A model for asymmetrical cell division
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1.
Institute of Natural and Mathematical Sciences, Massey University, Auckland
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2.
Institute of Fundamental Sciences, Massey University, Palmerston North
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Received:
01 August 2014
Accepted:
29 June 2018
Published:
01 January 2015
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MSC :
Primary: 34K08, 35L02, 34L10; Secondary: 92C37.
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We present a model that describes the growth, division and death of a cell population structured by size. The model is an extension of that studied by Hall and Wake (1989) and incorporates the asymmetric division of cells. We consider the case of binary asymmetrical splitting in which a cell of size $\xi$ divides into two daughter cells of different sizes and find the steady size distribution (SSD) solution to the non-local differential equation. We then discuss the shape of the SSD solution. The existence of higher eigenfunctions is also discussed.
Citation: Ali Ashher Zaidi, Bruce Van Brunt, Graeme Charles Wake. A model for asymmetrical cell division[J]. Mathematical Biosciences and Engineering, 2015, 12(3): 491-501. doi: 10.3934/mbe.2015.12.491
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Abstract
We present a model that describes the growth, division and death of a cell population structured by size. The model is an extension of that studied by Hall and Wake (1989) and incorporates the asymmetric division of cells. We consider the case of binary asymmetrical splitting in which a cell of size $\xi$ divides into two daughter cells of different sizes and find the steady size distribution (SSD) solution to the non-local differential equation. We then discuss the shape of the SSD solution. The existence of higher eigenfunctions is also discussed.
References
|
[1]
|
J. Math. Biol., 49 (2004), 329-357.
|
|
[2]
|
Mathematical medicine and biology, 21 (2004), 49-61.
|
|
[3]
|
Ph.D thesis, University of Canterbury, New Zealand, 2007.
|
|
[4]
|
Mathematical medicine and biology, 22 (2005), 371-390.
|
|
[5]
|
Communications in Applied and Industrial Mathematics, 1 (2010), 299-308.
|
|
[6]
|
Journal de Mathémathiques Pures et Appliquée, 96 (2011), 334-362.
|
|
[7]
|
J.evol.equ., 1 (2001), 405-409.
|
|
[8]
|
Jour. Math. Biol., 19 (1984), 227-248.
|
|
[9]
|
J. Aust. Math. Soc. Ser. B, 30 (1989), 424-435.
|
|
[10]
|
J. Math. Biol., 30 (1991), 101-123.
|
|
[11]
|
Mathematical Biosciences, 72 (1984), 19-50.
|
|
[12]
|
Commun. Math. Sci., 7 (2009), 503-510.
|
|
[13]
|
St. Paul's London, 1798.
|
|
[14]
|
Proc. Edinburgh Math. Soc., 44 (1926), 98-130.
|
|
[15]
|
Lecture Notes in Biomathematics, 68. Springer-Verlag, Berlin, 1986.
|
|
[16]
|
Comptes Rendus Mathematique, 338 (2004), 697-702.
|
|
[17]
|
J. Math. Pures Appl., 84 (2005), 1235-1260.
|
|
[18]
|
Genes Dev., 23 (2009), 2675-2699.
|
|
[19]
|
Journal of Differential Equations, 210 (2005), 155-177.
|
|
[20]
|
Differential and Integral Equations, 24 (2011), 787-799.
|
|
[21]
|
European Journal of Applied Mathematics, 12 (2001), 625-644.
|
|
[22]
|
ANZIAM J., 51 (2010), 383-393.
|
-
-
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