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Mathematical Biosciences and Engineering

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: 01 August 2014 Accepted: 29 June 2018 Published: 01 January 2015

  • MSC : Primary: 34K08, 35L02, 34L10; Secondary: 92C37.

  • 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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  • 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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  • 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, 2016, 95, 0003-6811, 2565, 10.1080/00036811.2015.1102890
    2. Messoud Efendiev, Bruce Brunt, Ali A. Zaidi, Touqeer H. Shah, Asymmetric cell division with stochastic growth rate. Dedicated to the memory of the late Spartak Agamirzayev, 2018, 41, 0170-4214, 8059, 10.1002/mma.5269
    3. Graeme Wake, 2015, Chapter 27, 978-3-319-22128-1, 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, 2019, 533, 03784371, 122079, 10.1016/j.physa.2019.122079
    5. STEPHEN TAYLOR, XUESHAN YANG, ESTIMATES FOR APPROXIMATE SOLUTIONS TO A FUNCTIONAL DIFFERENTIAL EQUATION MODEL OF CELL DIVISION, 2021, 1446-1811, 1, 10.1017/S1446181121000055
    6. S. T. H. Shah, A. A. Zaidi, On the existence of solutions to an inhomogeneous pantograph type equation with singular coefficients, 2020, 6, 2296-9020, 935, 10.1007/s41808-020-00089-3
    7. M. MOHSIN, A. A. ZAIDI, ON EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A PANTOGRAPH TYPE EQUATION, 2021, 1446-1811, 1, 10.1017/S144618112100002X
    8. Muhammad Mohsin, Syed Touqeer H. Shah, Ali A. Zaidi, Wing-Sum Cheung, On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients, 2022, 2022, 1687-0409, 1, 10.1155/2022/5849405
    9. Bertrand Cloez, Benoîte de Saporta, Tristan Roget, Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process, 2021, 83, 0303-6812, 10.1007/s00285-021-01695-y
    10. A. A. ZAIDI, B. VAN BRUNT, ASYMMETRICAL CELL DIVISION WITH EXPONENTIAL GROWTH, 2021, 63, 1446-1811, 70, 10.1017/S1446181121000109
    11. G. Derfel, B. van Brunt, On the balanced pantograph equation of mixed type, 2024, 75, 1027-3190, 1627, 10.3842/umzh.v75i12.7654
    12. G. Derfel, B. van Brunt, On the Balanced Pantograph Equation of Mixed Type, 2024, 0041-5995, 10.1007/s11253-024-02295-x
    13. Bruce van Brunt, Gregory Derfel, Ali Ashher Zaidi, On the advanced balanced pantograph equation, 2025, 0, 1534-0392, 0, 10.3934/cpaa.2025064
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  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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