circular micropatterns. Phys Rev Lett 114(22):228102
Serra-Picamal X, Conte V, Vincent R, Anon E, Tambe DT, Bazellieres E, Butler JP, Fredberg JJ, Trepat X (2012) Mechanical waves during tissue expansion. Nat Phys 8(8):628
Shraiman BI (2005) Mechanical feedback as a possible regulator of tissue growth. Proc Natl Acad Sci 102(9):3318–3323
Staddon MF, Bi D, Tabatabai AP, Ajeti V, Murrell MP, Banerjee S (2018) Cooperation of dual modes of cell motility promotes epithelial stress relaxation to accelerate wound healing. PLoS Comput Biol 14(10):e1006502
Style RW, Boltyanskiy R, German GK, Hyland C, MacMinn CW, Mertz AF, Wilen LA, Xu Y, Dufresne ER (2014) Traction force microscopy in physics and biology. Soft Matter 10(23):4047
Suarez C, Kovar DR (2016) Internetwork competition for monomers governs actin cytoskeleton organization. Nat Rev Mol Cell Biol 17(12):799
Tambe DT, Hardin CC, Angelini TE, Rajendran K, Park CY, Serra-Picamal X, Zhou EH, Zaman MH, Butler JP, Weitz DA et al (2011) Collective cell guidance by cooperative intercellular forces. Nat Mater 10(6):469
Tanner K, Mori H, Mroue R, Bruni-Cardoso A, Bissell MJ (2012) Coherent angular motion in the establishment of multicellular architecture of glandular tissues. Proc Nat Acad Sci 109(6):1973
Théry M (2012) Cell mechanics: Wave of migration. Nat Phys 8(8):583
Théry M, Piel M (2009) Adhesive micropatterns for cells: a microcontact printing protocol. Cold Spring Harb Protoc 2009(7):pdb
Trepat X, Wasserman MR, Angelini TE, Millet E, Weitz DA, Butler JP, Fredberg JJ (2009) Physical forces during collective cell migration. Nat Phys 5(6):426
Vedula SRK, Peyret G, Cheddadi I, Chen T, Brugués A, Hirata H, Lopez-Menendez H, Toyama Y, De Almeida LN, Trepat X, et al (2015) Mechanics of epithelial closure over non-adherent environments. Nat Commun 6:6111
Vicsek T, Czirók A, Ben-Jacob E, Cohen I, Shochet O (1995) Novel type of phase transition in a system of self-driven particles. Phys Rev Lett 75(6):1226
Vincent R, Bazellières E, Pérez-González C, Uroz M, Serra-Picamal X, Trepat X (2015) Active tensile modulus of an epithelial monolayer. Phys Rev Lett 115(24):248103
Walcott S, Sun SX (2010) Cytoskeletal cross-linking and bundling in motor-independent contraction. Proc Nat Acad Sci 107(17):7757
Wayne Brodland G, Wiebe CJ (2004) Mechanical effects of cell anisotropy on epithelia. Comput Methods Biomech Biomed Eng 7(2):91
Wood W, Jacinto A, Grose R, Woolner S, Gale J, Wilson C, Martin P (2002) Wound healing recapitulates morphogenesis in Drosophila embryos. Nat Cell Biol 4(11):907
Wozniak MA, Chen CS (2009) Mechanotransduction in development: a growing role for contractility. Nat Rev Mol Cell Biol 10(1):34
Yabunaka S, Marcq P (2017) Cell growth, division, and death in cohesive tissues: A thermodynamic approach. Phys Rev E 96(2):022406
Yarrow JC, Perlman ZE, Westwood NJ, Mitchison TJ (2004) A high-throughput cell migration assay using scratch wound healing, a comparison of image-based readout methods. BMC Biotechnol 4(1):21
Zemel A, Rehfeldt F, Brown A, Discher D, Safran S (2010) Optimal matrix rigidity for stress-fibre polarization in stem cells. Nat Phys 6(6):468
Ziebert F, Swaminathan S, Aranson IS (2011) Model for self-polarization and motility of keratocyte fragments. J R Soc Interface p. rsif20110433
Acknowledgements
SB acknowledges support from a Strategic Fellowship at the Institute for the Physics of Living Systems at UCL, UCL Global Engagement Fund, Royal Society Tata University Research Fellowship (URF\R1\180187), and Human Frontiers Science Program (HFSP RGY0073/2018). MCM was supported by the National Science Foundation at Syracuse University through award DMR-1609208 and at KITP under Grant PHY-1748958, and by the Simons Foundation through a Targeted Grant Award No. 342354. MCM thanks M. Czajkowski for useful discussions and the KITP for hospitality during completion of some of this work.
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Banerjee, S., Marchetti, M.C. (2019). Continuum Models of Collective Cell Migration. 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_4
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