An Application of General Branching Processes to a Cell Cycle Model with Two Uncoupled Subcycles
Marina Alexandersson
Dept of Mathematical Statistics, Chalmers Univ of Tech, Gothenburg, Sweden
Abstract
We use multitype branching process theory to construct a cell population model where the cell cycle consists of two simultaneously running subcycles: the DNA division cycle (DDC) and the cell growth cycle (CGC).
In this model we assume the existence of a critical cell size, which each cell has to pass before division. Every individual cell grows exponentially with the same rate as the mother until it reaches the critical size. Then it chooses a new growth rate influenced by a latent growth factor inherited from the mother, which generates a similarity between the growth of two sister cells. The division is assumed to be unequal.
Instead of having a two-dimensional type, the birth size and the growth rate, we shift the cell cycle to begin at the critical size and let only the growth rate be the type. We get a new population of pseudo-cells, where all have the same birth size and without changing growth rates during their life.
We give an explicit expression for the stable birth type distribution and from this we derive asymptotic objects for the real cell population, such as the $\alpha$- and $\beta$-curves, the birth size distribution, and the division size distribution.
