Dynamics of cell growth: Exponential growth and division after a minimum cell size

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dc.citation.volume11
dc.contributor.authorMohsin M
dc.contributor.authorZaidi AA
dc.contributor.authorVan Brunt B
dc.date.accessioned2024-10-15T21:58:05Z
dc.date.available2024-10-15T21:58:05Z
dc.date.issued2024-09
dc.description.abstractIn this paper, we consider a mathematical model for cell division using a Pantograph-type nonlocal partial differential equation, accompanied by relevant initial and boundary conditions. This formulation results in a nonlocal singular eigenvalue problem. We explore the possible eigenvalues that may lead to nontrivial solutions. We then consider cells that divide once they achieve a minimum size. Our model incorporates asymmetric cell division and exponential growth. We show that, unlike the constant growth rate case, a probability density function eigenvalue can be determined explicitly. Additionally, we demonstrate that a stochastic growth rate produces eigenfunctions expressed as an infinite series of modified Bessel functions. We extend our findings to encompass a wider range of dispersion and growth rates. The implications of this work are significant for understanding the dynamics of cell populations in biological systems. The work has potential applications in cancer research and developmental biology, where cell growth and division play critical roles.
dc.description.confidentialfalse
dc.edition.editionSeptember 2024
dc.identifier.citationMohsin M, Zaidi AA, van Brunt B. (2024). Dynamics of cell growth: Exponential growth and division after a minimum cell size. Partial Differential Equations in Applied Mathematics. 11.
dc.identifier.doi10.1016/j.padiff.2024.100814
dc.identifier.eissn2666-8181
dc.identifier.elements-typejournal-article
dc.identifier.number100814
dc.identifier.piiS2666818124002006
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/71730
dc.languageEnglish
dc.publisherElsevier BV
dc.publisher.urihttps://www.sciencedirect.com/science/article/pii/S2666818124002006
dc.relation.isPartOfPartial Differential Equations in Applied Mathematics
dc.rights(c) 2024 The Author/s
dc.rightsCC BY-NC-ND 4.0
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectFunctional partial differential equations
dc.subjectNonlocal partial differential equations
dc.titleDynamics of cell growth: Exponential growth and division after a minimum cell size
dc.typeJournal article
pubs.elements-id490928
pubs.organisational-groupOther
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