A model for asymmetrical cell division
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2014-12-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.491 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590111687049216 |
|---|---|
| author | Ali Ashher Zaidi Bruce Van Brunt Graeme Charles Wake |
| author_facet | Ali Ashher Zaidi Bruce Van Brunt Graeme Charles Wake |
| author_sort | Ali Ashher Zaidi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4402bdd8d8a642acacbb8062d5d9e924 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-4402bdd8d8a642acacbb8062d5d9e9242025-01-24T02:31:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-12-0112349150110.3934/mbe.2015.12.491A model for asymmetrical cell divisionAli Ashher Zaidi0Bruce Van Brunt1Graeme Charles Wake2Institute of Natural and Mathematical Sciences, Massey University, AucklandInstitute of Fundamental Sciences, Massey University, Palmerston NorthInstitute of Natural and Mathematical Sciences, Massey University, AucklandWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.491eigenfunctionsfunctional differential equationshyperbolic partial differential equations.cell biology |
| spellingShingle | Ali Ashher Zaidi Bruce Van Brunt Graeme Charles Wake A model for asymmetrical cell division Mathematical Biosciences and Engineering eigenfunctions functional differential equations hyperbolic partial differential equations. cell biology |
| title | A model for asymmetrical cell division |
| title_full | A model for asymmetrical cell division |
| title_fullStr | A model for asymmetrical cell division |
| title_full_unstemmed | A model for asymmetrical cell division |
| title_short | A model for asymmetrical cell division |
| title_sort | model for asymmetrical cell division |
| topic | eigenfunctions functional differential equations hyperbolic partial differential equations. cell biology |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.491 |
| work_keys_str_mv | AT aliashherzaidi amodelforasymmetricalcelldivision AT brucevanbrunt amodelforasymmetricalcelldivision AT graemecharleswake amodelforasymmetricalcelldivision AT aliashherzaidi modelforasymmetricalcelldivision AT brucevanbrunt modelforasymmetricalcelldivision AT graemecharleswake modelforasymmetricalcelldivision |