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Volumn 4, Issue 3, 2009, Pages 183-209

Comparison of perron and floquet eigenvalues in age structured cell division cycle models

Author keywords

cell cycle; chronotherapy; circadian rhythms; delay differential equations; structured pdes

Indexed keywords

CELL CULTURE; CELL PROLIFERATION; CELLS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; GROWTH RATE;

EID: 77950847287     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20094308     Document Type: Article
Times cited : (26)

References (26)
  • 1
    • 0029321234 scopus 로고
    • A survey of structured cell population dynamics
    • O. Arino. A survey of structured cell population dynamics. Acta Biotheor., 43 (1995), 3-25.
    • (1995) Acta Biotheor , vol.43 , pp. 3-25
    • Arino, O.1
  • 2
    • 0027678317 scopus 로고
    • Comparison of approaches to modeling of cell population dynamics
    • O. Arino and M. Kimmel. Comparison of approaches to modeling of cell population dynamics. SIAM J. Appl. Math., 53(1993), No. 5, 1480-1504.
    • (1993) SIAM J. Appl. Math. , vol.53 , Issue.5 , pp. 1480-1504
    • Arino, O.1    Kimmel, M.2
  • 3
    • 0006339222 scopus 로고    scopus 로고
    • A survey of cell population dynamics
    • O. Arino and E. Sanchez. A survey of cell population dynamics. J. Theor. Med., 1 (1997), No. 1, 35-51.
    • (1997) J. Theor. Med. , vol.1 , Issue.1 , pp. 35-51
    • Arino, O.1    Sanchez, E.2
  • 4
    • 34447508363 scopus 로고    scopus 로고
    • Why do cells cycle with a 24 hour period?
    • S. Bernard and H. Herzel. Why do cells cycle with a 24 hour period? Genome Inform., 17, (2006), No. 1, 72-79.
    • (2006) Genome Inform. , vol.17 , Issue.1 , pp. 72-79
    • Bernard, S.1    Herzel, H.2
  • 5
    • 40249088253 scopus 로고    scopus 로고
    • Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle
    • DOI 10.1016/j.mcm.2007.06.008, PII S0895717707002038
    • F. Bekkal Brikci, J. Clairambault, and B. Perthame. Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle. Math. Comput. Modelling, 47 (2008), No. 7-8, 699-713. (Pubitemid 351335335)
    • (2008) Mathematical and Computer Modelling , vol.47 , Issue.7-8 , pp. 699-713
    • Brikci, F.B.1    Clairambault, J.2    Perthame, B.3
  • 6
    • 42149136787 scopus 로고    scopus 로고
    • An age-and-cyclin-structured cell population model for healthy and tumoral tissues
    • F. Bekkal Brikci, J. Clairambault, B. Ribba, and B. Perthame. An age-and-cyclin-structured cell population model for healthy and tumoral tissues. J. Math. Biol., 57 (2008), No. 1, 91-110.
    • (2008) J. Math. Biol. , vol.57 , Issue.1 , pp. 91-110
    • Bekkal Brikci, F.1    Clairambault, J.2    Ribba, B.3    Perthame, B.4
  • 7
    • 36248946181 scopus 로고    scopus 로고
    • An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations
    • J. Clairambault, S. Gaubert, and B. Perthame. An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations. C. R. Math. Acad. Sci. Paris, 345 (2007), No. 10, 549-554.
    • (2007) C. R. Math. Acad. Sci. Paris , vol.345 , Issue.10 , pp. 549-554
    • Clairambault, J.1    Gaubert, S.2    Perthame, B.3
  • 8
    • 30344469914 scopus 로고    scopus 로고
    • Rythme circadien et croissance tumorale
    • DOI 10.1016/j.crma.2005.10.029, PII S1631073X05004930
    • J. Clairambault, P. Michel, and B. Perthame. Circadian rhythm and tumour growth. C. R. Acad. Sci., 342 (2006), No. 1, 17-22. (Pubitemid 43055624)
    • (2006) Comptes Rendus Mathematique , vol.342 , Issue.1 , pp. 17-22
    • Clairambault, J.1    Michel, P.2    Perthame, B.3
  • 9
    • 79951579537 scopus 로고    scopus 로고
    • A mathematical model of the cell cycle and its circadian control, to appear
    • A. Deutsch and L. Brusch and H. Byrne and G. de Vries and H.-P. Herzel (eds), Birkháuser proceedings of ECMTB conference, Dresden 2005)
    • J. Clairambault, P. Michel, and B. Perthame. (2007) A mathematical model of the cell cycle and its circadian control, to appear in Mathematical modeling of Biological Systems, Volume I. A. Deutsch and L. Brusch and H. Byrne and G. de Vries and H.-P. Herzel (eds), Birkháuser, pp 247-259 proceedings of ECMTB conference, Dresden 2005).
    • (2007) Mathematical Modeling of Biological Systems , vol.1 , pp. 247-259
    • Clairambault, J.1    Michel, P.2    Perthame, B.3
  • 11
    • 67650875133 scopus 로고    scopus 로고
    • Analysis of a population model structured by the cells molecular content
    • M. Doumic. Analysis of a population model structured by the cells molecular content. Mathematical Modelling of Natural Phenomena, 2 (2007), No. 3, 121-152.
    • (2007) Mathematical Modelling of Natural Phenomena , vol.2 , Issue.3 , pp. 121-152
    • Doumic, M.1
  • 15
    • 0004151494 scopus 로고
    • Cambridge University Press, New York, NY, USA
    • R. A. Horn and C. R. Johnson. Matrix analysis. Cambridge University Press, New York, NY, USA, 1986.
    • (1986) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 17
    • 51049123421 scopus 로고    scopus 로고
    • Implications of circadian clocks for the rhythmic delivery of cancer therapeutics
    • F. Levi, A. Altinok, J. Clairambault, and A. Goldbeter. Implications of circadian clocks for the rhythmic delivery of cancer therapeutics. Phil. Trans. R. Soc. A, 366 (2008), 3575-3598.
    • (2008) Phil. Trans. R. Soc. A , vol.366 , pp. 3575-3598
    • Levi, F.1    Altinok, A.2    Clairambault, J.3    Goldbeter, A.4
  • 18
    • 33847075354 scopus 로고    scopus 로고
    • Circadian rhythms: Mechanisms and therapeutic implications
    • F. Levi and U. Schibler. Circadian rhythms: mechanisms and therapeutic implications. Annu. Rev. Pharmacol. Toxicol., 47 (2007), 593-628.
    • (2007) Annu. Rev. Pharmacol. Toxicol. , vol.47 , pp. 593-628
    • Levi, F.1    Schibler, U.2
  • 19
    • 0003157238 scopus 로고
    • The dynamics of physiologically structured populations
    • Springer
    • J.A.J. Metz and O. Diekmann. The dynamics of physiologically structured populations, volume 68 of L.N. in biomathematics. Springer, 1986.
    • (1986) L.N. in Biomathematics , vol.68
    • Metz, J.A.J.1    Diekmann, O.2
  • 20
    • 24044522878 scopus 로고    scopus 로고
    • General relative entropy inequality: An illustration on growth models
    • DOI 10.1016/j.matpur.2005.04.001, PII S0021782405000528
    • P. Michel, S. Mischler, and B. Perthame. General relative entropy inequality: an illustration on growth models. J. Math. Pures et Appl., 84 (May 2005), No. 9, 1235-1260. (Pubitemid 41213693)
    • (2005) Journal des Mathematiques Pures et Appliquees , vol.84 , Issue.9 , pp. 1235-1260
    • Michel, P.1    Mischler, S.2    Perthame, B.3
  • 21
    • 79960778152 scopus 로고    scopus 로고
    • The cell cycle
    • Oxford University Press
    • D. O Morgan. The Cell Cycle. Primers in Biology. Oxford University Press, 2007.
    • (2007) Primers in Biology
    • Morgan, D.O.1
  • 23
    • 79960814675 scopus 로고    scopus 로고
    • Modeling the cell division cycle
    • Lund(Sweden), April 15-18
    • B. Novak. Modeling the cell division cycle. Lund(Sweden), April 15-18 1999. Bioinformatics' 99. Available online at: http://cellcycle.mkt.bme.hu/ people/bnovak/pdfek/lund/talk.pdf.
    • (1999) Bioinformatics' 99
    • Novak, B.1
  • 24
    • 36249025671 scopus 로고    scopus 로고
    • Transport equations in biology
    • B. Perthame. Transport equations in biology. Birkháuser, 2007.
    • (2007) Birkháuser
    • Perthame, B.1
  • 25
    • 79960819588 scopus 로고    scopus 로고
    • A report on the discretization of a one-phase model of the cell cycle
    • E. Seijo Solis. A report on the discretization of a one-phase model of the cell cycle. Inria internship report, INRIA, 2006.
    • (2006) Inria Internship Report, INRIA
    • Seijo Solis, E.1


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