MATHEMATICAL MODELLING OF CANCER INVASION OF TISSUE: DYNAMIC HETEROGENEITY

Networks and Heterogeneous Media

Volumn 1, Issue 3, 2006, Pages 399-439

  Chaplain, M A J ^a   Lolas, G ^a  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

cancer invasion of tissue; chemotaxis; haptotaxis; matrix degrading enzyme; spatio temporal heterogeneity

Indexed keywords

BIOCHEMISTRY; CELLS; CHEMICAL ACTIVATION; CYTOLOGY; DISEASES; ENZYME ACTIVITY; ENZYME INHIBITION; TUMORS;

CANCER INVASION; CANCER INVASION OF TISSUE; CHEMOTAXI; DEGRADING ENZYMES; HAPTOTAXI; MATRIX; MATRIX DEGRADING ENZYME; SPATIO-TEMPORAL; SPATIO-TEMPORAL HETEROGENEITY; TEMPORAL HETEROGENEITIES;

CANCER CELLS;

EID: 85182867322     PISSN: 15561801     EISSN: 1556181X     Source Type: Journal    
DOI: 10.3934/nhm.2006.1.399     Document Type: Article

References (85)

1. Aguirre Ghiso J.A., Alonso D.F., Farías E.F., Gomez D.E. and and Bal De Kier Joffè E.,Deregulation of the signaling pathways controlling urokinase production. Its relationship with the invasive phenotype, European Journal of Biochemistry, 263 (1999), 295–304.
2. Alberts B., Bray D., Lewis J., Raff M., Roberts K., Watson J.D., Molecular Biology of the Cell, Garland Publishing (1994).
3. Alitalo K., Tammela T. and Petrova T.V., Lymphangiogenesis in development and human disease, Nature, 438 (2005), 946–953.
4. Anderson A.R.A. and Chaplain M.A.J., Newman E.L., Steele R.J.C., and Thompson A.M., Mathematical modelling of tumour invasion and metastasis, Journal of Theoretical Medicine, 2 (2000), 129 –154.
5. Anderson A.R.A., A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion, Mathematical Medicine and Biology, (2) 22 (2005), 163–186.
6. Andreasen P.A., Kjøller L., Christensen L. and Duffy M.J., The urokinase-type plasminogen activator system in cancer metastasis: A review, International Journal of Cancer, 72 (1997), 1–22.
7. Andreasen P.A., Egelund R. and Petersen H.H., The plasminogen activation system in tumor growth, invasion, and metastasis, Cellular and Molecular Life Sciences, 57 (2000), 25–40.
8. Atkins P.W., Physical Chemistry 3rd edition, Oxford University Press (1989).
9. Aznavoorian S., Stracke M.L., Krutzsch H., Schiffmann E. and Liotta L.A., Signal transduction for chemotaxis and haptotaxis by matrix molecules in tumor cells, The Journal of Cell Biology, 110 (1990), 1427–1438.
10. Aznavoorian S., Murphy A.N., Stetler-Stevenson W.G. and Liotta L.A., Molecular aspects of tumor cell invasion and metastasis, Cancer, 71 (1993), 1368–1383.
11. Bajpai A., and Baker J.B., Cryptic urokinase binding sites on human foreskin fibroblasts, Biochemical and Biophysical Research Communications, 133 (1985), 475–482.
12. Besser D., Verde P., Nagamine Y., and Blasi F., Signal transduction and the u-PA/u-PAR system, Fibrinolysis, 10 (1996), 215–237.
13. Blasi F., Vassalli J-D., and Danø K., Urokinase-type plasminogen activator: Proenzyme, receptor, and inhibitors, Journal of Cell Biology, 104 (1987), 801–804.
14. Bray D., Cell Movements: From molecules to motility, Garland Publishing (2000).
15. Busso N., Masur S.K., Lazega D., Waxman S., and Ossowski L., Induction of cell migration by pro-urokinase binding to its receptor: possible mechanism for signal-transduction in human epithelial cells, Journal of Cell Biology, 126 (1994), 259–270.
16. Byrne H.M., Chaplain M.A.J., Pettet G.J., and McElwain D.L.S., A mathematical model of trophoblast invasion, Journal of Theoretical Medicine, 1 (1998), 275–286.
17. Carter S.B., Haptotaxis and the mechanism of cell motility, Nature, 213 (1967), 256–260.
18. Chambers A.F., and Matrisian L.M., Changing views of the role of matrix metalloproteinases in metastasis, Journal of the National Cancer Institute, 89 (1997), 1260–1270.
19. Chambers A.F., Groom A.C., and MacDonald I.C., Dissemination and growth of cancer cells in metastatic sites, Nature Revies, 2 (2002), 563–572.
20. Chaplain M.A.J. and Stuart A.M., A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue, IMA Journal of Mathematics Applied in Medicine & Biology, 8 (1991), 191–220.
21. Chaplain M.A.J., The mathematical modelling of tumour angiogenesis and invasion, Acta Biotheoretica, 43 (1995), 387–402.
22. Chaplain M.A.J., and Anderson A.R.A., Mathematical modelling, simulation and prediction of tumour-induced angiogenesis, Invasion & Metastasis, 16 (1996), 222–234.
23. Chaplain M.A.J. and Lolas, G., Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system, Mathematical Models and Methods in Applied Sciences, 15 (2005), 1685–1734.
24. Chapman H.A., Plasminogen activators, integrins, and the coordinated regulation of cell adhesion and migration, Current Opinion in Cell Biology, 9 (1997), 714–724.
25. Collen D., Zamarron C., Lijnen H.R., and Hoylaerts M., Activation of plasminogen by prourokinase, Journal of Biological Chemistry, 261, 1259–1266, (1986).
26. Comper W.D., Extracellular Matrix Volume 2 Molecular Components and Interactions, Harwood Academic Publishers (1996).
27. Conese M., and Blasi F., The urokinase/urokinase-receptor system and cancer-invasion, Baillière’s Clinical Haematology, 8 (1995), 365–389.
28. Conese M., Blasi F., Urokinase/urokinase receptor system: Internalization/degradation of urokinase-serpin complexes. Mechanism and regulation, Biological Chemistry Hoppe-Seyler, 376 (1995), 143–155.
29. Curtis A.S.G., The measurement of cell adhesiveness by an absolute method, Journal of Embryology and Experimental Morphology, 22 (1969), 305–325.
30. Czekay R-P., Aertgeerts K., Curriden S.A., and Loskutoff D.J., Plasminogen activator inhibitor-1 detaches cells from extracellular matrices by inactivating integrins, Journal of Cell Biology, (5) 160 (2003) 781–791.
31. Danø K., Anderson P.A., Grondahl-Hansen J., Kristensen P., Nielsen L.S. and Skriver L., Plasminogen activators, tissue degradation and cancer, Advanced Cancer Research, 44 (1985), 139–266.
32. Danø K., Behrendt N., Brunner N., Ellis V., Ploug M. and Pyke C., The urokinase receptor. Protein structure and role in plasminogen activation and cancer invasion, Fibrinolysis, 8 (1994), 189–203.
33. Danø K., Behrendt N., Høyer-Hansen G., Johnsen M., Lund L.R., Ploug M. and Rømer J., Plasminogen activation and cancer, Thrombosis and Haemostasis, 93 (2005), 676–681.
34. Deng G., Curriden S.A., Wang S., Rosenberg S., Loskutoff D.J., Is plasminogen activator inhibitor-1 the molecular switch that governs urokinase receptor-mediated cell adhesion and release? Journal of Cell Biology, 134 (1996), 1563–1571.
35. uffy M.J., Urokinase plasminogen activator: A prognostic marker in multiple types of cancer, Journal of Surgical Oncology, 71 (1999), 130–135.
36. Edelstein-Keshet L., Mathematical Models in Biology, McGraw-Hill, Inc (1988).
37. Estreicher A., Mühlhauser, Carpentier J-L., Orci L., and Vassali J-D., The receptor for urokinase type plasminogen activator polarizes expression of the protease to the leading edge of migrating monocytes and promotes degradation of enzyme inhibitor complexes, Journal of Cell Biology, 111 (1990), 783–792.
38. Fazioli F., Resnati M., Sidenius N., Higashimoto Y., Appella E., and Blasi F., A urokinase-sensitive region of the human urokinase receptor is responsible for its chemotactic activity, The EMBO Journal, 16 (1997), 7279–7286.
39. Fidler I.J., The biology of cancer metastasis or, “you cannot fix it if you do not know how it works”, Bioessays, 13 (1991), 551–554.
40. Fidler I.J., The pathogenesis of cancer metastasis: the ‘seed and soil’ hypothesis revisited, Nature Reviews, 3 (2002), 1–6.
41. Folkman J., Tumour angiogenesis, Advances in Cancer Research, 19 (1974), 331–358.
42. Folkman J., The vascularization of tumours, Scientific American, 234 (1976), 58–73.
43. Fox S.B, Taylor M., Grøndahl-Hansen J., Kakolyris S., Gatter K.C., and Harris A.L., Plasminogen activator inhibitor-1 as a measure of vascular remodelling in breast cancer, Journal of Pathology, 195 (2001), 236–243.
44. Gatenby R.A., and Gawlinski, E.T., A reaction-diffusion model of cancer invasion, Cancer Research, 56 (1996), 5745–5753.
45. Gyetko M.R., Todd R.F.,III, Wilkinson C.C., and Sitrin R.G., The urokinase receptor is required for human monocyte chemotaxis in vitro, Journal of Clinical Investigation, 93 (1994), 1380–1387.
46. Hanahan D., and Weinberg R.A., The hallmarks of cancer, Cell, 100 (2000), 57–70.
47. Irigoyen J.P., Muñoz-Cánoves P., Montero L., Koziczak M., and Nagamine Y., The plasminogen activator system: biology and regulation, Cellular and Molecular Life Sciences, 56 (1999), 104–132.
48. Kanse S.M., Kost C., Wilhelm O.G., Andreasen P.A., and Preissner K.T., The urokinase receptor is a major vitronectin-binding protein on endothelial cells, Experimental Cell Research, 224 (1996), 344–353.
49. Kjøller L., Kanse S.M., Kirkegaard T., Rodenburg K.W., Rønne E., Goodmann S.L., Preissner K.T., Ossowski L., and Andreasen P.A., Plasminogen activator inhibitor-1 represses integrin-and vitronectin-mediated cell migration independently of its function as an inhibitor of plasminogen activation, Experimental Cell Research, 232 (1997), 420–429.
50. Kjøller L., The urokinase plasminogen activator receptor in the regulation of the actin cytoskeleton and cell motility, Biological Chemistry, 383 (2002), 5–19.
51. Kohn E.C., and Liotta L.A., Molecular insights into cancer invasion: strategies for prevention and intervention, Cancer Research, 51, 1856–1862, (1995).
52. Lachowicz, M., Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours, Mathematical Models and Methods in Applied Sciences, 11 (2005), 1667–1683.
53. Lackie, J.M. and Wilkinson, P.C. (Eds.), Biology of the Chemotactic Response, Cambridge University Press, Cambridge (1981).
54. Lauffenburger D., A simple model for the effects of receptor-mediated cell-substratum adhesion on cell migration, Chemical Engineering Science, 44 (1989), 1903–1914.
55. Lauffenburger D.A. and Horwitz A.F., Cell migration: A physically integrated molecular process, Cell, 84 (1996), 359–369.
56. Liotta L.A., Tumour invasion and metastases: role of the extracellular matrix, Cancer Research, 46 (1986), 1–7.
57. Liotta L.A., and Stetler-Stevenson W.G., Tumor invasion and metastasis as targets for cancer therapy, Cancer Research, 51 (1991), 5054–5059.
58. Liotta L.A., and Clair T., Checkpoint for invasion, Nature, 405 (2000), 287–288.
59. Lolas, G., Mathematical modelling of the urokinase plasminogen activation system and its role in cancer invasion of tissue, PhD Thesis, University of Dundee (2003).
60. Mantzaris, N.V., Webb, S. and Othmer, H.G., Mathematical modelling of tumour-induced angiogenesis, 49 (2004), 111–187.
61. Mignatti P. and Rifkin D.B., Biology and biochemistry of proteinases in tumor invasion, Physiological Reviews, 73 (1993), 161–195.
62. Murray J.D., Mathematical Biology: Spatial Models and Biomedical Applications, Spinger-Verlag (2003).
63. Naski M.C., Lawrence D.A., Mosher D.F., Podor T.J., and Ginsburg D., Kinetics of inactivation of α-thrombin by plasminogen activator inhibitor-1, Journal of Biological Chemistry, 268, 12367–12372, (1993).
64. Nguyen D.H.D., Hussaini I.M., and Gonias S.L., Binding of urokinase-type plasminogen activator to its receptor in MCF-7 cells activates extracellular signal-regulated kinase 1 and 2 which is required for increased cellular motility, The Journal of Biological Chemistry, 273 (1998), 8502–8507.
65. Nykjær A., Conese M., Christensen E.I., Olson D., Cremona O., Gliemann J. and Blasi F., Recycling of the urokinase receptor upon internalization of the uPA: serpin complexes, The EMBO Journal, 16 (1997), 2610–2620.
66. Orme M.E. and Chaplain M.A.J., A mathematical model of vascular tumour growth and invasion, Mathematical and Computer Modelling, 23 (1996), 43–60.
67. Pepper M.S., Sappino A.-P., Stöcklin R., Montesano R., Orci L., and Vassalli J.-D., Upregulation of urokinase receptor expression on migrating endothelial cells, The Journal of Cell Biology, 122 (1993), 673–684.
68. Pepper M.S., Role of the matrix metalloproteinase and plasminogen activator-plasmin systems in angiogenesis, Arteriosclerosis, Thrombosis and Vascular Biology, 21 (2001a), 1104–1117.
69. Perumpanani A.J., Sherratt J.A., Norbury J., Byrne H.M., Biological inferences from a mathematical model for malignant invasion, Invasion & Metastasis, 16 (1996), 209–221.
70. Perumpanani A.J., Simmons D.L., Gearing A.J.H., Miller K.M., Ward G., Norbury J., Schneemann M., and Sherratt J.A., Extracellular matrix-mediated chemotaxis can impede cell migration, Proceedings of the Royal Society of London, Series B, 265 (1998), 2347–2352.
71. Plesner T., Behrendt N., and Ploug M., Structure, function and expression on blood and bone marrow cells of the urokinase-type plasminogen activator receptor, uPAR, STEM Cells, 15 (1997), 398–408.
72. Preziosi, L. (Ed.), Cancer Modelling and Simulation, Chapman & Hall/CRC Press (2003).
73. Rakic J.M., Maillard C., Jost, M., Bajou K., Masson V., Devy L., Lambert V., Foidart J.M., and Noël A., Role of plasminogen activator-plasmin system in tumor angiogenesis, Cellular and Molecular Life Sciences, 60, 463–473, (2003).
74. Resnati M., Guttinger M., Valcamonica S., Sidenius N, Blasi F., and Fazioli F., Proteolytic cleavage of the urokinase receptor substitutes for the agonist-induced chemotactic effect, EMBO Journal, 9 (1996), 467–470.
75. Sherratt J.A., and Murray J.D., Models of epidermal wound healing, Proceedings of the Royal Society of London Series B, 241 (1990), 29–36.
76. Sherratt J.A., Chemotaxis and chemokinesis in eukaryotic cells: The Keller-Segel equations as an approximation to a detailed model, Bulletin of Mathematical Biology, 56 (1994), 129–146.
77. Stokes C.L., Lauffenburger D.A., and Williams S.K., Migration of individual microvessel endothelial cells: stochastic model and parameter measurement, Journal of Cell Science, 99 (1991), 419–430.
78. Stokes C.L., and Lauffenburger D., Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis, Journal of Theoretical Biology, 152 (1991), 377–403.
79. Stoppelli M.P., Corti A. Soffientini A., Cassani G., Blasi F., and Assoian R.K., Differentiation-enhanced binding of the amino-terminal fragment of human urokinase plasminogen activator to a specific receptor on U937 monocytes, Proceedings of the National Academy of Sciences USA, 82 (1985), 4939–4943.
80. Tarui T., Mazar A.P., Cines D.B., and Takada Y., Urokinase-type plasminogen activator receptor (CD87) is a ligand for integrins and mediates cell-cell interaction, The Journal of Biological Chemistry, 276 (2001), 3983–3990.
81. Waltz D.A. and Chapman H.A., Reversible cellular adhesion to vitronectin linked to urokinase receptor occupancy, Journal of Biological Chemistry, 269 (1994), 14746–14750.
82. Waltz D.A, Natkin L.R., Fujita R.M., Wei Y., and Chapman H.A., Plasmin and plasminogen activator inhibitor type 1 promote cellular motility by regulating the interaction between the urokinase receptor and vitronectin, Journal of Clinical Investigation, 100 (1997), 58–67.
83. Wei Y., Waltz D.A., Rao N., Drummond R.J., Rosenberg S., and Chapman H.A., Identification of the urokinase receptor as an adhesion receptor for vitronectin, The Journal of Biological Chemistry, 269 (1994), 32380–32388.
84. Yebra M., Goretzki L., Pfeifer M., and Mueller B.M., Urokinase-type plasminogen activator binding to its receptor stimulates tumor cell migration by enhancing integrin-mediated signal transduction, Experimental Cell Research, 250 (1999), 231–240.
85. Yu, W., Kim, J. and Ossowski, L., Reduction in surface urokinase receptor forces malignant cells into a protracted state of dormancy, Journal of Cell Biology, 137 (1997), 767–777.