Oscillations in a molecular structured cell population model

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 4, 2011, Pages 1911-1922

  Borges, Ricardo ^a   Calsina, Àngel ^a   Cuadrado, Sílvia ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Numerical simulation; Oscillations; Structured cell population

Indexed keywords

CELL POPULATIONS; EXISTENCE OF SOLUTIONS; NUMERICAL SIMULATION; OSCILLATIONS; STEADY STATE; STRUCTURED CELL POPULATION; STRUCTURED MODEL;

CELL CULTURE; CELL PROLIFERATION; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; POPULATION STATISTICS;

MATHEMATICAL MODELS;

EID: 79955521918     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.12.007     Document Type: Article

References (30)

1. H. Von Foerster Some remarks on changing populations Frederick Stohlman, The Kinetics of Cellular Proliferation 1959 Grune and Stratton New York 382 407
2. G. Bell, and E. Anderson Cell growth and division. Mathematical model with applications to cell volume distributions in mammalian suspension cultures Biophys. J. 7 1967 329 351
3. J.A.J. Metz, and O. Diekmann The Dynamics of Physiologically Structured Populations, Amsterdam, 1983 Lecture Notes in Biomath. vol. 68 1986 Springer Berlin
4. O. Arino A survey of structured cell population dynamics Acta Biotheor. 43 1995 3 25
5. O. Arino, E. Snchez, and G.F. Webb Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence J. Math. Anal. Appl. 215 2 1997 499 513 (Pubitemid 127175053)
6. M. Adimy, and L. Pujo-Menjouet Asymptotic behavior of a singular transport equation modelling cell division Discrete Contin. Dyn. Syst. Ser. B 3 3 2003 439 456 (Pubitemid 37056597)
7. M. Gyllenberg, and G. Webb Age-size structure in populations with quiescence Math. Biosci. 86 1 1987 67 95
8. B. Rossa Asynchronous exponential growth in a size structured cell population with quiescent compartment O. Arino, D. Axelrod, M. Kimmel, Mathematical Population Dynamics vol. 2 1995 Wuerz Canada
9. J. Dyson, R. Vilella-Bressan, and G. Webb Asynchronous exponential growth in an age structured population of proliferating and quiescent cells Math. Biosci. 177178 2002 73 83 (Pubitemid 34457384)
10. F. Bekkal Brikci, J. Clairambault, B. Ribba, and B. Perthame An age-and-cyclin-structured cell population model with proliferation and quiescence J. Math. Biol. 57 1 2008 91 110
11. F. Bekkal Brikci, J. Clairambault, and B. Perthame Analysis of a molecular structured population model with possible polinomial growth for the cell division cycle Math. Comput. Modelling 47 78 2008 699 713 (Pubitemid 351335335)
12. L.H. Hartwell, and M.B. Kastan Cell cycle control and cancer Science 266 1994 1821 1828
13. M. Umeda, A. Shimotohno, and M. Yamaguchi Control of cell division and transcription by cyclin-dependent kinase-activating kinases in plants Plant Cell Physiol. 46 9 2005 1437 1442 (Pubitemid 41436585)
14. M. Hitomi, and D.W. Stacey 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 (Pubitemid 29289500)
15. D.W. Stacey Cyclin D1 serves as a cell cycle regulatory switch in actively proliferating cells Curr. Option. Cell Biol. 15 2 2003 158 163 (Pubitemid 36332190)
16. M. Doumic Analysis of a population model structured by the cells molecular content Math. Model. Nat. Phenom. 2 3 2007 121 152
17. R. Borges,. Calsina, and S. Cuadrado Equilibria of a cyclin structured cell population model Discrete Contin. Dyn. Syst. Ser. B 11 2009 613 627
18. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J.D. Watson Molecular Biology of the Cell 1994 Garland New York
19. C.P. Bagowski, J. Besser, C.R. Frey, and J.E. Ferrell The JNK cascade as a biochemical switch in mammalian cells: ultrasensitive and all-or-none responses Curr. Biol. 13 4 2003 315 320 (Pubitemid 36230022)
20. C.J. Sherr D-type cyclins Trends Biochem. Sci. 20 5 1995 187 190
21. K. Yang, M. Hitomi, and D.W. Stacey Variations in cyclin D1 levels through the cell cycle determine the proliferative fate of a cell Cell Div. 1 32 2006
22. M. Kimmel, Z. Darzynkiewicz, O. Arino, and F. Traganos Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis J. Theoret. Biol. 110 4 1984 637 664 (Pubitemid 15185681)
23. O. Arino, and M. Kimmel Asymptotic analysis of a cell cycle model based on unequal division SIAM J. Appl. Math. 47 1987 128 145 (Pubitemid 17515963)
24. O. Arino, and M. Kimmel Asymptotic behavior of a nonlinear functional-integral equation of cell kinetics with unequal division J. Math. Biol. 27 1989 341 354
25. F. Bekkal-Brikci, G. Chiorino, and K. Boushaba G1/S transition and cell population dynamics Netw. Heterog. Media 4 1 2009 67 90
26. C. Foley, S. Bernard, and M.C. Mackey Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses J. Theoret. Biol. 238 4 2006 754 763 (Pubitemid 43175826)
27. D. Sulsky Numerical solution of structured population models. II. Mass structure J. Math. Biol. 32 5 1994 491 514
28. O. Angulo, and J.C. Lpez-Marcos Numerical schemes for size-structured population equations Math. Biosci. 157 12 1999 169 188 (Pubitemid 29165066)
29. T. Kostova An explicit third-order numerical method for size-structured population equations Numer. Methods Partial Differential Equations 19 1 2003 1 21
30. L. Abia, O. Angulo, J.C. Lpez-Marcos, and M.A. Lpez-Marcos Numerical schemes for a size-structured cell population model with equal fission Math. Comput. Modelling 50 2009 653 664