Travelling waves of attached and detached cells in a wound-healing cell migration assay. (English) Zbl 1296.92093
Summary: During a wound-healing cell migration assay experiment, cells are observed to detach and undergo mitosis before reattaching as a pair of cells on the substrate. During experiments with mice 3T3 fibroblasts, cell detachment can be confined to the wavefront region or it can occur over the whole wave profile. A multi-species continuum approach to modelling a wound-healing assay is taken to account for this phenomenon. The first cell population is composed of attached motile cells, while the second population is composed of detached immotile cells undergoing mitosis and returning to the migrating population after successful division. The first model describes cell division occurring only in the wavefront region, while a second model describes cell division over the whole of the scrape wound. The first model reverts to the Fisher equation when the reattachment rate relative to the detachment rate is large, while the second case does not revert to the Fisher equation in any limit. The models yield travelling wave solutions. The minimum wave speed is slower than the minimum Fisher wave speed and its dependence on the cell detachment and reattachment rate parameters is analysed. Approximate travelling wave profiles of the two cell populations are determined asymptotically under certain parameter regimes.
MSC:
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35K57 | Reaction-diffusion equations |
| 92C50 | Medical applications (general) |
Keywords:
cell migration; diffusion; proliferation; wound healing; travelling wave; attached; detachedReferences:
| [1] | Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P., 2002. Molecular Biology of the Cell, 4th edn. Garland Science, New York. |
| [2] | Assoian, R.K., 1997. Anchorage-dependent cell cycle progression. J. Cell. Biol. 136, 1–4. · doi:10.1083/jcb.136.1.1 |
| [3] | Boucher, A., Doisy, A., Ronot, X., Garbay, C., 1998. Cell migration analysis after in vitro wounding injury with a multi-agent approach. Artif. Intell. Rev. 12, 137–62. · doi:10.1023/A:1006500808998 |
| [4] | Cai, A.Q., Hughes, B.D., Landman, K.A., 2007. Multi-scale modeling of a wound-healing cell migration assay. J. Theor. Biol. 245, 576–94. · Zbl 1296.92093 · doi:10.1016/j.jtbi.2006.10.024 |
| [5] | Canosa, J., 1973. On a nonlinear diffusion equation describing population growth. IBM J. Res. Dev. 17(4), 307–13. · Zbl 0266.65080 · doi:10.1147/rd.174.0307 |
| [6] | Dale, P.D., Maini, P.K., Sherratt, J.A., 1994. Mathematical modeling of corneal epithelial wound healing. Math. Biosci. 124, 127–47. · Zbl 0818.92007 · doi:10.1016/0025-5564(94)90040-X |
| [7] | Denman, P.K., McElwain, D.L.S., Norbury, J., 2007. Analysis of travelling waves associated with the modelling of aerosolised skin grafts. Bull. Math. Biol. 69, 495–23. · Zbl 1138.92343 · doi:10.1007/s11538-006-9138-0 |
| [8] | Frisch, S.M., Francis, H., 1994. Disruption of epithelial cell-matrix interactions induces apoptosis. J. Cell. Biol. 124(4), 619–26. · doi:10.1083/jcb.124.4.619 |
| [9] | Galle, J., Loeffler, M., Drasdo, D., 2005. Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. Biophys. J. 88, 62–5. · doi:10.1529/biophysj.104.041459 |
| [10] | Harris, S., 2003. Traveling waves with dispersive variability and time delay. Phys. Rev. E 68, 031912. · doi:10.1103/PhysRevE.68.031912 |
| [11] | Lackie, J.M., 1986. Cell Movement and Cell Behaviour. Allen & Unwin, London. |
| [12] | Maini, P.K., McElwain, D.L.S., Leavesley, D., 2004a. Travelling waves in a wound healing assay. App. Math. Lett. 17, 575–80. · Zbl 1055.92025 · doi:10.1016/S0893-9659(04)90128-0 |
| [13] | Maini, P.K., McElwain, D.L.S., Leavesley, D., 2004b. Travelling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng. 10, 475–82. · doi:10.1089/107632704323061834 |
| [14] | Meredith Jr., J.E., Fazeli, B., Schwartz, M.A., 1993. The extracellular matrix as a cell survival factor. Mol. Biol. Cell. 4, 953–61. |
| [15] | Murray, J.D., 2002. Mathematical Biology, vol. 1, 3rd edn. Springer, New York. · Zbl 1006.92001 |
| [16] | Okubo, A., Levin, S.A., 2001. Diffusion and Ecological Problems: Mathematical models. Interdisciplinary Applied Mathematics, 2nd edn. Springer, New York. |
| [17] | Shigesada, N., 1980. Spatial distribution of dispersing animals. J. Math. Biol. 9, 85–6. · Zbl 0427.92015 · doi:10.1007/BF00276037 |
| [18] | Savla, U., Olson, L.E., Waters, C.M., 2004. Mathematical modeling of airway epithelial wound closure. J. Appl. Physiol. 96, 566–74. · doi:10.1152/japplphysiol.00510.2003 |
| [19] | 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. · doi:10.1016/j.jtbi.2006.06.021 |
| [20] | Takamizawa, K., Niu, S., Matsuda, T., 1997. Mathematical simulation of unidirectional tissue formation: in vitro transanastomotic endothelialization model. J. Biomater. Sci. Polym. Ed. 8, 323–34. · doi:10.1163/156856296X00336 |
| [21] | Tirtaatmadja, N., 2005. Cell motility and scaffold production for tissue engineering. Internal report. Department of Chemical and Biomolecular Engineering, The University of Melbourne. |
| [22] | Ura, H., Takeda, F., Okochi, H., 2004. An in vitro outgrowth culture system for normal human keratinocytes. J. Dermatol. Sci. 35, 19–8. · doi:10.1016/j.jdermsci.2004.03.005 |
| [23] | Zahm, J.M., Kaplan, H., Hérard, A., Doriot, F., Pierrot, D., Somelette, P., Puchelle, E., 1997. Cell migration and proliferation during the in vitro repair of the respiratory epithelium. Cell Motil. Cytoskelet. 37, 33–3. · doi:10.1002/(SICI)1097-0169(1997)37:1<33::AID-CM4>3.0.CO;2-I |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
