Mathematical Biosciences and Engineering, 2015, 12(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

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.
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Keywords eigenfunctions; Functional differential equations; hyperbolic partial differential equations.; cell biology

Citation: Ali Ashher Zaidi, Bruce Van Brunt, Graeme Charles Wake. A model for asymmetrical cell division. Mathematical Biosciences and Engineering, 2015, 12(3): 491-501. doi: 10.3934/mbe.2015.12.491

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This article has been cited by

  • 1. Ali A. Zaidi, Bruce van-Brunt, Graeme C. Wake, Probability density function solutions to a Bessel type pantograph equation, Applicable Analysis, 2016, 95, 11, 2565, 10.1080/00036811.2015.1102890
  • 2. Messoud Efendiev, Bruce van Brunt, Ali A. Zaidi, Touqeer H. Shah, Asymmetric cell division with stochastic growth rate. Dedicated to the memory of the late Spartak Agamirzayev, Mathematical Methods in the Applied Sciences, 2018, 10.1002/mma.5269
  • 3. Graeme Wake, , Extended Abstracts Spring 2014, 2015, Chapter 27, 155, 10.1007/978-3-319-22129-8_27
  • 4. C.F. Lo, Exact solution of the functional Fokker–Planck equation for cell growth with asymmetric cell division, Physica A: Statistical Mechanics and its Applications, 2019, 533, 122079, 10.1016/j.physa.2019.122079

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Copyright Info: 2015, Ali Ashher Zaidi, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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