Cell Biochemistry and Biophysics

, Volume 49, Issue 1, pp 14–28

Mathematical Models of Cell Motility

Original Paper

Abstract

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today’s computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

Keywords

Mathematical Modeling Cell Motility 

References

  1. 1.
    Park, S., et al. (2005). Cell motility and local viscoelasticity of fibroblasts. Biophysical Journal, 89(6), 4330–4342.PubMedCrossRefGoogle Scholar
  2. 2.
    Li, S., Huang, N. F., & Hsu, S. (2005). Mechanotransduction in endothelial cell migration. Journal of Cellular Biochemistry, 96(6), 1110–11126.PubMedCrossRefGoogle Scholar
  3. 3.
    Selmeczi, D., et al. (2005). Cell motility as persistent random motion: Theories from experiments. Biophysical Journal, 89(2), 912–931.PubMedCrossRefGoogle Scholar
  4. 4.
    Bereiter-Hahn, J. (2005). Mechanics of crawling cells. Medical Engineering & Physics, 27(9), 743–753.CrossRefGoogle Scholar
  5. 5.
    Curtis, A. (2005). Cell forces in tissues. Medical Engineering & Physics, 27(9), 773–779.CrossRefGoogle Scholar
  6. 6.
    Novak, I. L., et al. (2004). Cooperativity between cell contractility and adhesion. Physical Review Letters, 93(26 Pt 1), 268109.PubMedCrossRefGoogle Scholar
  7. 7.
    Horwitz, A. R., & Parsons, J. T. (1999). Cell biology: Cell migration-movin’ on. Science, 286(5442), 1102–1103.PubMedCrossRefGoogle Scholar
  8. 8.
    Webb, D. J., Zhang, H., & Horwitz, A. F. (2005). Cell migration: An overview. Methods in Molecular Biology, 294, 3–11.PubMedGoogle Scholar
  9. 9.
    Fletcher, D. A., & Theriot, J. A. (2004). An introduction to cell motility for the physical scientist. Physical Biology, 1(1–2), T1–T10.PubMedCrossRefGoogle Scholar
  10. 10.
    Levchenko, A., & Iglesias, P. (2002). Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils. Biophysical Journal, 82, 50–63.PubMedGoogle Scholar
  11. 11.
    Zhelev, D., Alteraifi, A. M., & Chondniewicz, D. (2004). Controlled Pseudopod extension of human neutrophils stimulated with different chemoattractants. Biophysical Journal, 87, 688–695.PubMedCrossRefGoogle Scholar
  12. 12.
    Rappel, W. J., Thomas, P. J., et al. (2002). Establishing direction during chemotaxis in eukaryotic cells. Biophysical Journal, 83, 1361–1367.Google Scholar
  13. 13.
    Schneider, I. C., & Haugh, J. M. (2004). Spatial analysis of 3′ phosphoinositide signaling in living fibroblasts: Parameter estimates for individual cells from experiments. Biophysical Journal, 86, 599–608.PubMedGoogle Scholar
  14. 14.
    Lo, C. M., Wang, H. B., Dembo, M., & Wang, Y. (2000). Cell movement is guided by the rigidity of the substrate. Biophysical Journal, 79, 144–152.PubMedCrossRefGoogle Scholar
  15. 15.
    Pelham, R. J. Jr., & Wang, Y. (1997). Cell locomotion and focal adhesions are regulated by substrate flexibility. Proceedings of the National Academy of Sciences of the USA, 94(25), 13661–13665.PubMedCrossRefGoogle Scholar
  16. 16.
    Zhao, M., et al. (2002). Membrane lipids, EGF receptors, and intracellular signals colocalize and are polarized in epithelial cells moving directionally in a physiological electric field. FASEB Journal, 16(8), 857–859.PubMedGoogle Scholar
  17. 17.
    Curtze, S., et al. (2004). Dynamic changes in traction forces with DC electric field in osteoblast-like cells. Journal of Cell Science, 117, 2721–2729.PubMedCrossRefGoogle Scholar
  18. 18.
    Mallet, D. G., & Pettet, G. J. (2006). A mathematical model of integrin-mediated haptotactic cell migration. Bulletin of Mathematical Biology, 68(2), 231–253.PubMedCrossRefGoogle Scholar
  19. 19.
    Adams, D. S. (1992). Mechanisms of cell shape change: The cytomechanics of cellular response to chemical environment and mechanical loading. Journal of Cell Biology, 117(1), 83–93.PubMedCrossRefGoogle Scholar
  20. 20.
    Lim, C. T., Zhou, E. H., & Quek, S. T. (2006). Mechanical models for living cells—a review. Journal of Biomechanics, 39(2), 195–216.PubMedCrossRefGoogle Scholar
  21. 21.
    Bailly, M., & Condeelis, J. (2002). Cell motility: Insights from the backstage. Nature Cell Biology, 4(12), E292–E294.PubMedCrossRefGoogle Scholar
  22. 22.
    Mitchison, T. J., & Cramer, L. P. (1996). Actin-based cell motility and cell locomotion. Cell, 84(3), 371–379.PubMedCrossRefGoogle Scholar
  23. 23.
    Svitkina, T. M., et al. (1997). Analysis of the actin-myosin II system in fish epidermal keratocytes: Mechanism of cell body translocation. Journal of Cell Biology, 139(2), 397–415.PubMedCrossRefGoogle Scholar
  24. 24.
    Mogilner, A., & Oster, G. (2003). Polymer motors: Pushing out the front and pulling up the back. Current Biology, 13(18), R721–R733.PubMedCrossRefGoogle Scholar
  25. 25.
    Mogilner, A., & Oster, G (1996). Cell motility driven by actin polymerization. Biophysical Journal, 71(6), 3030–3045.PubMedGoogle Scholar
  26. 26.
    Marcy, Y., et al. (2004). Forces generated during actin-based propulsion: A direct measurement by micromanipulation. Proceedings of the National Academy of Sciences of the USA, 101(16), 5992–5997.PubMedCrossRefGoogle Scholar
  27. 27.
    Grimm, H. P., et al. (2003). Analysis of actin dynamics at the leading edge of crawling cells: Implications for the shape of keratocyte lamellipodia. European Biophysics Journal, 32(6), 563–577.PubMedCrossRefGoogle Scholar
  28. 28.
    Orsello, C. E., Lauffenburger, D. A., & Hammer, D. A. (2001). Molecular properties in cell adhesion: A physical and engineering perspective. Trends in Biotechnology, 19(8), 310–316.PubMedCrossRefGoogle Scholar
  29. 29.
    Beningo, K. A., Dembo, M., Kaverina, I., Small, J. V., & Wang, Y. (2001). Nascent focal adhesions are responsible for the generation of strong propulsive forces in migrating fibroblasts. Journal of Cell Biology, 153, 881–887.PubMedCrossRefGoogle Scholar
  30. 30.
    Munevar, S., Wang, Y., & Dembo, M. (2001). Traction force microscopy of migrating normal and H-ras transformed 3T3 fibroblasts. Biophysical Journal, 80(4), 1744–1757.PubMedGoogle Scholar
  31. 31.
    Zamir, E., & Geiger, B. (2001). Molecular complexity and dynamics of cell-matrix adhesions. Journal of Cell Science, 114(Pt 20), 3583–3590.PubMedGoogle Scholar
  32. 32.
    Mogilner, A., & Edelstein-Keshet, L. (2002). Regulation of actin dynamics in rapidly moving cells: A quantitative analysis. Biophysical Journal, 83(3), 1237–1258.PubMedGoogle Scholar
  33. 33.
    Mogilner, A., & Rubinstein, B. (2005). The physics of filopodial protrusion. Biophysical Journal, 89(2), 782–795.PubMedCrossRefGoogle Scholar
  34. 34.
    Atilgan, E., Wirtz, D., & Sun, S. X. (2006). Mechanics and dynamics of actin-driven thin membrane protrusions. Biophysical Journal, 90(1), 65–76.PubMedCrossRefGoogle Scholar
  35. 35.
    Atilgan, E., Wirtz, D., & Sun, S. X. (2005). Morphology of the lamellipodium and organization of actin filaments at the leading edge of crawling cells. Biophysical Journal, 89, 3589–3602.PubMedCrossRefGoogle Scholar
  36. 36.
    Carlsson, A. E. (2001). Growth of branched actin networks against obstacles. Biophysical Journal, 81(4), 1907–1923.PubMedGoogle Scholar
  37. 37.
    Li, G.-H., Qin, C.-D., & Li, M.-H. (1994). On the mechanisms of growth cone locomotion: Modeling and computer simulation. Journal of Theoretical Biology, 169(4), 355–362.PubMedCrossRefGoogle Scholar
  38. 38.
    DiMilla, P. A., Barbee, K., & Lauffenburger, D. A. (1991). Mathematical model for the effects of adhesion and mechanics on cell migration speed. Biophysical Journal, 60(1), 15–37.PubMedGoogle Scholar
  39. 39.
    Gracheva, M. E., & Othmer, H. G. (2004). A continuum model of motility in ameboid cells. Bulletin of Mathematical Biology, 66(1), 167–193.PubMedCrossRefGoogle Scholar
  40. 40.
    Bottino, D., et al. (2002). How nematode sperm crawl. Journal of Cell Science, 115(Pt 2), 367–384.PubMedGoogle Scholar
  41. 41.
    Oliver, J. M., et al. (2005). Thin-film theories for two-phase reactive flow models of active cell motion. Mathematical Medicine and Biology, 22(1), 53–98.PubMedCrossRefGoogle Scholar
  42. 42.
    Zaman, M. H., et al. (2005). Computational model for cell migration in three-dimensional matrices 10.1529/biophysj.105.060723. Biophysical Journal, 89(2), 1389–1397.PubMedCrossRefGoogle Scholar
  43. 43.
    Shreiber, D. I., Barocas, V. H., & Tranquillo, R. T. (2003). Temporal variations in cell migration and traction during fibroblast-mediated gel compaction. Biophysical Journal, 84(6), 4102–4114.PubMedGoogle Scholar
  44. 44.
    Liu, W. K., et al. (2006). Immersed finite element method and its applications to biological systems. Computer Methods in Applied Mechanics and Engineering. A Tribute to Thomas J.R. Hughes on the Occasion of his 60th Birthday, 195(13–16), 1722–1749.Google Scholar
  45. 45.
    Mogilner, A., & Verzi, D. W. (2003). A simple 1-D physical model for the crawling nematode sperm cell. Journal of Statistical Physics, 110(3), 1169–1189.CrossRefPubMedGoogle Scholar
  46. 46.
    Herant, M., Marganski, W. A., & Dembo, M. (2003). The mechanics of neutrophils: Synthetic modeling of three experiments. Biophysical Journal, 84(5), 3389–3413.PubMedGoogle Scholar
  47. 47.
    Jean, R. P., Chen, C. S., & Spector, A. A. (2005). Finite-element analysis of the adhesion-cytoskeleton-nucleus mechanotransduction pathway during endothelial cell rounding: Axisymmetric model. Journal of Biomechanical Engineering, 127(4), 594–600.PubMedCrossRefGoogle Scholar
  48. 48.
    Rotsch, C., Jacobson, K., & Radmacher, M. (1999). Dimensional and mechanical dynamics of active and stable edges in motile fibroblasts investigated by using atomic force microscopy. Proceedings of the National Academy of Sciences of the USA, 96(3), 921–926.PubMedCrossRefGoogle Scholar
  49. 49.
    Prass, M., et al. (2006). Direct measurement of the lamellipodial protrusive force in a migrating cell. Journal of Cell Biology, 174(6), 767–772.PubMedCrossRefGoogle Scholar
  50. 50.
    Rubinstein, B., Jacobson, K., & Mogilner, A. (2005). Multiscale two-dimensional modeling of a motile simple-shaped cell. Multiscale Modeling & Simulation, 3(2), 413–439.CrossRefGoogle Scholar
  51. 51.
    Carra, A., Promayon, E., & Martiel, J.-L. (2005). A physically-based model for cell plasticity and motility. In Journées Ouvertes Biologie Informatique Mathématiques, JOBIM2005.Google Scholar
  52. 52.
    Jaasma, M. J., Jackson, W. M., & Keaveny, T. M. (2006). The effects of morphology, confluency, and phenotype on whole-cell mechanical behavior. Annals of Biomedical Engineering, 34(5), 759–768.PubMedCrossRefGoogle Scholar

Copyright information

© Humana Press Inc. 2007

Authors and Affiliations

  • Brendan Flaherty
    • 1
    • 2
  • J. P. McGarry
    • 1
    • 2
  • P. E. McHugh
    • 1
    • 2
  1. 1.National Centre for Biomedical Engineering ScienceNational University of IrelandGalwayIreland
  2. 2.Department of Mechanical and Biomedical EngineeringNational University of IrelandGalwayIreland

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