A model for asymmetrical cell division

Ali Ashher Zaidi; Bruce Van Brunt; Graeme Charles Wake

doi:10.3934/mbe.2015.12.491

Article Contents

2015, Volume 12, Issue 3: 491-501. Doi: 10.3934/mbe.2015.12.491

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A model for asymmetrical cell division

1.
Institute of Natural and Mathematical Sciences, Massey University, Auckland
2.
Institute of Fundamental Sciences, Massey University, Palmerston North

Received: July 31, 2014

Revised: October 31, 2014

Published: December 2014

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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.

Keywords:

Functional differential equations,
eigenfunctions,
cell biology,
hyperbolic partial differential equations.

Mathematics Subject Classification: Primary: 34K08, 35L02, 34L10; Secondary: 92C37.

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References

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