Advertisement

Journal of Biological Physics

, Volume 40, Issue 3, pp 285–308 | Cite as

Influence of individual cell motility on the 2D front roughness dynamics of tumour cell colonies

  • N. E. Muzzio
  • M. A. Pasquale
  • P. H. González
  • A. J. Arvia
Original Paper

Abstract

The dynamics of in situ 2D HeLa cell quasi-linear and quasi-radial colony fronts in a standard culture medium is investigated. For quasi-radial colonies, as the cell population increased, a kinetic transition from an exponential to a constant front average velocity regime was observed. Special attention was paid to individual cell motility evolution under constant average colony front velocity looking for its impact on the dynamics of the 2D colony front roughness. From the directionalities and velocity components of cell trajectories in colonies with different cell populations, the influence of both local cell density and cell crowding effects on individual cell motility was determined. The average dynamic behaviour of individual cells in the colony and its dependence on both local spatio-temporal heterogeneities and growth geometry suggested that cell motion undergoes under a concerted cell migration mechanism, in which both a limiting random walk-like and a limiting ballistic-like contribution were involved. These results were interesting to infer how biased cell trajectories influenced both the 2D colony spreading dynamics and the front roughness characteristics by local biased contributions to individual cell motion. These data are consistent with previous experimental and theoretical cell colony spreading data and provide additional evidence of the validity of the Kardar-Parisi-Zhang equation, within a certain range of time and colony front size, for describing the dynamics of 2D colony front roughness.

Keywords

Cell population Colony spatio-temporal heterogeneity Crowding effects Biased cell trajectories Cell migration concerted mechanism 

Notes

Acknowledgments

This work was supported by the Consejo Nacional de Investigaciones Cientficas y Técnicas of Argentina (PIP 2231). P.H.G. thanks the Comisión de Investigaciones Científicas (CIC), Pcia. Bs. As., for financial support. We acknowledge Silvia Coronato for technical assistance. N.E.M. thanks the Universidad Nacional de La Plata and the Ministerio Nacional de Educación for the scholarship from the program ‘Estímulo a las Vocaciones Científicas’.

References

  1. 1.
    Gurtner, G.C., Werner, S., Barrandon, Y., Longaker, M.T.: Wound repair and regeneration. Nature 453, 314–321 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    Lecaudey, V., Gilmour, D.: Organizing moving groups during morphogenesis. Curr. Opin. Cell Biol. 18, 102–107 (2006)CrossRefGoogle Scholar
  3. 3.
    Chicoine, M. R., Silbergeld, D.L.: The in vitro motility of human gliomas increases with increasing grade of malignancy. Cancer 75, 2904–2909 (1995)CrossRefGoogle Scholar
  4. 4.
    Kumar, S., Weaver, M.V.: Mechanics, malignancy, and metastasis: The force journey of a tumor cell. Cancer Metast. Rev. 28, 113–127 (2009)CrossRefGoogle Scholar
  5. 5.
    Yamazaki, D., Kurisu, S., Takenawa, T.: Regulation of cancer cell motility through actin reorganization. Cancer Sci. 96, 379–386 (2005)CrossRefGoogle Scholar
  6. 6.
    Li, S., Guan, J-L., Chien, S.: Biochemistry and biomechanics of cell motility. Annu. Rev. Biomed. Eng. 7, 105–150 (2005)CrossRefGoogle Scholar
  7. 7.
    Fletcher, D.A., Theriot, J.A.: An introduction to cell motility for the physical scientist. Phys. Biol. 1, T1–T10 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    Selmeczi, D., Mosler, S., Hagedorn, P.H., Larsen, N.B., Flyvbjerg, H.: Cell motility as persistent random motion: theories from experiments. Biophys. J. 89, 912–931 (2005)CrossRefGoogle Scholar
  9. 9.
    Douezan, S., Dumond, J., Brochard-Wyart, F.: Wetting transitions of cellular aggregates induced by substrate rigidity. Soft Matt. 8, 4578–4583 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    DiMilla, P.A., Stone, J.A., Quinn, J.A., Albelda, S. M., Lauffenburger, D.A.: Maximal migration of human smooth muscle cells on fibronectin and type IV collagen occurs at an intermediate attachment strength. J. Cell Biol. 122, 729–737 (1993)CrossRefGoogle Scholar
  11. 11.
    Montell, D.J.: Morphogenetic cell movements: diversity from modular mechanical properties. Science 322, 1502–1505 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Alt-Holland, A., Zhang, W., Margulis, A., Garlick, J.A.: Microenvironmental control of premalignant disease: the role of intercellular adhesion in the progression of squamous cell carcinoma. Semin. Cancer Biol. 15, 84–96 (2005)CrossRefGoogle Scholar
  13. 13.
    Tzvetkova-Chevolleau, T., Stéphanou, A., Fuard, D., Ohayon, J., Schiavone, P., Tracqui, P.: The motility of normal and cancer cells in response to the combined influence of the substrate rigidity and anisotropic microstructure. Biomaterials 29, 1541–1551 (2008)CrossRefGoogle Scholar
  14. 14.
    Friedl, P., Glimour, D.: Collective cell migration in morphogenesis, regeneration and cancer. Nat. Rev. Mol. Cell Biol. 10, 445–457 (2009)CrossRefGoogle Scholar
  15. 15.
    Yin, J., Xu, K., Zhang, J., Kumar, A., Yu, F.-S.X.: Wound-induced ATP release and EGF receptor activation in epithelial cells. J. Cell Sci. 120, 815–825 (2007)CrossRefGoogle Scholar
  16. 16.
    Nicklić, D. L., Boettiger, A. N., Bar-Sagi, D., Carbeck, J. D., Shvartsman, S. Y.: Role of boundary conditions in an experimental model of epithelial wound healing. Am. J. Physiol. Cell Physiol. 291, C68–C78 (2006)CrossRefGoogle Scholar
  17. 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. Natl. Acad. Sci. USA 104, 15988–15993 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    Sengers, B.G., Please, C.P., Oreffo, R.O.C.: Experimental Characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration. J. R. Soc. Interface 4, 1107–1117 (2007)CrossRefGoogle Scholar
  19. 19.
    Farooqui, R., Fenteany, G.: Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement. J. Cell Sci. 118, 51–63 (2005)CrossRefGoogle Scholar
  20. 20.
    Bindschadler, M., McGrath, J.L.: Sheet migration by wounded monolayers as an emergent property of single-cell dynamics. J. Cell Sci. 120, 876–884 (2006)CrossRefGoogle Scholar
  21. 21.
    Takamizawa, K., Niu, S., Matsuda, T.: Mathematical simulation of unidirectional tissue formation: in vitro transanastomotic endothelization model. J. Biomater. Sci. Polym. Ed. 8, 323–334 (1996)CrossRefGoogle Scholar
  22. 22.
    Savla, U., Olson, L.E., Waters, C.M.: Mathematical modeling of airway epithelial wound closure during cyclic mechanical strain. J. Appl. Physiol. 96, 566–574 (2004)CrossRefGoogle Scholar
  23. 23.
    Cai, A.Q., Landman, K.A., Hughes, B.D.: Multi-scale modeling of a wound-healing cell migration assay. J. Theor. Biol. 245, 576–594 (2007)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Lushnikov, P.M., Chen, N., Alber, M.: Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact. Phys. Rev. E 78, 061904 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    Radszuweit, M., Block, M., Hengstler, J.G., Schöll, E., Drasdo, D.: Comparing the growth kinetics of cell populations in two and three dimensions. Phys. Rev. E 79, 051907 (2009)ADSCrossRefMathSciNetGoogle Scholar
  26. 26.
    Simpson, M.J., Baker, R.E., McCue, S.W.: Models of collective cell spreading with variable cell aspect ratio: a motivation for degenerate diffusion models. Phys. Rev. E 83, 021901 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    Barabasi, A.L., Stanley, H.E.: Fractal concepts in surface growth. Cambridge University Press, Cambridge (1993)Google Scholar
  28. 28.
    Meakin, P.: Fractal, Scaling and Growth Far from Equilibrium. Cambridge University Press, Cambridge (1998)Google Scholar
  29. 29.
    Huergo, M.A.C., Pasquale, M.A., Bolzán, A.E., González, P.H., Arvia, A.J.: Growth dynamics of cancer cell colonies and their comparison with noncancerous cells. Phys. Rev. E 85, 011918 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    Kardar, M., Parisi, G., Zhang, Y-C.: Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889–892 (1986)ADSCrossRefzbMATHGoogle Scholar
  31. 31.
    Block, M., Schöll, E., Drasdo, D.: Classifying the expansion kinetics and critical surface dynamics of growing cell populations. Phys. Rev. Lett. 99, 248101 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    Trepat, X., Wasserman, M.R., Angelini, T.E., Millet, E., Weitz, D.A., Butler, J.P., Fredberg, J.J.: Physical forces during collective cell migration. Nat. Phys. 5, 426–430 (2009)CrossRefGoogle Scholar
  33. 33.
    Tambe, D.T., Hardin, C.C., Angelini, T.E., Rajendran, K., Park, C.Y., Serra-Picamal, X., Zhou, E.H., Zaman, M.H., Butler, J.P., Weitz, D.A., Fredberg, J.J., Trepat, X.: Collective cell guidance by cooperative intercellular forces. Nat. Mater. 10, 469–475 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    Huergo, M.A.C., Pasquale, M.A., Bolzán, A.E., Arvia, A.J., González, P.H.: Morphology and dynamic scaling analysis of cell colonies with linear growth fronts. Phys. Rev. E 82, 031903 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    Huergo, M.A.C., Pasquale, M.A., Bolzán, A.E., González, P.H., Arvia, A.J.: Dynamics and morphology characteristics of cell colonies with radially spreading growth fronts. Phys. Rev. E 84, 021917 (2011)ADSCrossRefGoogle Scholar
  36. 36.
    Rieu, J.P., Upadhyaya, A., Glazier, J.A., Ouchi, N.B., Sawada, Y.: Diffusion and deformations of single hydra cells in cellular aggregates. Biophys. J. 79, 1903–1914 (2000)CrossRefGoogle Scholar
  37. 37.
    Diambra, L., Cintra, L.C., Chen, Q., Schubert, D., Costa, L., da, F.: Cell adhesion protein decreases cell motion: statistical characterization of locomotion activity. Physica. A 365, 481–490 (2006)ADSCrossRefGoogle Scholar
  38. 38.
    Li, L., Wang, B.H., Wang, S., Moalim-Nour, L., Mohib, K., Lohnes, D., Wang, L.: Individual cell movement, asymmetric colony expansion, rho-associated kinase, and E-cadherin impact the clonogenicity of human embryonic stem cells. Biophys. J. 98, 2442–2451 (2010)ADSCrossRefGoogle Scholar
  39. 39.
    Chen, E.H., Grote, E., Mohler, W., Vignery, A.: Cell-cell fusion. FEBS Lett. 581, 2181–2193 (2007)CrossRefGoogle Scholar
  40. 40.
    Straight, A.F., Cheung, A., Limouze, J., Chen, I., Westwood, N.J., Sellers, J.R., Mitchison, T.J.: Dissecting temporal and spatial control of cytokinesis with a myosin II inhibitor. Science 299, 1743–1747 (2003)ADSCrossRefGoogle Scholar
  41. 41.
    Haga, H., Irahara, C., Kobayashi, R., Nakagaki, T., Kawabata, K.: Collective movement of epithelial cells on a collagen gel substrate. Biophys. J. 88, 2250–2256 (2005)CrossRefGoogle Scholar
  42. 42.
    Freyer, J.P., Sutherland, R.M.: A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth. J. Cell. Physiol. 124, 516–24 (1985)CrossRefGoogle Scholar
  43. 43.
    Mueller-Klieser, W., Freyer, J.P., Sutherland, R.M.: Influence of glucose and oxygen supply conditions on the oxygenation of multicellular spheroids. Br. J. Cancer 53, 345–353 (1986)CrossRefGoogle Scholar
  44. 44.
    Brú, A., Albertos, S., Subiza, J.L., García-Asenjo, J.L., Brú, I.: The universal dynamics of tumor growth. Biophys. J. 85, 2948–2961 (2003)ADSCrossRefGoogle Scholar
  45. 45.
    Galle, J., Hoffmann, M., Aust, G.: From single cells to tissue architecture: a bottom-up approach to modelling the spatio-temporal organisation of complex multi-cellular systems. J. Math. Biol. 58, 261–283 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  46. 46.
    Galle, J., Sittig, D., Hanisch, I., Wobus, M., Wandel, E., Loeffler, M., Aust, G.: Individual cell-based models of tumor-environment interactions: multiple effects of CD97 on tumor invasion. Am. J. Phathol. 169, 1802–1811 (2006)CrossRefGoogle Scholar
  47. 47.
    Drasdo, D., Hoehme, S.: A single-cell-based model of tumor growth in vitro: monolayers and spheroids. Phys. Biol. 2, 133–147 (2005)ADSCrossRefGoogle Scholar
  48. 48.
    Menchón, S.A., Condat, C.A.: Cancer growth: Predictions of a realistic model. Phys. Rev. E 78, 022901 (2008)ADSCrossRefGoogle Scholar
  49. 49.
    Galle, J., Loeffler, M., Drasdo, D.: Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. Biophys. J. 88, 62–75 (2005)ADSCrossRefGoogle Scholar
  50. 50.
    Drasdo, D., Hoehme, S., Block, M.: On the role of physics in the growth and pattern formation of multi-cellular systems: What can we learn from individual cell-based models. J. Stat. Phys. 128, 287–345 (2007)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  51. 51.
    Dulbeco, R., Stoker, M.G.: Conditions determining initiation of DNA synthesis in 3T3 cells. Proc. Natl. Acad. Sci. USA 66, 204–210 (1970)ADSCrossRefGoogle Scholar
  52. 52.
    Todaro, G.J., Lazar, K.G., Green, H.: The initiation of cell division in a contact-inhibited mammalian cell line. J. Cell. Physiol. 66, 325–333 (1965)CrossRefGoogle Scholar
  53. 53.
    Turner, S., Sherratt, J.A.: Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts Model. J. Theor. Biol. 216, 85–100 (2002)CrossRefMathSciNetGoogle Scholar
  54. 54.
    Aubert, M., Badoual, M., Grammaticos, B.: A model for short- and long range interactions of migrating tumor cells. Acta Biotheor. 56, 297–314 (2008)CrossRefGoogle Scholar
  55. 55.
    Barkey, P. D.: Structure and pattern formation in electrodeposition. In: Alkire, R.C. (ed.) Advances in Electrochemical Science and Engineering, pp 151–192. J. Wiley-VHC-Verlag, New York, Frankfurt a/M (2001)Google Scholar
  56. 56.
    Angelini, T.E., Hannezo, E., Trepat, X., Fredberg, J.J., Weitz, D.A.: Cell migration driven by cooperative substrate deformation patterns. Phys. Rev. Lett. 104, 168104 (2010)ADSCrossRefGoogle Scholar
  57. 57.
    Murray, J. D.: Mathematical Biology: I. An Introduction. Springer-Verlag, Berlin (2002)Google Scholar
  58. 58.
    Okubo, A.: Diffusion and Ecological Problems. Springer-Verlag, Berlin (1980)zbMATHGoogle Scholar
  59. 59.
    Aubert, M., Badoual, M., Christov, C., Grammaticos, B.: A model for glioma cell migration on collagen and astrocytes. J. R. Soc. Interface 5, 75–83 (2008)CrossRefGoogle Scholar
  60. 60.
    López, J.M., Cuerno, R.: Power spectrum scaling in anomalous kinetic roughening of surfaces. Physica. A 246, 329–347 (1997)ADSCrossRefGoogle Scholar
  61. 61.
    Ramasco, J.J., López, J.M., Rodríguez, M.A.: Generic dynamic scaling in kinetic roughening. Phys. Rev. Lett 84, 2199–2202 (2000)ADSCrossRefGoogle Scholar
  62. 62.
    Wio, H.S., Escudero, C., Revelli, J.A., Deza, R.R, de la Lama, M.S.: Recent developments on the Kardar–Parisi–Zhang surface-growth equation. Phil. Trans. R. Soc. A 369, 396–411 (2011)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  63. 63.
    Wio, H.S., Revelli, J.A., Deza, R.R., Escudero, C, de la Lama, M.S.: KPZ equation: Galilean-invariance violation, consistency, and fluctuation-dissipation issues in real-space discretization. Europhys. Lett. 89, 40008 (2010)ADSCrossRefGoogle Scholar
  64. 64.
    Sasamoto, T., Spohn, H.: One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality. Phys. Rev. Lett. 104, 230602 (2010)ADSCrossRefGoogle Scholar
  65. 65.
    Calabrese, P., Le Doussal, P.: Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions. Phys. Rev. Lett 106, 250603 (2011)ADSCrossRefGoogle Scholar
  66. 66.
    Khanin, K., Nechaev, S., Oshanin, G., Sobolevski, A., Vasilyev, O.: Ballistic deposition patterns beneath a growing Kardar-Parisi-Zhang interface. Phys. Rev. E 82, 061107 (2010)ADSCrossRefMathSciNetGoogle Scholar
  67. 67.
    Takeuchi, A.K., Sano, M.: Universal fluctuations of growing interfaces: evidence in turbulent liquid crystals. Phys. Rev. Lett. 104, 230601 (2010)ADSCrossRefGoogle Scholar
  68. 68.
    Takeuchi, A.K., Sano, M., Sasamoto, T., Spohn, H.: Growing interfaces uncover universal fluctuations behind scale invariance. Sci. Rep. 1, 34 (2011). doi: 10.1038/srep00034 ADSCrossRefGoogle Scholar
  69. 69.
    Takeuchi, A.K., Sano, M.: Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid crystal turbulence. J. Stat. Phys. 147, 853–890 (2012)ADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • N. E. Muzzio
    • 1
  • M. A. Pasquale
    • 1
  • P. H. González
    • 2
  • A. J. Arvia
    • 1
  1. 1.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA)Universidad Nacional de La Plata (UNLP), CONICETLa PlataArgentina
  2. 2.Cátedra de PatologíaFacultad de Ciencias Médicas, UNLP, CICLa PlataArgentina

Personalised recommendations