A mathematical model of integrin-mediated haptotactic cell migration

Bulletin of Mathematical Biology

Volumn 68, Issue 2, 2006, Pages 231-253

  Mallet, D G ^a   Pettet, G J ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Cell migration; Haptotaxis; Integrin; Travelling waves; Wall of singularities

Indexed keywords

INTEGRIN; PEPTIDE HYDROLASE;

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL MOTION; COMPUTER SIMULATION; EXTRACELLULAR MATRIX; FOCAL ADHESION; HUMAN; KINETICS; METABOLISM; PHYSIOLOGY;

ALGORITHMS; ANIMALS; CELL MOVEMENT; COMPUTER SIMULATION; EXTRACELLULAR MATRIX; FOCAL ADHESIONS; HUMANS; INTEGRINS; KINETICS; MODELS, BIOLOGICAL; PEPTIDE HYDROLASES;

EID: 33746613711     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-005-9032-1     Document Type: Article

References (39)

1. Anderson, A.R.A., Chaplain, M.A.J., 1998. Continuous and discrete mathematical models of tumor induced angiogenesis. Bull. Math. Biol. 60, 877-900.
2. Anderson, A.R.A., Chaplain, M.A.J., Newman, E.L., Steele, R.J.C., Thompson, A.M., 2000. Mathematical modelling of tumour invasion and metastasis. J. Theor. Med. 2, 129-154.
3. Aplin, A.E., Howe, A., Alahari, S.K., Juliano, R.L., 1998. Signal transduction and signal modulation by cell adhesion receptors: The role of integrins, cadherins, immunoglobulin-cell adhesion molecules, and selectins. Pharmacol. Rev. 50, 197-252.
4. Bray, D., 1992. Cell Movements. Garland Publishing, New York.
5. Carter, S.B., 1965. Principles of cell motility: The direction of cell movement and cancer invasion. Nature 208, 1183-1187.
6. Dallon, J.C., Othmer, H.G., 1997. A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum. Phil. Trans. R. Soc. Lond. B 352(1351), 391-417.
7. Dallon, J.C., Othmer, H.G., 1998. A continuum analysis of the chemotactic signal seen by Dictyostelium discoideum. J. Theor. Biol. 194, 461-483.
8. DiMilla, P.A., Barbee, K., Lauffenburger, D.A., 1991. Mathematical model for the effects of adhesion and mechanics on cell migration speed. Biophys. J. 60, 15-37.
9. Frisch, S.M., Ruoslahti, E., 1997. Integrins and anoikis. Curr. Opin. Cell Biol. 9, 701-706.
10. Hoefer, T., Sherratt, J.A., Maini, P.K., 1995a. Dictyostelium discoideum: Cellular self-organization in an excitable biological medium. Proc. R. Soc. Lond. B 259, 249-257.
11. Hoefer, T., Sherratt, J.A., Maini, P.K., 1995b. Cellular pattern formation during Dictyostelium aggregation. Physica D 85, 425-444.
12. Lauffenburger, D., 1989. A simple model for the effects of receptor-mediated cell-substratum adhesion on cell migration. Chem. Eng. Sci. 44(9), 1903-1914.
13. Lauffenburger, D.A., Linderman, J.J., 1993. Receptors: Models for Binding, Trafficking and Signalling. Oxford University Press, Oxford.
14. MacArthur, B.D., 2002. Mathematical modelling of malignant growth and invasion, PhD Thesis, University of Southampton, Southampton, UK.
15. Maheshwari, G., Lauffenburger, D.A., 1998. Deconstructing (and reconstructing) cell migration. Microsc. Res. Tech. 43, 358-368.
16. Maini, P.K., 1989. Spatial and spatio-temporal patterns in a cell-haptotaxis model. J. Math. Biol. 27, 507-522.
17. Marchant, B., 1999. Modelling cell invasion, DPhil Thesis, University of Oxford, Oxford.
18. Marusic, M., Bajzer, Z., Freyer, J.P., Vuk-Pavlovic, S., 1994. Analysis of growth of multicellular tumor spheroids by mathematical models. Cell Prolif. 27, 73-94.
19. Mignatti, P., Rifkin, D.B., 1993. Biology and biochemistry of proteinases in tumor invasion. Physiol. Rev. 73, 161-195.
20. Murray, J.D., 1993. Mathematical Biology, 2nd ed. Springer-Verlag, New York.
21. Olsen, L., Sherratt, J.A., Maini, P.K., 1995. A mechanical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile. J. Theor. Biol. 177, 113-128.
22. Olsen, L., Sherratt, J.A., Maini, P.K., 1996. A mathematical model for fibroproliferative wound healing disorders. Bull. Math. Biol. 58(4), 787-808.
23. Orme, M.E., Chaplain, M.A.J., 1996. A mathematical model of vascular tumour growth and invasion. Math. Comput. Model. 23(10), 43-60.
24. Othmer, H.G., Lilly, B., Dallon, J.C., 2000. Pattern formation in a cellular slime mould. In: Doedel, E., Tuckerman, L.S. (Eds.), Numerical Methods for Bifurcation Problems and Large Scale Dynamical Systems. IMA Proc. 119, 359-383.
25. Owen, M.R., Sherratt, J.A., 1997. Pattern formation and spatiotemporal irregularity in a model for macrophage-tumour interactions. J. Theor. Biol. 189, 63-80.
26. Perumpanani, A.J., Byrne, H.M., 1999. Extracellular matrix concentration exerts selection pressure on invasive cells. Eur. J. Cancer 35(8), 1274-1280.
27. Perumpanani, A.J., Norbury, J., Sherratt, J.A., Byrne, H.M., 1996. Biological inferences from a mathematical model for malignant invasion. Invasion Metastasis 16, 209-221.
28. Perumpanani, A.J., Simmons, D.L., Gearing, A.J.H., Miller, K.M., Ward, G., Norbury, J., Schneemann, M., and Sherratt, J.A. 1998. Extracellular matrix-mediated chemotaxis can impede cell migration. Proc. R. Soc. Lond. B 265, 2347-2352.
29. Perumpanani, A.J., Sherratt, J.A., Norbury, J., Byrne, H.M., 1999. A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion. Physica D 126, 145-159.
30. Pettet, G.J., 1996. Modelling wound healing angiogenesis and other chemotactically driven growth processes, PhD Thesis, University of Newcastle, Australia.
31. Pettet, G.J., McElwain, D.L.S., Norbury, J., 2001. Lotka-Volterra equations with chemotaxis: Walls, barriers and travelling waves. IMA J. Math. Appl. Med. Biol. 17(4), 395-413.
32. Sherratt, J.A., 1994. Chemotaxis and chemokinesis in eukaryotic cells: The Keller-Segel equations as an approximation to a detailed model. Bull. Math. Biol. 56(1), 129-146.
33. Sherratt, J.A., Murray, J.D., 1990. Models of epidermal wound healing. Proc. R. Soc. Lond. B 241, 29-36.
34. Sherratt, J.A., Nowak, M.A., 1992. Oncogenes, anti-oncogenes and the immune response to cancer: A mathematical model. Proc. R. Soc. Lond. B 248, 261-271.
35. Sherratt, J.A., Helene Sage, E., Murray, J.D., 1993. Chemical control of eukaryotic cell movement: A new model. J. Theor. Biol. 162, 23-40.
36. Stetler-Stevenson, W.G., Aznavoorian, S., Liotta, L.A., 1993. Tumor cell interactions with the extracellular matrix during invasion and metastasis. Annu. Rev. Cell Biol. 9, 541-573.
37. Stokes, C.L., Lauffenburger, D.A., 1991. Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J. Theor. Biol. 152, 377-403.
38. Terranova, V.P., Diflorio, R., Lyall, R.M., Hic, S., Friesel, R., Maciag, T., 1985. Human endothelial cells maintained in the absence of fibroblast growth factor undergo structural and functional alterations that are incompatible with their in vivo differentiated properties. J. Cell Biol. 83, 468-486.
39. Tracqui, P., 1995. From passive diffusion to active cellular migration in mathematical models of tumour invasion. Acta Biotheor. 43, 443-464.