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Distinguishing between Directed and Undirected Cell Motility within an Invading Cell Population

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Abstract

Cell invasion is the basis of several fundamental biological systems including developmental morphogenesis and disease progression. Invasion processes involve combined cell motility and proliferation. Standard experimental approaches to characterize invasion systems focus on measuring population-level wavespeed data. However, continuum models which incorporate either directed or undirected motility both give rise to traveling wave solutions with a well-defined wavespeed in terms of the motility parameters. Therefore, such population-level models and experimental data cannot be used to determine whether the motility is directed or undirected. This is a major impediment limiting our ability to interpret experimental observations of cell invasion. We demonstrate how to overcome this difficulty using individual-level data and discrete models. This approach can be used to interpret and design time-lapse imaging data to determine whether the cell motility is directed or undirected. Making a distinction between directed and undirected motility has profound implications regarding our ability to design strategies to manage development and disease associated with cell invasion.

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References

  • Anderson, A.R.A., Chaplain, M.A.J., 1998. Continuous and discrete models of tumour-induced angiogenesis. Bull. Math. Biol. 60, 857–00.

    Article  MATH  Google Scholar 

  • Berg, H.C., 1983. Random Walks in Biology. Expanded Edition. Princeton University Press, Princeton.

    Google Scholar 

  • Beven, K., 2006. A manifesto for the equifinality thesis. J. Hydrol. 320, 18–6.

    Article  Google Scholar 

  • Cai, A., Landman, K.A., Hughes, B.D., 2006. Modelling directional guidance and motility regulation in cell migration. Bull. Math. Biol. 68, 25–2.

    Article  MathSciNet  Google Scholar 

  • Cai, A., Landman, K.A., Hughes, B.D., 2007. Multi-scale modeling of a wound-healing cell migration assay. J. Theor. Biol. 245, 576–94.

    Article  MathSciNet  Google Scholar 

  • Canosa, J., 1973. On a nonlinear diffusion equation describing population growth. IBM J. Res. Dev. 17, 307–13.

    Article  MATH  MathSciNet  Google Scholar 

  • Chowdhury, D., Schadschneider, A., Nishinari, K., 2005. Phys. Life Rev. 2, 318–52.

    Article  Google Scholar 

  • Crank, J., 1975. The Mathematics of Diffusion, 2nd edn. Oxford University Press, Oxford.

    Google Scholar 

  • Druckenbrod, N.R., Epstein, M.L., 2005. The pattern of neural crest advance in the cecum and colon. Dev. Biol. 287, 125–33.

    Article  Google Scholar 

  • Druckenbrod, N.R., Epstein, M.L., 2007. Behavior of enteric neural crest-derived cells varies with respect to the migratory wavefront. Dev. Dyn. 236, 84–2.

    Article  Google Scholar 

  • Fisher, R.A., 1937. The wave of advance of advantageous genes. Ann. Eugen. 7, 353–69.

    Google Scholar 

  • Gianino, S., Grider, J.R., Cresswell, J., Enomoto, H., Heuckeroth, R.O., 2003. GDNF availability determines enteric neuron number by controlling precursor proliferation. Development 130, 2187–198.

    Article  Google Scholar 

  • Hughes, B.D., 1995. Random Walks and Random Environments, Vol. 1. Oxford University Press, Oxford.

    MATH  Google Scholar 

  • Landman, K.A., Simpson, M.J., Slater, J.L., Newgreen, D.F., 2005. Diffusive and chemotactic cellular migration: Smooth and discontinuous travelling wave solutions. SIAM J. Appl. Math. 65, 1420–442.

    Article  MATH  MathSciNet  Google Scholar 

  • Liggett, T.M., 1999. Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin.

    MATH  Google Scholar 

  • Longo, D., Peirce, S.M., Skalak, T.C., Davidson, L., Marsden, M., Dzamba, B., DeSimone, D.W., 2004. Multicellular computer simulation of morphogenesis: blastocoel roof thinning and matrix assembly in Xenopus laevis. Dev. Biol. 271, 210–22.

    Article  Google Scholar 

  • Maini, P.K., McElwain, D.L.S., Leavesley, D.I., 2004. Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng. 10, 475–82.

    Article  Google Scholar 

  • Marée, A.F.M., Hogeweg, P., 2001. How amoeboids self-organize into a fruiting body: multicellular coordination in Dictyostelium discoideum. Proc. Natl. Acad. Sci. 98, 3879–883.

    Article  Google Scholar 

  • Merks, R.H.M., Glazier, J.A., 2006. Dynamic mechanisms of blood vessel growth. Nonlinearity. 19, C1–C10.

    Article  MATH  MathSciNet  Google Scholar 

  • Murray, J.D., 2002. Mathematical Biology I: An Introduction, 3rd edn. Springer, Heidelberg.

    MATH  Google Scholar 

  • Sengers, B.G., Please, C.P., Oreffo, R.O.C., 2007. Experimental characterization and computational modeling of two-dimensional cell spreading for skeletal regeneration. J. R. Soc. Interface 4, 1107–117.

    Article  Google Scholar 

  • Simpson, M.J., Landman, K.A., Hughes, B.D., Newgreen, D.F., 2006. Looking inside an invasion wave of cells using continuum models: proliferation is the key. J. Theor. Biol. 243, 343–60.

    Article  MathSciNet  Google Scholar 

  • Simpson, M.J., Zheng, D.C., Mariani, M., Landman, K.A., Newgreen, D.F., 2007a. Cell prolfieration drives neural crest cell invasion of the intestine. Dev. Biol. 302, 553–68.

    Article  Google Scholar 

  • Simpson, M.J., Merrifield, A., Landman, K.A., Hughes, B.D., 2007b. Simulating invasion with cellular automata: Connecting cell-scale and population-scale properties. Phys. Rev. E 76, 021918.

    Article  Google Scholar 

  • Simpson, M.J., Landman, K.A., Hughes, B.D., 2009. Multi-species simple exclusion processes. Physica A 388, 399–06.

    Article  Google Scholar 

  • Stein, A.M., Demuth, T., Mobley, D., Berens, M., Sander, L.M., 2006. A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment. Biophys. J. 92, 356–65.

    Article  Google Scholar 

  • Thorne, B.C., Bailey, A.M., DeSimone, D.W., Peirce, S.M., 2007. Agent-based modeling of multicell morphogenic processes during development. Birth Defects Res. C 81, 344–53.

    Article  Google Scholar 

  • Whitham, G.B., 1974. Linear and Nonlinear Waves. Wiley, New York.

    MATH  Google Scholar 

  • Young, H.M., Bergner, A.J., Anderson, R.B., Enomoto, H., Milbrandt, J., Newgreen, D.F., Whitington, P.M., 2004. Dynamics of the neural crest-derived cell migration in the embryonic mouse gut. Dev. Biol. 270, 455–73.

    Article  Google Scholar 

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Correspondence to Matthew J. Simpson.

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The authors gratefully acknowledge the support from the Australian Research Council (ARC) Discovery Project DP0662804. MS is an ARC postdoctoral fellow, KL is an ARC professorial fellow.

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Simpson, M.J., Landman, K.A. & Hughes, B.D. Distinguishing between Directed and Undirected Cell Motility within an Invading Cell Population. Bull. Math. Biol. 71, 781–799 (2009). https://doi.org/10.1007/s11538-008-9381-7

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  • DOI: https://doi.org/10.1007/s11538-008-9381-7

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