Skip to main content
SpringerLink
Log in

Modeling Cell Migration Mechanics

  • Chapter
  • First Online:
Biomechanics in Oncology

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 1092))

Abstract

Cell migration is the physical movement of cells and is responsible for the extensive cellular invasion and metastasis that occur in high-grade tumors. Motivated by decades of direct observation of cell migration via light microscopy, theoretical models have emerged to capture various aspects of the fundamental physical phenomena underlying cell migration. Yet, the motility mechanisms actually used by tumor cells during invasion are still poorly understood, as is the role of cellular interactions with the extracellular environment. In this chapter, we review key physical principles of cytoskeletal self-assembly and force generation, membrane tension, biological adhesion, hydrostatic and osmotic pressures, and their integration in mathematical models of cell migration. With the goal of modeling-driven cancer therapy, we provide examples to guide oncologists and physical scientists in developing next-generation models to predict disease progression and treatment.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Abbreviations

ATP:

Adenosine triphosphate

CMS:

Cell migration simulator

ECM:

Extracellular matrix

FEM:

Finite element modeling

GBM:

Glioblastoma (grade IV glioma)

ODE:

Ordinary differential equations

PDE:

Partial differential equations

RGD:

Arginine-glycine-aspartic acid tripeptide

SDE:

Stochastic differential equations

SSA:

Stochastic simulation algorithm

Bibliography

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

    Article  CAS  PubMed  Google Scholar 

  2. Ridley AJ, Schwartz MA, Burridge K, Firtel RA, Ginsberg MH, Borisy G, Parsons JT, Horwitz AR (2003) Cell migration: integrating signals from front to back. Science 302(5651):1704–1709

    Article  CAS  PubMed  Google Scholar 

  3. Weigelt B, Peterse JL, van 't Veer LJ (2005) Breast cancer metastasis: markers and models. Nat Rev Cancer 5(8):591–602

    Article  CAS  PubMed  Google Scholar 

  4. Abercrombie M (1980) The Croonian lecture, 1978: the crawling movement of metazoan cells. Proc R Soc Lond B Biol Sci 207(1167):129–147

    Article  Google Scholar 

  5. Dickinson RB, Tranquillo RT (1993) A stochastic model for adhesion-mediated cell random motility and haptotaxis. J Math Biol 31(6):563–600

    Article  CAS  PubMed  Google Scholar 

  6. DiMilla PA, Barbee K, Lauffenburger DA (1991) Mathematical model for the effects of adhesion and mechanics on cell migration speed. Biophys J 60(1):15–37

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Friedl P, Wolf K (2010) Plasticity of cell migration: a multiscale tuning model. J Cell Biol 188(1):11–19

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Lämmermann T, Bader BL, Monkley SJ, Worbs T, Wedlich-Söldner R, Hirsch K, Keller M, Förster R, Critchley DR, Fässler R, Sixt M (2008) Rapid leukocyte migration by integrin-independent flowing and squeezing. Nature 453(7191):51–55

    Article  PubMed  CAS  Google Scholar 

  9. Renkawitz J, Schumann K, Weber M, Lämmermann T, Pflicke H, Piel M, Polleux J, Spatz JP, Sixt M (2009) Adaptive force transmission in amoeboid cell migration. Nat Cell Biol 11(12):1438–1443

    Article  CAS  PubMed  Google Scholar 

  10. Bergert M, Erzberger A, Desai RA, Aspalter IM, Oates AC, Charras G, Salbreux G, Paluch EK (2015) Force transmission during adhesion-independent migration. Nat Cell Biol 17(4):524–529

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Le Berre M, Liu YJ, Hu J, Maiuri P, Bénichou O, Voituriez R, Chen Y, Piel M (2013) Geometric friction directs cell migration. Phys Rev Lett 111(19):198101

    Article  PubMed  CAS  Google Scholar 

  12. Stroka KM, Jiang H, Chen SH, Tong Z, Wirtz D, Sun SX, Konstantopoulos K (2014b) Water permeation drives tumor cell migration in confined microenvironments. Cell 157(3):611–623

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Roca-Cusachs P, Conte V, Trepat X (2017) Quantifying forces in cell biology. Nat Cell Biol 19(7):742–751

    Article  CAS  PubMed  Google Scholar 

  14. Pelham RJ, Wang Yl (1997) Cell locomotion and focal adhesions are regulated by substrate flexibility. Proc Natl Acad Sci U S A 94(25):13661–13665

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Provenzano PP, Eliceiri KW, Campbell JM, Inman DR, White JG, Keely PJ (2006) Collagen reorganization at the tumor-stromal interface facilitates local invasion. BMC Med 4(1):38

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  16. Charras G, Sahai E (2014) Physical influences of the extracellular environment on cell migration. Nat Rev Mol Cell Biol 15(12):813–824

    Article  CAS  PubMed  Google Scholar 

  17. Beadle C, Assanah MC, Monzo P, Vallee R, Rosenfeld SS, Canoll P (2008) The role of myosin II in glioma invasion of the brain. Mol Biol Cell 19(8):3357–3368

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Hoffman BD, Grashoff C, Schwartz MA (2011) Dynamic molecular processes mediate cellular mechanotransduction. Nature 475(7356):316–323

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Condeelis J, Segall JE (2003) Intravital imaging of cell movement in tumours, Nat Rev Cancer 3(12):921–930

    CAS  PubMed  Google Scholar 

  20. Wolf K, Alexander S, Schacht V, Coussens LM, von Andrian UH, van Rheenen J, Deryugina E, Friedl P (2009) Collagen-based cell migration models in vitro and in vivo. Semin Cell Dev Biol 20(8):931–941

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Paul CD, Mistriotis P, Konstantopoulos K (2017) Cancer cell motility: lessons from migration in confined spaces. Nat Rev Cancer 17(2):131–140

    Article  CAS  PubMed  Google Scholar 

  22. Stroka KM, Gu Z, Sun SX, Konstantopoulos K (2014a) Bioengineering paradigms for cell migration in confined microenvironments. Curr Opin Cell Biol 30:41–50

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Danuser G, Allard J, Mogilner A (2013) Mathematical modeling of eukaryotic cell migration: insights beyond experiments. Annu Rev Cell Dev Biol 29:501–528

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Pollard TD, Borisy GG (2003) Cellular motility driven by assembly and disassembly of actin filaments. Cell 112(4):453–465

    Article  CAS  PubMed  Google Scholar 

  25. Svitkina TM, Borisy GG (1999) Arp2/3 complex and actin depolymerizing factor/cofilin in dendritic organization and treadmilling of actin filament array in lamellipodia. J Cell Biol 145(5):1009–1026

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Wu C, Asokan SB, Berginski ME, Haynes EM, Sharpless NE, Griffith JD, Gomez SM, Bear JE (2012) Arp2/3 is critical for lamellipodia and response to extracellular matrix cues but is dispensable for chemotaxis. Cell 148(5):973–987

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Abraham VC, Krishnamurthi V, Taylor DL, Lanni F (1999) The actin-based nanomachine at the leading edge of migrating cells. Biophys J 77(3):1721–1732

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. 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  CAS  PubMed  Google Scholar 

  29. Hill TL (1981) Microfilament or microtubule assembly or disassembly against a force. Proc Natl Acad Sci U S A 78(9):5613–5617

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Mogilner A, Oster G (1996) Cell motility driven by actin polymerization. Biophys J 71(6):3030–3045

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Peskin CS, Odell GM, Oster GF (1993) Cellular motions and thermal fluctuations: the Brownian ratchet. Biophys J 65(1):316–324

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Dickinson RB, Caro L, Purich DL (2004) Force generation by cytoskeletal filament end-tracking proteins. Biophys J 87(4):2838–2854

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Mogilner A, Edelstein-Keshet L (2002) Regulation of actin dynamics in rapidly moving cells: a quantitative analysis. Biophys J 83(3):1237–1258

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Mattila PK, Lappalainen P (2008) Filopodia: molecular architecture and cellular functions, Nat Rev Mol Cell Biol 9(6):446–454

    CAS  Google Scholar 

  35. Schoumacher M, Goldman RD, Louvard D, Vignjevic DM (2010) Actin, microtubules, and vimentin intermediate filaments cooperate for elongation of invadopodia. J Cell Biol 189(3):541–556

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Vignjevic D, Montagnac G (2008) Reorganisation of the dendritic actin network during cancer cell migration and invasion. Semin Cancer Biol 18(1):12–22

    Article  CAS  PubMed  Google Scholar 

  37. Chan CE, Odde DJ (2008) Traction dynamics of filopodia on compliant substrates. Science 322(5908):1687–1691

    Article  CAS  PubMed  Google Scholar 

  38. Wolgemuth CW (2005) Lamellipodial contractions during crawling and spreading. Biophys J 89(3):1643–1649

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. 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):486–498

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Prost J, Jülicher F, Joanny J (2015) Active gel physics. Nat Phys 11(2):111–117

    Article  CAS  Google Scholar 

  41. Salbreux G, Charras G, Paluch E (2012) Actin cortex mechanics and cellular morphogenesis. Trends Cell Biol 22(10):536–545

    Article  CAS  PubMed  Google Scholar 

  42. Janmey PA, Hvidt S, Käs J, Lerche D, Maggs A, Sackmann E, Schliwa M, Stossel TP (1994) The mechanical properties of actin gels. Elastic modulus and filament motions. J Biol Chem 269(51):32503–32513

    CAS  PubMed  Google Scholar 

  43. Jülicher F, Kruse K, Prost J, Joanny J (2007) Active behavior of the cytoskeleton. Phys Rep 449(1-3):3–28

    Article  CAS  Google Scholar 

  44. Aratyn-Schaus Y, Gardel ML (2010) Transient frictional slip between integrin and the ECM in focal adhesions under myosin II tension. Curr Biol 20(13):1145–1153

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Lin CH, Espreafico EM, Mooseker MS, Forscher P (1996) Myosin drives retrograde F-actin flow in neuronal growth cones. Neuron 16(4):769–782

    Article  CAS  PubMed  Google Scholar 

  46. Mogilner A, Oster G (2003) Force generation by actin polymerization II: the elastic ratchet and tethered filaments. Biophys J 84(3):1591–1605

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Molloy JE, Burns JE, Kendrick-Jones J, Tregear RT, White DC (1995) Movement and force produced by a single myosin head. Nature 378(6553):209–212

    Article  CAS  PubMed  Google Scholar 

  48. Mekhdjian AH, Kai F, Rubashkin MG, Prahl LS, Przybyla LM, McGregor AL, Bell ES, Barnes JM, DuFort CC, Ou G, Chang AC, Cassereau L, Tan SJ, Pickup MW, Lakins JN, Ye X, Davidson MW, Lammerding J, Odde DJ, Dunn AR, Weaver VM (2017) Integrin-mediated traction force enhances paxillin molecular associations and adhesion dynamics that increase the invasiveness of tumor cells into a three-dimensional extracellular matrix. Mol Biol Cell 28(11):1467–1488

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  49. Callan-Jones AC, Voituriez R (2016) Actin flows in cell migration: from locomotion and polarity to trajectories. Curr Opin Cell Biol 38:12–17

    Article  CAS  PubMed  Google Scholar 

  50. Gardel ML, Sabass B, Ji L, Danuser G, Schwarz US, Waterman CM (2008) Traction stress in focal adhesions correlates biphasically with actin retrograde flow speed. J Cell Biol 183(6):999–1005

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  51. Liu YJ, Le Berre M, Lautenschlaeger F, Maiuri P, Callan-Jones A, Heuzé M, Takaki T, Voituriez R, Piel M (2015) Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells. Cell 160(4):659–672

    Article  CAS  PubMed  Google Scholar 

  52. Lin CH, Forscher P (1995) Growth cone advance is inversely proportional to retrograde F-actin flow. Neuron 14(4):763–771

    Article  CAS  PubMed  Google Scholar 

  53. Hill AV (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci 126(843):136–195

    Article  Google Scholar 

  54. Cuda G, Pate E, Cooke R, Sellers JR (1997) In vitro actin filament sliding velocities produced by mixtures of different types of myosin. Biophys J 72(4):1767–1779

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Tsuda Y, Yasutake H, Ishijima A, Yanagida T (1996) Torsional rigidity of single actin filaments and actin-actin bond breaking force under torsion measured directly by in vitro micromanipulation. Proc Natl Acad Sci U S A 93(23):12937–12942

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  56. Stam S, Alberts J, Gardel ML, Munro E (2015) Isoforms confer characteristic force generation and mechanosensation by myosin II filaments. Biophys J 108(8):1997–2006

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  57. Sugi H, Chaen S (2003) Force-velocity relationships in actin-myosin interactions causing cytoplasmic streaming in algal cells. J Exp Biol 206(12):1971–1976

    Article  CAS  PubMed  Google Scholar 

  58. Barnhart EL, Lee KC, Keren K, Mogilner A, Theriot JA (2011) An adhesion-dependent switch between mechanisms that determine motile cell shape. PLoS Biol 9(5):e1001059

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. 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):1435–1445

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Satulovsky J, Lui R, Wang YL (2008) Exploring the control circuit of cell migration by mathematical modeling. Biophys J 94(9):3671–3683

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Maiuri P, Rupprecht JF, Wieser S, Ruprecht V, Bénichou O, Carpi N, Coppey M, De Beco S, Gov N, Heisenberg CP, Lage Crespo C, Lautenschlaeger F, Le Berre M, Lennon-Dumenil AM, Raab M, Thiam HR, Piel M, Sixt M, Voituriez R (2015) Actin flows mediate a universal coupling between cell speed and cell persistence. Cell 161(2):374–386

    Article  CAS  PubMed  Google Scholar 

  62. Ruprecht V, Wieser S, Callan-Jones A, Smutny M, Morita H, Sako K, Barone V, Ritsch-Marte M, Sixt M, Voituriez R, Heisenberg CP (2015) Cortical contractility triggers a stochastic switch to fast amoeboid cell motility. Cell 160(4):673–685

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. Hawkins RJ, Poincloux R, Bénichou O, Piel M, Chavrier P, Voituriez R (2011) Spontaneous contractility-mediated cortical flow generates cell migration in three-dimensional environments. Biophys J 101(5):1041–1045

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. Campbell ID, Humphries MJ (2011) Integrin structure, activation, and interactions. Cold Spring Harb Perspect Biol 3(3)

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  65. Ziegler WH, Gingras AR, Critchley DR, Emsley J (2008) Integrin connections to the cytoskeleton through Talin and vinculin. Biochem Soc Trans 36(Pt 2):235–239

    Article  CAS  PubMed  Google Scholar 

  66. Gardel ML, Schneider IC, Aratyn-Schaus Y, Waterman CM (2010) Mechanical integration of actin and adhesion dynamics in cell migration. Annu Rev Cell Dev Biol 26:315–333

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  67. Leckband DE, le Duc Q, Wang N, de Rooij J (2011) Mechanotransduction at cadherin-mediated adhesions. Curr Opin Cell Biol 23(5): 523–530

    Article  CAS  PubMed  Google Scholar 

  68. Ponta H, Sherman L, Herrlich PA (2003) CD44: from adhesion molecules to signalling regulators. Nat Rev Mol Cell Biol 4(1):33–45

    Article  CAS  PubMed  Google Scholar 

  69. Bell GI (1978) Models for the specific adhesion of cells to cells. Science 200(4342):618–627

    Article  CAS  PubMed  Google Scholar 

  70. Oakes PW, Banerjee S, Marchetti MC, Gardel ML (2014) Geometry regulates traction stresses in adherent cells. Biophys J 107(4):825–833

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Desgrosellier JS, Cheresh DA (2010) Integrins in cancer: biological implications and therapeutic opportunities. Nat Rev Cancer 10(1):9–22

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Winograd-Katz SE, Fässler R, Geiger B, Legate KR (2014) The integrin adhesome: from genes and proteins to human disease. Nat Rev Mol Cell Biol 15(4):273–288

    Article  CAS  PubMed  Google Scholar 

  73. Brown CM, Hebert B, Kolin DL, Zareno J, Whitmore L, Horwitz AR, Wiseman PW (2006) Probing the integrin-actin linkage using high-resolution protein velocity mapping. J Cell Sci 119(Pt 24): 5204–5214

    Article  CAS  PubMed  Google Scholar 

  74. Thievessen I, Thompson PM, Berlemont S, Plevock KM, Plotnikov SV, Zemljic-Harpf A, Ross RS, Davidson MW, Danuser G, Campbell SL, Waterman CM (2013) Vinculin-actin interaction couples actin retrograde flow to focal adhesions, but is dispensable for focal adhesion growth. J Cell Biol 202(1):163–177

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  75. Elosegui-Artola A, Bazellières E, Allen MD, Andreu I, Oria R, Sunyer R, Gomm JJ, Marshall JF, Jones JL, Trepat X, Roca-Cusachs P (2014) Rigidity sensing and adaptation through regulation of integrin types. Nat Mater 13(6):631–637

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  76. Engler AJ, Sen S, Sweeney HL, Discher DE (2006) Matrix elasticity directs stem cell lineage specification. Cell 126(4):677–689

    Article  CAS  PubMed  Google Scholar 

  77. Ulrich TA, de Juan Pardo EM, Kumar S (2009) The mechanical rigidity of the extracellular matrix regulates the structure, motility, and proliferation of glioma cells. Cancer Res 69(10):4167–4174

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Elosegui-Artola A, Oria R, Chen Y, Kosmalska A, Pérez-González C, Castro N, Zhu C, Trepat X, Roca-Cusachs P (2016) Mechanical regulation of a molecular clutch defines force transmission and transduction in response to matrix rigidity. Nat Cell Biol 18(5):540–548

    Article  CAS  PubMed  Google Scholar 

  79. Bangasser BL, Shamsan GA, Chan CE, Opoku KN, Tüzel E, Schlichtmann BW, Kasim JA, Fuller BJ, McCullough BR, Rosenfeld SS, Odde DJ (2017) Shifting the optimal stiffness for cell migration. Nat Commun 8:15313

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  80. Jiang G, Giannone G, Critchley DR, Fukumoto E, Sheetz MP (2003) Two-piconewton slip bond between fibronectin and the cytoskeleton depends on Talin. Nature 424(6946):334–337

    Article  CAS  PubMed  Google Scholar 

  81. Kong F, García AJ, Mould AP, Humphries MJ, Zhu C (2009) Demonstration of catch bonds between an integrin and its ligand. J Cell Biol 185(7): 1275–1284

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  82. Buckley CD, Tan J, Anderson KL, Hanein D, Volkmann N, Weis WI, Nelson WJ, Dunn AR (2014) Cell adhesion. The minimal cadherin-catenin complex binds to actin filaments under force. Science 346(6209):1254211

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  83. Pereverzev YV, Prezhdo OV, Forero M, Sokurenko EV, Thomas WE (2005) The two-pathway model for the catch-slip transition in biological adhesion. Biophys J 89(3):1446–1454

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  84. Yago T, Lou J, Wu T, Yang J, Miner JJ, Coburn L, López JA, Cruz MA, Dong JF, McIntire LV, McEver RP, Zhu C (2008) Platelet glycoprotein Ibalpha forms catch bonds with human WT vWF but not with type 2B von Willebrand disease vWF. J Clin Invest 118(9): 3195–3207

    CAS  PubMed  PubMed Central  Google Scholar 

  85. Chang AC, Mekhdjian AH, Morimatsu M, Denisin AK, Pruitt BL, Dunn AR (2016) Single molecule force measurements in living cells reveal a minimally tensioned integrin state. ACS Nano 10(12):10745–10752

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  86. Wang X, Sun J, Xu Q, Chowdhury F, Roein-Peikar M, Wang Y, Ha T (2015) Integrin molecular tension within motile focal adhesions. Biophys J 109(11):2259–2267

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Li Y, Bhimalapuram P, Dinner AR (2010) Model for how retrograde actin flow regulates adhesion traction stresses. J Phys Condens Matter 22(19):194113

    Article  PubMed  CAS  Google Scholar 

  88. Case LB, Waterman CM (2015) Integration of actin dynamics and cell adhesion by a three-dimensional, mechanosensitive molecular clutch. Nat Cell Biol 17(8):955–963

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  89. Bangasser BL, Rosenfeld SS, Odde DJ (2013) Determinants of maximal force transmission in a motor-clutch model of cell traction in a compliant microenvironment. Biophys J 105(3):581–592

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  90. Bangasser BL, Odde DJ (2013) Master equation-based analysis of a motor-clutch model for cell traction force. Cell Mol Bioeng 6(4):449–459

    Article  PubMed  Google Scholar 

  91. Plotnikov SV, Pasapera AM, Sabass B, Waterman CM (2012) Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration. Cell 151(7):1513–1527

    Article  CAS  PubMed  Google Scholar 

  92. Chaudhuri O, Gu L, Darnell M, Klumpers D, Bencherif SA, Weaver JC, Huebsch N, Mooney DJ (2015) Substrate stress relaxation regulates cell spreading. Nat Commun 6:6364

    Article  PubMed  CAS  Google Scholar 

  93. Weinberg SH, Mair DB, Lemmon CA (2017) Mechanotransduction dynamics at the cell-matrix interface. Biophys J 112(9):1962–1974

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  94. Hu K, Ji L, Applegate KT, Danuser G, Waterman-Storer CM (2007) Differential transmission of actin motion within focal adhesions. Science 315(5808):111–115

    Article  CAS  PubMed  Google Scholar 

  95. Sabass B, Schwarz US (2010) Modeling cytoskeletal flow over adhesion sites: competition between stochastic bond dynamics and intracellular relaxation. J Phys Condens Matter 22(19):194112

    Article  PubMed  CAS  Google Scholar 

  96. Welf ES, Johnson HE, Haugh JM (2013) Bidirectional coupling between integrin-mediated signaling and actomyosin mechanics explains matrix-dependent intermittency of leading-edge motility. Mol Biol Cell 24(24):3945–3955

    Article  PubMed  PubMed Central  Google Scholar 

  97. Craig EM, Stricker J, Gardel M, Mogilner A (2015) Model for adhesion clutch explains biphasic relationship between actin flow and traction at the cell leading edge. Phys Biol 12(3):035002

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  98. Webb DJ, Parsons JT, Horwitz AF (2002) Adhesion assembly, disassembly and turnover in migrating cells – over and over and over again. Nat Cell Biol 4(4):E97-100

    Article  CAS  PubMed  Google Scholar 

  99. 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  CAS  PubMed  Google Scholar 

  100. Galbraith CG, Yamada KM, Sheetz MP (2002) The relationship between force and focal complex development. J Cell Biol 159(4):695–705

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  101. Riveline D, Zamir E, Balaban NQ, Schwarz US, Ishizaki T, Narumiya S, Kam Z, Geiger B, Bershadsky AD (2001) Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism. J Cell Biol 153(6):1175–1186

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  102. Shemesh T, Bershadsky AD, Kozlov MM (2012) Physical model for self-organization of actin cytoskeleton and adhesion complexes at the cell front. Biophys J 102(8):1746–1756

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  103. Besser A, Safran SA (2006) Force-induced adsorption and anisotropic growth of focal adhesions. Biophys J 90(10):3469–3484

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  104. Cao X, Lin Y, Driscoll TP, Franco-Barraza J, Cukierman E, Mauck RL, Shenoy VB (2015) A chemomechanical model of matrix and nuclear rigidity regulation of focal adhesion size. Biophys J 109(9):1807–1817

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  105. Paszek MJ, Zahir N, Johnson KR, Lakins JN, Rozenberg GI, Gefen A, Reinhart-King CA, Margulies SS, Dembo M, Boettiger D, Hammer DA, Weaver VM (2005) Tensional homeostasis and the malignant phenotype. Cancer Cell 8(3): 241–254

    Article  CAS  PubMed  Google Scholar 

  106. Wang X, Ha T (2013) Defining single molecular forces required to activate integrin and notch signaling. Science 340(6135):991–994

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  107. Yao M, Goult BT, Chen H, Cong P, Sheetz MP, Yan J (2014) Mechanical activation of vinculin binding to Talin locks Talin in an unfolded conformation. Sci Rep 4:4610

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  108. Tozluoğlu M, Tournier AL, Jenkins RP, Hooper S, Bates PA, Sahai E (2013) Matrix geometry determines optimal cancer cell migration strategy and modulates response to interventions. Nat Cell Biol 15(7):751–762

    Article  PubMed  CAS  Google Scholar 

  109. Petrie RJ, Koo H, Yamada KM (2014) Generation of compartmentalized pressure by a nuclear piston governs cell motility in a 3D matrix. Science 345(6200):1062–1065

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  110. Petrie RJ, Harlin HM, Korsak LI, Yamada KM (2017) Activating the nuclear piston mechanism of 3D migration in tumor cells. J Cell Biol 216(1):93–100

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  111. Manoussaki D, Shin WD, Waterman CM, Chadwick RS (2015) Cytosolic pressure provides a propulsive force comparable to actin polymerization during lamellipod protrusion. Sci Rep 5:12314

    Article  PubMed  PubMed Central  Google Scholar 

  112. Davidson PM, Denais C, Bakshi MC, Lammerding J (2014) Nuclear deformability constitutes a rate-limiting step during cell migration in 3-D environments. Cell Mol Bioeng 7(3):293–306

    Article  CAS  PubMed  Google Scholar 

  113. Harada T, Swift J, Irianto J, Shin JW, Spinler KR, Athirasala A, Diegmiller R, Dingal PC, Ivanovska IL, Discher DE (2014) Nuclear Lamin stiffness is a barrier to 3D migration, but softness can limit survival. J Cell Biol 204(5):669–682

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  114. Umeshima H, Hirano T, Kengaku M (2007) Microtubule-based nuclear movement occurs independently of centrosome positioning in migrating neurons. Proc Natl Acad Sci U S A 104(41):16182–16187

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  115. Thiam HR, Vargas P, Carpi N, Crespo CL, Raab M, Terriac E, King MC, Jacobelli J, Alberts AS, Stradal T, Lennon-Dumenil AM, Piel M (2016) Perinuclear Arp2/3-driven actin polymerization enables nuclear deformation to facilitate cell migration through complex environments. Nat Commun 7:10997

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  116. Cao X, Moeendarbary E, Isermann P, Davidson PM, Wang X, Chen MB, Burkart AK, Lammerding J, Kamm RD, Shenoy VB (2016) A chemomechanical model for nuclear morphology and stresses during cell transendothelial migration. Biophys J 111(7):1541–1552

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  117. Aubry D, Thiam H, Piel M, Allena R (2015) A computational mechanics approach to assess the link between cell morphology and forces during confined migration. Biomech Model Mechanobiol 14(1):143–157

    Article  CAS  PubMed  Google Scholar 

  118. Klank RL, Decker Grunke SA, Bangasser BL, Forster CL, Price MA, Odde TJ, SantaCruz KS, Rosenfeld SS, Canoll P, Turley EA, McCarthy JB, Ohlfest JR, Odde DJ (2017) Biphasic dependence of glioma survival and cell migration on CD44 expression level. Cell Rep 18(1):23–31

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  119. Palecek SP, Loftus JC, Ginsberg MH, Lauffenburger DA, Horwitz AF (1997) Integrin-ligand binding properties govern cell migration speed through cell-substratum adhesiveness. Nature 385(6616):537–540

    Article  CAS  PubMed  Google Scholar 

  120. Tranquillo RT, Lauffenburger DA, Zigmond SH (1988) A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations. J Cell Biol 106(2):303–309

    Article  CAS  PubMed  Google Scholar 

  121. Owen LM, Adhikari AS, Patel M, Grimmer P, Leijnse N, Kim MC, Notbohm J, Franck C, Dunn AR (2017) A cytoskeletal clutch mediates cellular force transmission in a soft, three-dimensional extracellular matrix. Mol Biol Cell 28(14):1959–1974

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  122. Zaman MH, Kamm RD, Matsudaira P, Lauffenburger DA (2005) Computational model for cell migration in three-dimensional matrices. Biophys J 89(2):1389–1397

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  123. Estabridis HM, Jana A, Nain A, Odde DJ (2018) Cell migration in 1D and 2D nanofiber microenvironments. Ann Biomed Eng 46(3):392–403

    Article  PubMed  PubMed Central  Google Scholar 

  124. Ray A, Slama ZM, Morford RK, Madden SA, Provenzano PP (2017) Enhanced directional migration of cancer stem cells in 3D aligned collagen matrices. Biophys J 112(5):1023–1036

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  125. Zaman MH, Trapani LM, Sieminski AL, Siemeski A, Mackellar D, Gong H, Kamm RD, Wells A, Lauffenburger DA, Matsudaira P (2006) Migration of tumor cells in 3D matrices is governed by matrix stiffness along with cell-matrix adhesion and proteolysis. Proc Natl Acad Sci U S A 103(29):10889–10894

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  126. Kumar S, Weaver VM (2009) Mechanics, malignancy, and metastasis: the force journey of a tumor cell. Cancer Metastasis Rev 28(1-2):113–127

    Article  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  128. Stroka KM, Aranda-Espinoza H (2009) Neutrophils display biphasic relationship between migration and substrate stiffness. Cell Motil Cytoskeleton 66(6):328–341

    Article  CAS  PubMed  Google Scholar 

  129. Lo CM, Wang HB, Dembo M, Wang YL (2000) Cell movement is guided by the rigidity of the substrate. Biophys J 79(1):144–152

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  130. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361

    Article  CAS  Google Scholar 

  131. Acerbi I, Cassereau L, Dean I, Shi Q, Au A, Park C, Chen YY, Liphardt J, Hwang ES, Weaver VM (2015) Human breast cancer invasion and aggression correlates with ECM stiffening and immune cell infiltration. Integr Biol 7(10):1120–1134

    Article  CAS  Google Scholar 

  132. Morimatsu M, Mekhdjian AH, Adhikari AS, Dunn AR (2013) Molecular tension sensors report forces generated by single integrin molecules in living cells. Nano Lett 13(9):3985–3989

    Article  CAS  PubMed  Google Scholar 

  133. Kanteti R, Batra SK, Lennon FE, Salgia R (2016) FAK and paxillin, two potential targets in pancreatic cancer. Oncotarget 7(21):31586–31601

    Article  PubMed  PubMed Central  Google Scholar 

  134. Novak U, Kaye AH (2000) Extracellular matrix and the brain: components and function. J Clin Neurosci 7(4):280–290

    Article  CAS  PubMed  Google Scholar 

  135. Bhat KP, Balasubramaniyan V, Vaillant B, Ezhilarasan R, Hummelink K, Hollingsworth F, Wani K, Heathcock L, James JD, Goodman LD, Conroy S, Long L, Lelic N, Wang S, Gumin J, Raj D, Kodama Y, Raghunathan A, Olar A, Joshi K, Pelloski CE, Heimberger A, Kim SH, Cahill DP, Rao G, Den Dunnen WF, Boddeke HW, Phillips HS, Nakano I, Lang FF, Colman H, Sulman EP, Aldape K (2013) Mesenchymal differentiation mediated by NF-κB promotes radiation resistance in glioblastoma. Cancer Cell 24(3):331–346

    Article  CAS  PubMed  Google Scholar 

  136. Wei KC, Huang CY, Chen PY, Feng LY, Wu TW, Chen SM, Tsai HC, Lu YJ, Tsang NM, Tseng CK, Pai PC, Shin JW (2010) Evaluation of the prognostic value of CD44 in glioblastoma multiforme. Anticancer Res 30(1):253–259

    CAS  PubMed  Google Scholar 

  137. Ranuncolo SM, Ladeda V, Specterman S, Varela M, Lastiri J, Morandi A, Matos E, Bal de Kier Joffé E, Puricelli L, Pallotta MG (2002) CD44 expression in human gliomas. J Surg Oncol 79(1):30–35; discussion 35-6

    Article  CAS  PubMed  Google Scholar 

  138. Levin EG (2005) Cancer therapy through control of cell migration. Curr Cancer Drug Targets 5(7):505–518

    Article  CAS  PubMed  Google Scholar 

  139. Palmer TD, Ashby WJ, Lewis JD, Zijlstra A (2011) Targeting tumor cell motility to prevent metastasis. Adv Drug Deliv Rev 63(8):568–581

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  140. Marelli UK, Rechenmacher F, Sobahi TR, Mas-Moruno C, Kessler H (2013) Tumor targeting via integrin ligands. Front Oncol 3:222

    Article  PubMed  PubMed Central  Google Scholar 

  141. Mas-Moruno C, Rechenmacher F, Kessler H (2010) Cilengitide: the first anti-angiogenic small molecule drug candidate design, synthesis and clinical evaluation. Anti Cancer Agents Med Chem 10(10):753–768

    Article  CAS  Google Scholar 

  142. Baker AM, Bird D, Lang G, Cox TR, Erler JT (2013) Lysyl oxidase enzymatic function increases stiffness to drive colorectal cancer progression through FAK. Oncogene 32(14):1863–1868

    Article  CAS  PubMed  Google Scholar 

  143. Berg WA, Madsen KS, Schilling K, Tartar M, Pisano ED, Larsen LH, Narayanan D, Kalinyak JE (2012) Comparative effectiveness of positron emission mammography and MRI in the contralateral breast of women with newly diagnosed breast cancer. ARJ Am J Roentgenol 198(1):219–232

    Article  Google Scholar 

  144. Hayashi M, Yamamoto Y, Sueta A, Tomiguchi M, Yamamoto-Ibusuki M, Kawasoe T, Hamada A, Iwase H (2015) Associations between elastography findings and clinicopathological factors in breast cancer. Medicine 94(50):e2290

    Article  PubMed  PubMed Central  Google Scholar 

  145. Miroshnikova YA, Mouw JK, Barnes JM, Pickup MW, Lakins JN, Kim Y, Lobo K, Persson AI, Reis GF, McKnight TR, Holland EC, Phillips JJ, Weaver VM (2016) Tissue mechanics promote IDH1-dependent HIF1α-tenascin C feedback to regulate glioblastoma aggression. Nat Cell Biol 18(12):1336–1345

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  146. Samuel MS, Lopez JI, McGhee EJ, Croft DR, Strachan D, Timpson P, Munro J, Schröder E, Zhou J, Brunton VG, Barker N, Clevers H, Sansom OJ, Anderson KI, Weaver VM, Olson MF (2011) Actomyosin-mediated cellular tension drives increased tissue stiffness and β-catenin activation to induce epidermal hyperplasia and tumor growth. Cancer Cell 19(6):776–791

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  147. Borghi N, Sorokina M, Shcherbakova OG, Weis WI, Pruitt BL, Nelson WJ, Dunn AR (2012) E-cadherin is under constitutive actomyosin-generated tension that is increased at cell-cell contacts upon externally applied stretch. Proc Natl Acad Sci U S A 109(31):12568–12573

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  148. Angelini TE, Hannezo E, Trepat X, Marquez M, Fredberg JJ, Weitz DA (2011) Glass-like dynamics of collective cell migration. Proc Natl Acad Sci U S A 108(12):4714–4719

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  149. Garcia S, Hannezo E, Elgeti J, Joanny JF, Silberzan P, Gov NS (2015) Physics of active jamming during collective cellular motion in a monolayer. Proc Natl Acad Sci U S A 112(50):15314–15319

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  150. Sunyer R, Conte V, Escribano J, Elosegui-Artola A, Labernadie A, Valon L, Navajas D, García-Aznar JM, Muñoz JJ, Roca-Cusachs P, Trepat X (2016) Collective cell durotaxis emerges from long-range intercellular force transmission. Science 353(6304):1157–1161

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

The authors thank Ghaidan Shamsan and Brian Castle for their input in creating the figures and organizing the chapter. Louis S. Prahl acknowledges funding from an NSF Graduate Research Fellowship grant 00039202. David J. Odde acknowledges funding from NIH grants R01 CA172986 and U54 CA210190.

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering and Physical Sciences-Oncology Center, University of Minnesota-Twin Cities, Minneapolis, MN, USA

    Louis S. Prahl & David J. Odde

Authors
  1. Louis S. Prahl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David J. Odde
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Louis S. Prahl .

Editor information

Editors and Affiliations

  1. Department of Biomedical Engineering, Pennsylvania State University, University Park, PA, USA

    Cheng Dong

  2. Division of Cancer Biology, National Cancer Institute, National Institutes of Health, Rockville, MD, USA

    Nastaran Zahir

  3. Department of Chemical and Biomolecular Engineering Institute for NanoBioTechnology, Johns Hopkins University, Baltimore, MD, USA

    Konstantinos Konstantopoulos

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Prahl, L.S., Odde, D.J. (2018). Modeling Cell Migration Mechanics. In: Dong, C., Zahir, N., Konstantopoulos, K. (eds) Biomechanics in Oncology. Advances in Experimental Medicine and Biology, vol 1092. Springer, Cham. https://doi.org/10.1007/978-3-319-95294-9_9

Download citation

Publish with us

Policies and ethics

Search

Navigation