메뉴 건너뛰기




Volumn 47, Issue 7-8, 2008, Pages 699-713

Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle

Author keywords

Cell division cycle; Eigenelements; Entropy method; Structured population equations

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; MOLECULAR STRUCTURE; NONLINEAR ANALYSIS; POLYNOMIAL APPROXIMATION; TISSUE;

EID: 40249088253     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2007.06.008     Document Type: Article
Times cited : (35)

References (43)
  • 1
    • 15744401788 scopus 로고    scopus 로고
    • On the stability of a nonlinear maturity structured model of cellular proliferation
    • Adimy M., Crauste F., and Pujo-Menjouet L. On the stability of a nonlinear maturity structured model of cellular proliferation. Discrete Contin. Dyn. Syst. 12 3 (2005) 501-502
    • (2005) Discrete Contin. Dyn. Syst. , vol.12 , Issue.3 , pp. 501-502
    • Adimy, M.1    Crauste, F.2    Pujo-Menjouet, L.3
  • 3
    • 0029321234 scopus 로고
    • A survey of structured cell population dynamics
    • Arino O. A survey of structured cell population dynamics. Acta Biotheor. 43 (1995) 3-25
    • (1995) Acta Biotheor. , vol.43 , pp. 3-25
    • Arino, O.1
  • 4
    • 0031272189 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence
    • Arino O., Sanchez E., and Webb G.F. Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence. J. Math. Anal. Appl. 215 (1997) 499-513
    • (1997) J. Math. Anal. Appl. , vol.215 , pp. 499-513
    • Arino, O.1    Sanchez, E.2    Webb, G.F.3
  • 5
    • 0242515913 scopus 로고    scopus 로고
    • The JNK cascade as a biochemical switch in mammalian cells: Ultrasensitive and all-or-none responses
    • Bagowski C.P., Besser J., Frey C.R., and Ferrell J.E. The JNK cascade as a biochemical switch in mammalian cells: Ultrasensitive and all-or-none responses. Curr. Biol. 13 (2003) 315-320
    • (2003) Curr. Biol. , vol.13 , pp. 315-320
    • Bagowski, C.P.1    Besser, J.2    Frey, C.R.3    Ferrell, J.E.4
  • 6
    • 0036491845 scopus 로고    scopus 로고
    • The restriction point of the cell cycle
    • Blagosklonny M.V., and Pardee A.B. The restriction point of the cell cycle. Cell Cycle 1 2 (2002) 103-105
    • (2002) Cell Cycle , vol.1 , Issue.2 , pp. 103-105
    • Blagosklonny, M.V.1    Pardee, A.B.2
  • 7
    • 40249111097 scopus 로고    scopus 로고
    • F. Bekkal Brikci, Ph.D. Thesis, Univ. Paris 6, 2005
    • F. Bekkal Brikci, Ph.D. Thesis, Univ. Paris 6, 2005
  • 8
    • 40249094047 scopus 로고    scopus 로고
    • F. Bekkal Brikci, J. Clairambault, B. Ribba, B. Perthame, An age-and-cyclin-structured cell population model with proliferation and quiescence, J. Math. Biol. (2007) (in press)
    • F. Bekkal Brikci, J. Clairambault, B. Ribba, B. Perthame, An age-and-cyclin-structured cell population model with proliferation and quiescence, J. Math. Biol. (2007) (in press)
  • 10
    • 40249101349 scopus 로고    scopus 로고
    • F. Bouchut, Nonlinear stability of finite for volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Series 'Frontiers in Mathematics', Birkhauser, 2004
    • F. Bouchut, Nonlinear stability of finite for volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Series 'Frontiers in Mathematics', Birkhauser, 2004
  • 11
    • 33845228647 scopus 로고    scopus 로고
    • Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model
    • Carrillo J.A., Cuadrado S., and Perthame B. Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model. Math. Biosci. 205 1 (2007) 137-161
    • (2007) Math. Biosci. , vol.205 , Issue.1 , pp. 137-161
    • Carrillo, J.A.1    Cuadrado, S.2    Perthame, B.3
  • 13
    • 0031884748 scopus 로고    scopus 로고
    • On the proposal of a G0 phase and the restriction point
    • Cooper S. On the proposal of a G0 phase and the restriction point. FASEB J. 12 (1998) 367-373
    • (1998) FASEB J. , vol.12 , pp. 367-373
    • Cooper, S.1
  • 15
    • 26944481103 scopus 로고    scopus 로고
    • A single-cell-based model of tumor growth in vitro: Monolayers and spheroids
    • Drasdo D., and Höhme S. A single-cell-based model of tumor growth in vitro: Monolayers and spheroids. Phys. Biol. 2 3 (2005) 133-147
    • (2005) Phys. Biol. , vol.2 , Issue.3 , pp. 133-147
    • Drasdo, D.1    Höhme, S.2
  • 16
    • 0003561274 scopus 로고
    • Hyperbolic systems of conservation laws
    • Ellipses, Paris
    • Godlewski E., and Raviart P. Hyperbolic systems of conservation laws. Coll. SMAI, vols. 3-4 (1991), Ellipses, Paris
    • (1991) Coll. SMAI, vols. 3-4
    • Godlewski, E.1    Raviart, P.2
  • 18
    • 0025687227 scopus 로고
    • A nonlinear structured population model of tumor growth with quiescence
    • Gyllenberg M., and Webb G.F. A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol. 28 (1990) 671-694
    • (1990) J. Math. Biol. , vol.28 , pp. 671-694
    • Gyllenberg, M.1    Webb, G.F.2
  • 19
    • 38249034676 scopus 로고
    • Age-size structure in populations with quiescence
    • Gyllenberg M., and Webb G.F. Age-size structure in populations with quiescence. Math. Biosci. 86 (1987) 67-95
    • (1987) Math. Biosci. , vol.86 , pp. 67-95
    • Gyllenberg, M.1    Webb, G.F.2
  • 21
    • 0028568315 scopus 로고
    • Cell cycle control and cancer
    • Hartwell L.H., and Kastan M.B. Cell cycle control and cancer. Science 266 (1994) 1821-1828
    • (1994) Science , vol.266 , pp. 1821-1828
    • Hartwell, L.H.1    Kastan, M.B.2
  • 22
    • 0032999249 scopus 로고    scopus 로고
    • Cellular ras and cyclin D1 are required during different cell cycle phases in cycling NIH 3T3 cells
    • Hitomi M., and Stacey D.W. Cellular ras and cyclin D1 are required during different cell cycle phases in cycling NIH 3T3 cells. Mol. Cell. Biol. 19 7 (1999) 4623-4632
    • (1999) Mol. Cell. Biol. , vol.19 , Issue.7 , pp. 4623-4632
    • Hitomi, M.1    Stacey, D.W.2
  • 23
    • 0021689153 scopus 로고
    • Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis
    • Kimmel M., Darzynkiewicz Z., Arino O., and Traganos F. Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis. J. Theor. Biol. 110 (1984) 637-664
    • (1984) J. Theor. Biol. , vol.110 , pp. 637-664
    • Kimmel, M.1    Darzynkiewicz, Z.2    Arino, O.3    Traganos, F.4
  • 24
    • 40249083664 scopus 로고    scopus 로고
    • R.J. Leveque, Finite Volume Methods for Hyperbolic Problem, in: Cambridge Textbooks in Applied Mathematics, 2002
    • R.J. Leveque, Finite Volume Methods for Hyperbolic Problem, in: Cambridge Textbooks in Applied Mathematics, 2002
  • 25
    • 0142103779 scopus 로고    scopus 로고
    • Cdx1 inhibits the proliferation of human colon cancer cells by reducing cyclin D1 gene expression
    • Lynch J., Keller M., Guo R.J., Yang D., and Traber P. Cdx1 inhibits the proliferation of human colon cancer cells by reducing cyclin D1 gene expression. Oncogene 22 41 (2003) 6395-6407
    • (2003) Oncogene , vol.22 , Issue.41 , pp. 6395-6407
    • Lynch, J.1    Keller, M.2    Guo, R.J.3    Yang, D.4    Traber, P.5
  • 26
    • 0037541605 scopus 로고    scopus 로고
    • A new criterion for the global stability of simultaneous cell replication and maturation processes
    • Mackey M.C., and Rudnicki R. A new criterion for the global stability of simultaneous cell replication and maturation processes. J. Math. Biol. 38 (1999) 195-219
    • (1999) J. Math. Biol. , vol.38 , pp. 195-219
    • Mackey, M.C.1    Rudnicki, R.2
  • 27
    • 31744445362 scopus 로고    scopus 로고
    • Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses
    • Foley C., Bernard S., and Mackey M.C. Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses. J. Theor. Biol. 238 (2006) 754-763
    • (2006) J. Theor. Biol. , vol.238 , pp. 754-763
    • Foley, C.1    Bernard, S.2    Mackey, M.C.3
  • 28
    • 24044522878 scopus 로고    scopus 로고
    • General relative entropy inequality: An illustration on growth models
    • Michel P., Mischler S., and Perthame B. General relative entropy inequality: An illustration on growth models. J. Math. Pures Appl. 84 9 (2005) 1235-1260
    • (2005) J. Math. Pures Appl. , vol.84 , Issue.9 , pp. 1235-1260
    • Michel, P.1    Mischler, S.2    Perthame, B.3
  • 29
    • 33750058285 scopus 로고    scopus 로고
    • Existence of a solution to the cell division eigenproblem
    • Michel P. Existence of a solution to the cell division eigenproblem. Math. Models Methods Appl. Sci 16 Suppl. 1 (2006) 1125-1153
    • (2006) Math. Models Methods Appl. Sci , vol.16 , Issue.SUPPL. 1 , pp. 1125-1153
    • Michel, P.1
  • 31
    • 4444349425 scopus 로고    scopus 로고
    • A model for restriction point control of the mammalian cell cycle
    • Novak B., and Tyson J.J. A model for restriction point control of the mammalian cell cycle. J. Theor. Biol. 230 (2004) 563-579
    • (2004) J. Theor. Biol. , vol.230 , pp. 563-579
    • Novak, B.1    Tyson, J.J.2
  • 32
    • 0032834675 scopus 로고    scopus 로고
    • A model of cell cycle behavior dominated by kinetics of a pathway stimulated by growth factors
    • Obeyesekere M., and Zimmerman S.O. A model of cell cycle behavior dominated by kinetics of a pathway stimulated by growth factors. Bull. Math. Biol. 61 (1999) 917-934
    • (1999) Bull. Math. Biol. , vol.61 , pp. 917-934
    • Obeyesekere, M.1    Zimmerman, S.O.2
  • 33
    • 44349187159 scopus 로고    scopus 로고
    • Transport equations in biology
    • Birkhauser
    • Perthame B. Transport equations in biology. Frontiers in Mathematics (2006), Birkhauser
    • (2006) Frontiers in Mathematics
    • Perthame, B.1
  • 34
    • 12344315077 scopus 로고    scopus 로고
    • Exponential decay for the fragmentation or cell-division equation
    • Perthame B., and Ryzhik L. Exponential decay for the fragmentation or cell-division equation. J. Differential Equations 210 (2005) 155-177
    • (2005) J. Differential Equations , vol.210 , pp. 155-177
    • Perthame, B.1    Ryzhik, L.2
  • 35
    • 0037302108 scopus 로고    scopus 로고
    • Regulation of the mammalian cell cycle: A model of the G1-to-S transition
    • Qu Z., Weiss J.N., and MacLellan W.R. Regulation of the mammalian cell cycle: A model of the G1-to-S transition. Am. J. Physiol. Cell. Physiol. 284 (2003) 349-364
    • (2003) Am. J. Physiol. Cell. Physiol. , vol.284 , pp. 349-364
    • Qu, Z.1    Weiss, J.N.2    MacLellan, W.R.3
  • 36
    • 2142746050 scopus 로고
    • Asynchronous exponential growth in a size structured cell population with quiescent compartment
    • Arino O., et al. (Ed) (Chapter 14)
    • Rossa B. Asynchronous exponential growth in a size structured cell population with quiescent compartment. In: Arino O., et al. (Ed). Carcinogenesis and Cell and Tumor Growth. Vol. 2 (1995) 183-200 (Chapter 14)
    • (1995) Carcinogenesis and Cell and Tumor Growth. Vol. 2 , pp. 183-200
    • Rossa, B.1
  • 37
    • 0033529122 scopus 로고    scopus 로고
    • Molecular mechanisms underlying interferon-alpha-induced G0/G1 arrest: CKI-mediated regulation of G1 Cdk-complexes and activation of pocket proteins
    • May 6
    • Sangfelt O., Erickson S., Castro J., Heiden T., Gustafsson A., Einhorn S., and Grander D. Molecular mechanisms underlying interferon-alpha-induced G0/G1 arrest: CKI-mediated regulation of G1 Cdk-complexes and activation of pocket proteins. Oncogene 18 18 (1999) 2798-2810 May 6
    • (1999) Oncogene , vol.18 , Issue.18 , pp. 2798-2810
    • Sangfelt, O.1    Erickson, S.2    Castro, J.3    Heiden, T.4    Gustafsson, A.5    Einhorn, S.6    Grander, D.7
  • 39
    • 13944272143 scopus 로고    scopus 로고
    • Aging and death in an organism that reproduces by morphologically symmetric division
    • 0295-300
    • Stewart E.J., Madden R., Paul G., and Taddei F. Aging and death in an organism that reproduces by morphologically symmetric division. PLoS Biol. 3 2 (2005) e45 0295-300
    • (2005) PLoS Biol. , vol.3 , Issue.2
    • Stewart, E.J.1    Madden, R.2    Paul, G.3    Taddei, F.4
  • 41
    • 0006310426 scopus 로고    scopus 로고
    • A purely deterministic model for the population dynamics of budding yeast
    • Arino O., Axelrod D., and Kimmel M. (Eds), World Scientific
    • Val J., and Tyson J. A purely deterministic model for the population dynamics of budding yeast. In: Arino O., Axelrod D., and Kimmel M. (Eds). Advances in Mathematical Population Dynamics - Molecules, Cells and Man (1997), World Scientific
    • (1997) Advances in Mathematical Population Dynamics - Molecules, Cells and Man
    • Val, J.1    Tyson, J.2
  • 42
    • 0001888697 scopus 로고
    • Cell cycle progression and cell growth in mammalian cells: Kinetic aspects of transition events
    • Hutchinson C., and Glover D.M. (Eds), Oxford University Press, Oxford, New York
    • Zetterberg A., and Larsson O. Cell cycle progression and cell growth in mammalian cells: Kinetic aspects of transition events. In: Hutchinson C., and Glover D.M. (Eds). Cell Cycle Control (1995), Oxford University Press, Oxford, New York 206-227
    • (1995) Cell Cycle Control , pp. 206-227
    • Zetterberg, A.1    Larsson, O.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.