Modelling Directional Guidance and Motility Regulation in Cell Migration

  • Anna Q. Cai
  • Kerry A. Landman
  • Barry D. Hughes
Original Article


Although cell migration is an essential process in development, how cells reach their final destination is not well understood. Secreted molecules are known to have a migratory effect, but it remains unclear whether such molecules act as directional guidance cues or as motility regulators. There is potential to use signalling molecules in new medical therapies, so it is important to identify the exact role these molecules play. This paper focuses on distinguishing between inhibitory and repulsive effects produced by signalling molecules, based on recent experiments examining the effect of Slit, a secreted protein, on the migration of neurons from the brain. The primary role of Slit, whether it is an inhibitor or repellent of neurons, is in dispute. We present population-level continuum models and recast these in terms of transition probabilities governing individual cells. Various cell-sensing strategies are considered within this framework. The models are applied to the neuronal migration experiments. To resolve the particular role of Slit, simulations of the models characterising different cell-sensing strategies are compared at the population and individual cell level, providing two complementary perspectives on the system. Difficulties and limitations in deducing cell migration rules from time-lapse imaging are discussed.


Signalling molecule Cell migration Motility Directional guidance Repulsion Inhibition 


  1. Abercrombie, M., 1980. The crawling movement of cells. Proc. R. Soc. Lond. Ser. B 207, 129–147.CrossRefGoogle Scholar
  2. Anderson, A., Chaplain, M.A.J., 1998. Continuous and discrete mathematical models of tumor-induced Bull. angiogenesis. Math. Biol. 60, 857–900.MATHGoogle Scholar
  3. Alvarez-Buylla, A., 1997. Mechanism of migration of olfactory bulb interneurons. Semin. Cell Dev. Biol. 8, 207–213.CrossRefGoogle Scholar
  4. Franz, C.M., Jones, G.E., Ridley, A.J., 2002. Cell migration in development and disease. Dev. Cell 2, 153–158.CrossRefGoogle Scholar
  5. Hughes, B.D., 1995. Random Walks and Random Environments, vol. 1. Oxford University Press, Oxford.MATHGoogle Scholar
  6. Keller, E.F., Segel, L.A., 1971. Travelling bands of chemotactic bacteria: A theoretical analysis. J. Theor. Biol. 30, 235–248.CrossRefGoogle Scholar
  7. Landman, K.A., Pettet, G.J., Newgreen, D.F., 2003. Mathematical models of cell colonization of uniformly growing domains. Bull. Math. Biol. 65, 235–262.CrossRefGoogle Scholar
  8. Lauffenburger, D.A., Horwitz, A.F., 1996. Cell migration: A physically integrated molecular process. Cell Rev. 84, 359–369.CrossRefGoogle Scholar
  9. Lauffenburger, D.A., Linderman, J.J., 1993. Receptors, Models for Binding, Trafficking and Signalling. Oxford University Press, Oxford.Google Scholar
  10. Liggett, T.M., 1985. Interacting Particle Systems. Springer-Verlag, New York.MATHGoogle Scholar
  11. Mason, H.A., Ito, S., Corfas, G., 2001. Extracellular signals that regulate the tangential migration of olfactory bulb neuronal precursors: Inducers, inhibitors and repellents. J. Neurosci. 21, %(19): 7654–7663.Google Scholar
  12. Menezes, J.R.L., Marins, M., Alves, J.A.J., Fróes, M.M., Hedin-Pereira, C., 2002. Cell migration in the postnatal subventricular zone. %Brazilian Journal of Medical and Biological Research Brazil. J. Med. Biol. Res. 35, 1411–1421.Google Scholar
  13. Montroll, E.W., Weiss, G.H., 1965. Random walks on lattices. II. J. Math. Phys. 6, 167–181.CrossRefMathSciNetGoogle Scholar
  14. Murray, J.D., 2002. Mathematical Biology, vol. 1, 3rd edition. Springer-Verlag, New York.MATHGoogle Scholar
  15. Okubo, A., 1980. Diffusion and Ecological Problems: Mathematical Models. Springer-Verlag, New York.MATHGoogle Scholar
  16. Othmer, H.G., Stevens, A., 1997. Aggregation, blowup and collapse: The abc's of taxis in reinforced random walks. SIAM J. Appl. Math. 57, 1044–1081.MATHCrossRefMathSciNetGoogle Scholar
  17. Painter, K.J., Sherratt, J.A., 2003. Modelling the movement of interacting cell populations.J. Theor. Biol. 225, 327–339.CrossRefMathSciNetGoogle Scholar
  18. Simpson, M.J., Landman, K.A., Newgreen, D.F., 2006. Chemotactic and diffusive migration on a non-uniformly growing domain: Numerical algorithm development and applications. J. Compt. Appl. Math. In press. Available online.Google Scholar
  19. Ward, M., McCann, C., DeWulf, M., Wu, J., Rao, Y., 2003. Distinguishing between direction guidance and motility regulation in neuronal migration. J. Neurosci. 23, 5170–5177.Google Scholar
  20. Witt, C., Raychaudhuri, S., Chakraborty, A.K., 2005. Movies, measurement, and modeling: The three Ms of mechanistic immunology. J. Exp. Med. 201, 501–504.CrossRefGoogle Scholar
  21. Wolpert, L., 2002. Principles of Development, 2nd edition. %Current Biology, Oxford University Press, Oxford.Google Scholar
  22. Wu, W., Wong, K., Chen, J., Jiang, Z., Dupuis, S., Wu, J., Rao, Y., 1999. Directional guidance of neuronal migration in the olfactory system by the protein Slit. Nature 400, 331–336.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Anna Q. Cai
    • 1
  • Kerry A. Landman
    • 1
  • Barry D. Hughes
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneVictoriaAustralia

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