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Volumn 22, Issue 3, 2005, Pages 247-264

A mathematical model of dynamic glioma-host interactions: Receptor-mediated invasion and local proteolysis

Author keywords

Glioma; Hapto taxis; Integrin; Mathematical model; Proteinase

Indexed keywords

ENZYME ACTIVITY; PROTEOLYSIS;

EID: 24044462932     PISSN: 14778599     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb/dqi010     Document Type: Article
Times cited : (7)

References (57)
  • 2
    • 0019188958 scopus 로고
    • Biased random walk models for chemotaxis and related diffusion approximations
    • Alt, W. (1980) Biased random walk models for chemotaxis and related diffusion approximations. J. Math. Biol., 9, 147-177.
    • (1980) J. Math. Biol. , vol.9 , pp. 147-177
    • Alt, W.1
  • 4
    • 3843079723 scopus 로고    scopus 로고
    • A history of the study of solid tumour growth: The contribution of mathematical modelling
    • Araujo, R. & McElwain, D. L. S. (2004) A history of the study of solid tumour growth: The contribution of mathematical modelling. Bull. Math. Biol., 66, 1039-1091.
    • (2004) Bull. Math. Biol. , vol.66 , pp. 1039-1091
    • Araujo, R.1    McElwain, D.L.S.2
  • 6
    • 0033601769 scopus 로고    scopus 로고
    • Membrane-type matrix metalloprotease (MT1-MMP) enables invasive migration of glioma cells in central nervous system white matter
    • Beliën, A. T. J., Paganetti, P. A. & Schwab, M. E. (1999) Membrane-type matrix metalloprotease (MT1-MMP) enables invasive migration of glioma cells in central nervous system white matter. J. Cell Biol., 144, 373-384.
    • (1999) J. Cell Biol. , vol.144 , pp. 373-384
    • Beliën, A.T.J.1    Paganetti, P.A.2    Schwab, M.E.3
  • 7
    • 0020964054 scopus 로고
    • Mathematical model for contact inhibited cell division
    • Bergman, M. O. (1983) Mathematical model for contact inhibited cell division. J. Theor. Biol., 102, 375-386.
    • (1983) J. Theor. Biol. , vol.102 , pp. 375-386
    • Bergman, M.O.1
  • 8
    • 0022545416 scopus 로고
    • Glioma cell interactions with fetal rat brain aggregates in vitro and with brain tissue in vivo
    • Bjerkvig, R., Laerum, O. D. & Mella, O. (1986) Glioma cell interactions with fetal rat brain aggregates in vitro and with brain tissue in vivo. Cancer Res., 46, 4071-4079.
    • (1986) Cancer Res. , vol.46 , pp. 4071-4079
    • Bjerkvig, R.1    Laerum, O.D.2    Mella, O.3
  • 9
    • 0030832962 scopus 로고    scopus 로고
    • The interaction of growth rates and diffusion coefficients in a three-dimensional mathematical of gliomas
    • Burgess, P. K., Kulesa, P. M., Murray, J. D. & Alvord, E. C. (1997) The interaction of growth rates and diffusion coefficients in a three-dimensional mathematical of gliomas. J. Neuropathol. Exp. Neurol., 56, 704-713.
    • (1997) J. Neuropathol. Exp. Neurol. , vol.56 , pp. 704-713
    • Burgess, P.K.1    Kulesa, P.M.2    Murray, J.D.3    Alvord, E.C.4
  • 13
    • 0032844761 scopus 로고    scopus 로고
    • Matrix metalloproteinases and their biological function in human gliomas
    • Chintala, S. K., Tonn, J. C. & Rao, J. S. (1999) Matrix metalloproteinases and their biological function in human gliomas. Int. J. Dev. Neurosci., 17, 495-502.
    • (1999) Int. J. Dev. Neurosci. , vol.17 , pp. 495-502
    • Chintala, S.K.1    Tonn, J.C.2    Rao, J.S.3
  • 14
    • 0032556238 scopus 로고    scopus 로고
    • A continuum analysis of the chemotactic signal seen by Dictyostelium discoideum
    • Dallon, J. C. & Othmer, H. G. (1998) A continuum analysis of the chemotactic signal seen by Dictyostelium discoideum. J. Theor. Biol. 194, 461-483.
    • (1998) J. Theor. Biol. , vol.194 , pp. 461-483
    • Dallon, J.C.1    Othmer, H.G.2
  • 15
    • 0034792908 scopus 로고    scopus 로고
    • Migratory activity of human glioma cell lines in vitro assessed by continuous single cell observation
    • Demuth, T., Hopf, N. J., Kempski, O., Sauner, D., Herr, M., Giese, A. & Perneczky, A. (2001) Migratory activity of human glioma cell lines in vitro assessed by continuous single cell observation. Clin. Exp. Metastasis, 18, 589-597.
    • (2001) Clin. Exp. Metastasis , vol.18 , pp. 589-597
    • Demuth, T.1    Hopf, N.J.2    Kempski, O.3    Sauner, D.4    Herr, M.5    Giese, A.6    Perneczky, A.7
  • 17
    • 0025062882 scopus 로고
    • Quantitative relationships between single-cell and cell-population model parameters for chemosensory migration responses of alveolar macrophages to c5a
    • Farrell, B. E., Daniele, R. P. & Lauffenburger, D. A. (1990) Quantitative relationships between single-cell and cell-population model parameters for chemosensory migration responses of alveolar macrophages to c5a. Cell Motil. Cytoskeleton, 16, 279-293.
    • (1990) Cell Motil. Cytoskeleton , vol.16 , pp. 279-293
    • Farrell, B.E.1    Daniele, R.P.2    Lauffenburger, D.A.3
  • 19
    • 0029995767 scopus 로고    scopus 로고
    • Glioma invasion in the central nervous system
    • Giese, A. & Westphal, M. (1996) Glioma invasion in the central nervous system. Neurosurgery, 39, 235-252.
    • (1996) Neurosurgery , vol.39 , pp. 235-252
    • Giese, A.1    Westphal, M.2
  • 20
    • 0141681060 scopus 로고    scopus 로고
    • Complex dynamics of tumours: Modelling an emerging brain tumor system with coupled reaction-diffusion equations
    • Habib, S.,Molina-Paris, C. & Deisboeck, T. S. (2003) Complex dynamics of tumours: Modelling an emerging brain tumor system with coupled reaction-diffusion equations. Physica A, 327, 501-524.
    • (2003) Physica A , vol.327 , pp. 501-524
    • Habib, S.1    Molina-Paris, C.2    Deisboeck, T.S.3
  • 21
    • 0033997062 scopus 로고    scopus 로고
    • Locomotion and proliferation of glioblastoma cells in vitro: Statistical evaluation of videomicroscopic observations
    • Hegedüs, B., Czirók, A., Fazekas, I., Bábel, T., Madarász, E. & Vicsek, T. (2000) Locomotion and proliferation of glioblastoma cells in vitro: Statistical evaluation of videomicroscopic observations. J. Neurosurg., 92, 428-434.
    • (2000) J. Neurosurg. , vol.92 , pp. 428-434
    • Hegedüs, B.1    Czirók, A.2    Fazekas, I.3    Bábel, T.4    Madarász, E.5    Vicsek, T.6
  • 22
    • 58149209141 scopus 로고
    • Cellular pattern formation during dictyostelium aggregation
    • Hoefer, T., Sherratt, J. A. & Maini, P. K. (1995) Cellular pattern formation during dictyostelium aggregation. Physica D, 85, 425-444.
    • (1995) Physica D , vol.85 , pp. 425-444
    • Hoefer, T.1    Sherratt, J.A.2    Maini, P.K.3
  • 23
    • 0026770377 scopus 로고
    • Integrins: Versatility, modulation, and signalling in cell adhesion
    • Hynes, R. O. (1992) Integrins: Versatility, modulation, and signalling in cell adhesion. Cell, 69, 11-25.
    • (1992) Cell , vol.69 , pp. 11-25
    • Hynes, R.O.1
  • 24
    • 0036846937 scopus 로고    scopus 로고
    • A mechanical model of tumour encapsulation and transcapsular spread
    • Jackson, T. L. & Byrne, H. M. (2002) A mechanical model of tumour encapsulation and transcapsular spread. Math. Biosci., 18, 307-328.
    • (2002) Math. Biosci. , vol.18 , pp. 307-328
    • Jackson, T.L.1    Byrne, H.M.2
  • 26
    • 0015010990 scopus 로고
    • Travelling bands of chemotactic bacteria: A theoretical analysis
    • Keller, E. F. & Segel, L. A. (1971b) Travelling bands of chemotactic bacteria: A theoretical analysis. J. Theor. Biol., 30, 235-248.
    • (1971) J. Theor. Biol. , vol.30 , pp. 235-248
    • Keller, E.F.1    Segel, L.A.2
  • 28
    • 0017117005 scopus 로고
    • Model for the chemotactic response of a bacterial population
    • Lapidus, I. R. & Schiller, R. (1976) Model for the chemotactic response of a bacterial population. Biophys. J., 16, 779-789.
    • (1976) Biophys. J. , vol.16 , pp. 779-789
    • Lapidus, I.R.1    Schiller, R.2
  • 29
    • 0024927313 scopus 로고
    • A simple model for the effects of receptor-mediated cell-substratum adhesion on cell migration
    • Lauffenburger, D. (1989) A simple model for the effects of receptor-mediated cell-substratum adhesion on cell migration. Chem. Eng. Sci., 44, 1903-1914.
    • (1989) Chem. Eng. Sci. , vol.44 , pp. 1903-1914
    • Lauffenburger, D.1
  • 30
    • 0020687624 scopus 로고
    • Measurement of phenomenological parameters for leukocyte motility and chemotaxis
    • Lauffenburger, D. A. (1983) Measurement of phenomenological parameters for leukocyte motility and chemotaxis. Agents Actions Suppl., 12, 34-53.
    • (1983) Agents Actions Suppl. , vol.12 , pp. 34-53
    • Lauffenburger, D.A.1
  • 31
    • 0010346306 scopus 로고
    • Travelling bands of chemotactic bacteria in the context of population growth
    • Lauffenburger, D., Kennedy, C. R. & Aris, R. (1984) Travelling bands of chemotactic bacteria in the context of population growth. Bull. Math. Biol., 46, 19-40.
    • (1984) Bull. Math. Biol. , vol.46 , pp. 19-40
    • Lauffenburger, D.1    Kennedy, C.R.2    Aris, R.3
  • 33
    • 2342646187 scopus 로고    scopus 로고
    • Travelling wave model to interpret a woundhealing cell migration assay for human peritoneal mesothelial cells
    • Maini, P. K., McElwain, D. L. S. & Leavesley, D. I. (2004) Travelling wave model to interpret a woundhealing cell migration assay for human peritoneal mesothelial cells. Tissue Eng., 10, 475-482.
    • (2004) Tissue Eng. , vol.10 , pp. 475-482
    • Maini, P.K.1    McElwain, D.L.S.2    Leavesley, D.I.3
  • 34
    • 0344845476 scopus 로고    scopus 로고
    • Modelling cell invasion
    • PhD Thesis, Oxford University, Oxford, UK
    • Marchant, B. (1999) Modelling cell invasion. PhD Thesis, Oxford University, Oxford, UK.
    • (1999)
    • Marchant, B.1
  • 35
    • 0034564115 scopus 로고    scopus 로고
    • Travelling shock waves arising in a model of malignant invasion
    • Marchant, B. P., Norbury, J. & Perumpanani, A. J. (2000) Travelling shock waves arising in a model of malignant invasion. SIAM J. Appl. Math., 60, 463-476.
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 463-476
    • Marchant, B.P.1    Norbury, J.2    Perumpanani, A.J.3
  • 36
    • 0035511361 scopus 로고    scopus 로고
    • Travelling wave solutions to a haptotaxis-dominated model of malignant invasion
    • Marchant, B. P., Norbury, J. & Sherratt, J. A. (2001) Travelling wave solutions to a haptotaxis-dominated model of malignant invasion. Nonlinearity, 14, 1653-1671.
    • (2001) Nonlinearity , vol.14 , pp. 1653-1671
    • Marchant, B.P.1    Norbury, J.2    Sherratt, J.A.3
  • 37
    • 0032721665 scopus 로고    scopus 로고
    • Role of integrins in cancer: Survey of expression patterns
    • Mizejewski, G. J. (1999) Role of integrins in cancer: Survey of expression patterns. Proc. Soc. Exp. Biol. Med., 222, 124-138.
    • (1999) Proc. Soc. Exp. Biol. Med. , vol.222 , pp. 124-138
    • Mizejewski, G.J.1
  • 38
    • 0032820711 scopus 로고    scopus 로고
    • Proteolysis and cell migration: Creating a path?
    • Murphy, G. & Gavrilovic, J. (1999) Proteolysis and cell migration: creating a path? Curr. Opin. Cell. Biol., 11, 614-621.
    • (1999) Curr. Opin. Cell. Biol. , vol.11 , pp. 614-621
    • Murphy, G.1    Gavrilovic, J.2
  • 41
    • 0031976733 scopus 로고    scopus 로고
    • Physical and biochemical regulation of integrin release during rear detachment of migrating cells
    • Palecek, S. P., Huttenlocher, A., Horwitz, A. F. & Lauffenburger, D. A. (1998) Physical and biochemical regulation of integrin release during rear detachment of migrating cells. J. Cell Sci., 111, 929-940.
    • (1998) J. Cell Sci. , vol.111 , pp. 929-940
    • Palecek, S.P.1    Huttenlocher, A.2    Horwitz, A.F.3    Lauffenburger, D.A.4
  • 42
    • 0032767250 scopus 로고    scopus 로고
    • Extracellular matrix concentration exerts selection pressure on invasive cells
    • Perumpanani, A. J. & Byrne, H. M. (1999) Extracellular matrix concentration exerts selection pressure on invasive cells. Eur. J. Cancer, 35, 1274-1280.
    • (1999) Eur. J. Cancer , vol.35 , pp. 1274-1280
    • Perumpanani, A.J.1    Byrne, H.M.2
  • 44
    • 0028003498 scopus 로고
    • Chemotaxis and chemokinesis in eukaryotic cells: The Keller-Segel equations as an approximation to a detailed model
    • 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, 129-146.
    • (1994) Bull. Math. Biol. , vol.56 , pp. 129-146
    • Sherratt, J.A.1
  • 45
    • 0027214763 scopus 로고
    • Chemical control of eukaryotic cell movement: A new model
    • Sherratt, J. A., Sage, E. H. & Murray, J. D. (1993) Chemical control of eukaryotic cell movement: A new model. J. Theor. Biol., 162, 23-40.
    • (1993) J. Theor. Biol. , vol.162 , pp. 23-40
    • Sherratt, J.A.1    Sage, E.H.2    Murray, J.D.3
  • 46
    • 0035000670 scopus 로고    scopus 로고
    • Proteases in invasion: Matrix metalloproteinases
    • Stetler-Stevenson, W. G. & Yu, A. E. (2001) Proteases in invasion: matrix metalloproteinases. Semin. Cancer Biol., 11, 143-152.
    • (2001) Semin. Cancer Biol. , vol.11 , pp. 143-152
    • Stetler-Stevenson, W.G.1    Yu, A.E.2
  • 47
    • 0033752019 scopus 로고    scopus 로고
    • A quantitative model for differential motility of gliomas in grey and white matter
    • Swanson, K. R., Alvord, E. C. & Murray, J. D. (2000) A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif., 33, 317-329.
    • (2000) Cell Prolif. , vol.33 , pp. 317-329
    • Swanson, K.R.1    Alvord, E.C.2    Murray, J.D.3
  • 48
    • 0037033735 scopus 로고    scopus 로고
    • Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy
    • Swanson, K. R., Alvord, E. C. & Murray, J. D. (2002) Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Br. J. Cancer, 86, 14-18.
    • (2002) Br. J. Cancer , vol.86 , pp. 14-18
    • Swanson, K.R.1    Alvord, E.C.2    Murray, J.D.3
  • 49
    • 0037560896 scopus 로고    scopus 로고
    • Virtual resection of gliomas: Effect of extent of resection on recurrence
    • Swanson, K. R., Alvord, E. C. & Murray, J. D. (2003a) Virtual resection of gliomas: Effect of extent of resection on recurrence. Math. Comput. Model., 37, 1177-1190.
    • (2003) Math. Comput. Model. , vol.37 , pp. 1177-1190
    • Swanson, K.R.1    Alvord, E.C.2    Murray, J.D.3
  • 50
    • 0242607878 scopus 로고    scopus 로고
    • Virtual and real brain tumours: Using mathematical modelling to quantify glioma growth and invasion
    • Swanson, K. R., Bridge, C., Murray, J. D. & Alvord, E. C. (2003b) Virtual and real brain tumours: Using mathematical modelling to quantify glioma growth and invasion. J. Neurol. Sci., 216, 1-10.
    • (2003) J. Neurol. Sci. , vol.216 , pp. 1-10
    • Swanson, K.R.1    Bridge, C.2    Murray, J.D.3    Alvord, E.C.4
  • 51
    • 0028936012 scopus 로고
    • A mathematical model of glioma growth: The effect of chemotherapy on spatio-temporal growth
    • Tracqui, P., Cruywagen, G. C., Woodward, D. E., Bartoo, G. T., Murray, J. D. & Alvord, E. C. (1995) A mathematical model of glioma growth: The effect of chemotherapy on spatio-temporal growth. Cell Prolif., 28, 17-31.
    • (1995) Cell Prolif. , vol.28 , pp. 17-31
    • Tracqui, P.1    Cruywagen, G.C.2    Woodward, D.E.3    Bartoo, G.T.4    Murray, J.D.5    Alvord, E.C.6
  • 52
    • 0023779971 scopus 로고
    • Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay
    • Tranquillo, R. T., Zigmond, S. H. & Lauffenburger, D. A. (1988) Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay. Cell Motil. Cytoskeleton, 11, 1-15.
    • (1988) Cell Motil. Cytoskeleton , vol.11 , pp. 1-15
    • Tranquillo, R.T.1    Zigmond, S.H.2    Lauffenburger, D.A.3
  • 53
    • 0033556841 scopus 로고    scopus 로고
    • The role of integrins in the malignant phenotype of gliomas
    • Uhm, J. H., Gladston, C. L. & Rao, J. S. (1999) The role of integrins in the malignant phenotype of gliomas. Front. Biosci., 4, 188-199.
    • (1999) Front. Biosci. , vol.4 , pp. 188-199
    • Uhm, J.H.1    Gladston, C.L.2    Rao, J.S.3
  • 55
    • 0034234046 scopus 로고    scopus 로고
    • Cell kinetics: Mathematical models and experimental bases
    • White, R. A. & Terry, N. A. H. (2000) Cell kinetics: Mathematical models and experimental bases. Math. Comput. Model, 32, 113-124.
    • (2000) Math. Comput. Model , vol.32 , pp. 113-124
    • White, R.A.1    Terry, N.A.H.2
  • 56
  • 57


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