Differential and Integral Equations

Asymmetric cell division in a size-structured growth model

T. Suebcharoen, B. Van Brunt, and G.C. Wake

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Abstract

A model for the simultaneous growth and division of a cell population structured by size is examined. The case considered here is that of asymmetrical cell division when cells are dividing into $\beta_1$ and $\beta_2$ daughter cells at a constant rate and the parameters for growth and mortality are constants. The model has a steady-size distribution solution which satisfies a nonlocal differential equation. The solution is in the form of a Dirichlet series which is shown to be the unique probability density function for the steady-size distribution.

Article information

Source
Differential Integral Equations, Volume 24, Number 7/8 (2011), 787-799.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356628833

Mathematical Reviews number (MathSciNet)
MR2830708

Zentralblatt MATH identifier
1249.92001

Subjects
Primary: 30B50: Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX] 35A21: Propagation of singularities 92C37: Cell biology 95Q99

Citation

Suebcharoen, T.; Van Brunt, B.; Wake, G.C. Asymmetric cell division in a size-structured growth model. Differential Integral Equations 24 (2011), no. 7/8, 787--799. https://projecteuclid.org/euclid.die/1356628833


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