Interplay Between the Persistent Random Walk and the Contact Inhibition of Locomotion Leads to Collective Cell Behaviors

  • Abdel-Rahman Hassan
  • Thomas Biel
  • David M. Umulis
  • Taeyoon KimEmail author
Special Issue: Multi-scale Modeling of Tissue Growth and Shape


Cell migration plays an important role in physiology and pathophysiology. It was observed in the experiments that cells, such as fibroblast, leukocytes, and cancer cells, exhibit a wide variety of migratory behaviors, such as persistent random walk, contact inhibition of locomotion, and ordered behaviors. To identify biophysical mechanisms for these cellular behaviors, we developed a rigorous computational model of cell migration on a two-dimensional non-deformable substrate. Cells in the model undergo motion driven by mechanical interactions between cellular protrusions and the substrate via the balance of tensile forces. Properties of dynamic formation of lamellipodia induced the persistent random walk behavior of a migrating cell. When multiple cells are included in the simulation, the model recapitulated the contact inhibition of locomotion between cells at low density without any phenomenological assumptions or momentum transfer. Instead, the model showed that contact inhibition of locomotion can emerge via indirect interactions between the cells through their interactions with the underlying substrate. At high density, contact inhibition of locomotion between numerous cells gave rise to confined motions or ordered behaviors, depending on cell density and how likely lamellipodia turn over due to contact with other cells. Results in our study suggest that various collective migratory behaviors may emerge without more restrictive assumptions or direct cell-to-cell biomechanical interactions.


Cell migration Simulation Persistent random walk Contact inhibition of locomotion Nematic order 



The authors gratefully acknowledge the support from the National Institute of Health (1R01GM126256). This work used the Extreme Science and Engineering Discovery Environment (XSEDE) (Moore et al. 2014; Towns et al. 2014), which is supported by National Science Foundation grant number ACI-1548562. The computations were conducted on the Comet supercomputer, which is supported by NSF Award Number ACI-1341698, at the San Diego Supercomputing Center (SDSC).

Supplementary material

11538_2019_585_MOESM1_ESM.pdf (905 kb)
Supplementary material 1 (PDF 904 kb)
11538_2019_585_MOESM2_ESM.avi (9.6 mb)
Supplementary material 2 (AVI 9877 kb)
11538_2019_585_MOESM3_ESM.avi (9.7 mb)
Supplementary material 3 (AVI 9922 kb)
11538_2019_585_MOESM4_ESM.avi (9.6 mb)
Supplementary material 4 (AVI 9851 kb)


  1. Abercrombie M (1970) Contact inhibition in tissue culture. In vitro 6:128–142. CrossRefGoogle Scholar
  2. Abercrombie M (1979) Contact inhibition and malignancy. Nature 281:259–262. CrossRefGoogle Scholar
  3. Abercrombie M, Heaysman JE (1953) Observations on the social behaviour of cells in tissue culture. I. Speed of movement of chick heart fibroblasts in relation to their mutual contacts. Exp Cell Res 5:111–131. CrossRefGoogle Scholar
  4. Aman A, Piotrowski T (2010) Cell migration during morphogenesis. Dev Biol 341:20–33. CrossRefGoogle Scholar
  5. Blanchoin L, Boujemaa-Paterski R, Sykes C, Plastino J (2014) Actin dynamics, architecture, and mechanics in cell motility. Physiol Rev 94:235–263. CrossRefGoogle Scholar
  6. Bravo-Cordero JJ, Magalhaes MA, Eddy RJ, Hodgson L, Condeelis J (2013) Functions of cofilin in cell locomotion and invasion. Nat Rev Mol Cell Biol 14:405–415. CrossRefGoogle Scholar
  7. Choi CK, Vicente-Manzanares M, Zareno J, Whitmore LA, Mogilner A, Horwitz AR (2008) Actin and alpha-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor-independent manner. Nat Cell Biol 10:1039–1050. CrossRefGoogle Scholar
  8. Dieterich P, Klages R, Preuss R, Schwab A (2008) Anomalous dynamics of cell migration. Proc Natl Acad Sci USA 105:459–463. CrossRefGoogle Scholar
  9. Duclos G, Garcia S, Yevick HG, Silberzan P (2014) Perfect nematic order in confined monolayers of spindle-shaped cells. Soft Matter 10:2346–2353. CrossRefGoogle Scholar
  10. Duclos G, Erlenkamper C, Joanny JF, Silberzan P (2017) Topological defects in confined populations of spindle-shaped cells. Nat Phys 13:58–62. CrossRefGoogle Scholar
  11. Friedl P, Gilmour D (2009) Collective cell migration in morphogenesis, regeneration and cancer. Nat Rev Mol Cell Biol 10:445–457. CrossRefGoogle Scholar
  12. 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 USA 112:15314–15319. CrossRefGoogle Scholar
  13. 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. CrossRefGoogle Scholar
  14. Graner F, Glazier JA (1992) Simulation of biological cell sorting using a 2-dimensional extended Potts-model. Phys Rev Lett 69:2013–2016. CrossRefGoogle Scholar
  15. Gruver JS et al (2010) Bimodal analysis reveals a general scaling law governing nondirected and chemotactic cell motility. Biophys J 99:367–376. CrossRefGoogle Scholar
  16. Harms BD, Bassi GM, Horwitz AR, Lauffenburger DA (2005) Directional persistence of EGF-induced cell migration is associated with stabilization of lamellipodial protrusions. Biophys J 88:1479–1488. CrossRefGoogle Scholar
  17. Hayes AP (2011) The Adams–Bashforth–Moulton integration methods generalized to an adaptive grid. arXiv:1104.3187
  18. Horwitz R, Webb D (2003) Cell migration. Curr Biol 13:R756–R759. CrossRefGoogle Scholar
  19. Kim MC, Neal DM, Kamm RD, Asada HH (2013) Dynamic modeling of cell migration and spreading behaviors on fibronectin coated planar substrates and micropatterned geometries. PLoS Comput Biol 9:e1002926. MathSciNetCrossRefGoogle Scholar
  20. Li R, Gundersen GG (2008) Beyond polymer polarity: how the cytoskeleton builds a polarized cell. Nat Rev Mol Cell Biol 9:860–873. CrossRefGoogle Scholar
  21. Masuzzo P, Huyck L, Simiczyjew A, Ampe C, Martens L, Van Troys M (2017) An end-to-end software solution for the analysis of high-throughput single-cell migration data. Sci Rep 7:42383. CrossRefGoogle Scholar
  22. Mayor R, Carmona-Fontaine C (2010) Keeping in touch with contact inhibition of locomotion. Trends Cell Biol 20:319–328. CrossRefGoogle Scholar
  23. Mehes E, Vicsek T (2014) Collective motion of cells: from experiments to models. Integr Biol 6:831–854. CrossRefGoogle Scholar
  24. Moore RL et al (2014) Gateways to discovery: cyberinfrastructure for the long tail of science. In: Annual conference on extreme science and engineering discovery environment, Atlanta, GA, USA, 13–18 July, 2014. ACM, New York, NY, USAGoogle Scholar
  25. Nnetu KD, Knorr M, Kas J, Zink M (2012) The impact of jamming on boundaries of collectively moving weak-interacting cells. New J Phys 14:115012. CrossRefGoogle Scholar
  26. Rey R, Garcia-Aznar JM (2013) A phenomenological approach to modelling collective cell movement in 2D. Biomech Model Mechanobiol 12:1089–1100. CrossRefGoogle Scholar
  27. Rink I, Rink J, Helmer D, Sachs D, Schmitz K (2015) A haptotaxis assay for leukocytes based on surface-bound chemokine gradients. J Immunol 194:5549–5558. CrossRefGoogle Scholar
  28. Roycroft A, Mayor R (2016) Molecular basis of contact inhibition of locomotion. Cell Mol Life Sci 73:1119–1130. CrossRefGoogle Scholar
  29. Saupe A (1968) Recent results in the field of liquid crystals. Angew Chem Int Ed Engl 7: 97–112CrossRefGoogle Scholar
  30. Selmeczi D, Mosler S, Hagedorn PH, Larsen NB, Flyvbjerg H (2005) Cell motility as persistent random motion: Theories from experiments. Biophys J 89:912–931. CrossRefGoogle Scholar
  31. Sepulveda N, Petitjean L, Cochet O, Grasland-Mongrain E, Silberzan P, Hakim V (2013) Collective cell motion in an epithelial sheet can be quantitatively described by a stochastic interacting particle model. PLoS Comput Biol 9:e1002944. MathSciNetCrossRefGoogle Scholar
  32. Souza Vilela Podesta T, Venzel Rosembach T, Aparecida Dos Santos A, Lobato Martins M (2017) Anomalous diffusion and q-Weibull velocity distributions in epithelial cell migration. PLoS ONE 12:e0180777. CrossRefGoogle Scholar
  33. Stramer B, Mayor R (2016) Mechanisms and in vivo functions of contact inhibition of locomotion. Nat Rev Mol Cell Biol 18:43–55. CrossRefGoogle Scholar
  34. Svensson CM, Medyukhina A, Belyaev I, Al-Zaben N, Figge MT (2018) Untangling cell tracks: quantifying cell migration by time lapse image data analysis. Cytom Part A J Int Soc Anal Cytol 93:357–370. CrossRefGoogle Scholar
  35. Szabo B, Szollosi GJ, Gonci B, Juranyi Z, Selmeczi D, Vicsek T (2006) Phase transition in the collective migration of tissue cells: experiment and model. Phys Rev E: Stat, Nonlin, Soft Matter Phys 74:061908. CrossRefGoogle Scholar
  36. Towns J et al (2014) XSEDE: accelerating scientific discovery. Comput Sci Eng 16:62–74. CrossRefGoogle Scholar
  37. Trepat X, Wasserman MR, Angelini TE, Millet E, Weitz DA, Butler JP, Fredberg JJ (2009) Physical forces during collective cell migration. Nat Phys 5:426–430. CrossRefGoogle Scholar
  38. van Zijl F, Krupitza G, Mikulits W (2011) Initial steps of metastasis: cell invasion and endothelial transmigration. Mutat Res 728:23–34. CrossRefGoogle Scholar
  39. Vedel S, Tay S, Johnston DM, Bruus H, Quake SR (2013) Migration of cells in a social context. Proc Natl Acad Sci USA 110:129–134. CrossRefGoogle Scholar
  40. Vedula SR, Leong MC, Lai TL, Hersen P, Kabla AJ, Lim CT, Ladoux B (2012) Emerging modes of collective cell migration induced by geometrical constraints. Proc Natl Acad Sci USA 109:12974–12979. CrossRefGoogle Scholar
  41. Vicsek T, Czirok A, Ben-Jacob E, Cohen II, Shochet O (1995) Novel type of phase transition in a system of self-driven particles. Phys Rev Lett 75:1226–1229. MathSciNetCrossRefGoogle Scholar
  42. Weiger MC, Ahmed S, Welf ES, Haugh JM (2010) Directional persistence of cell migration coincides with stability of asymmetric intracellular signaling. Biophys J 98:67–75. CrossRefGoogle Scholar
  43. Weijer CJ (2009) Collective cell migration in development. J Cell Sci 122:3215–3223. CrossRefGoogle Scholar
  44. Weiner OD, Marganski WA, Wu LF, Altschuler SJ, Kirschner MW (2007) An actin-based wave generator organizes cell motility. PLoS Biol 5:e221. CrossRefGoogle Scholar
  45. Yamashiro S, Watanabe N (2014) A new link between the retrograde actin flow and focal adhesions. J Biochem 156:239–248. CrossRefGoogle Scholar
  46. Zimmermann J, Camley BA, Rappel WJ, Levine H (2016) Contact inhibition of locomotion determines cell-cell and cell-substrate forces in tissues. Proc Natl Acad Sci USA 113:2660–2665. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Weldon School of Biomedical EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Department of Agricultural and Biological EngineeringPurdue UniversityWest LafayetteUSA

Personalised recommendations