  We employ the framework of multitype Galton-Watson processes to model a
population of dividing cells. The cellular type is represented by its
biological age, defined as the count of harmful proteins hosted by the cell.
The stochastic evolution of the biological age of a cell is modeled as a
discrete Markov chain with a finite state space $\{0,1,\ldots,n\}$, where $n$
signifies the absorbing state corresponding to the senescent state of the cell.
Consequently, the set of individual types in the multitype Galton-Watson
process becomes $\{0,\ldots,n-1\}$. In our setting, a dividing cell may undergo
rejuvenation meaning that its biological ages reduces due to transfer of
harmful proteins to the daughter cell. For the proposed model, we define and
study several biologically meaningful features, such as rejuvenation states,
expected replicative lifespan, population growth rate, stable biological age
distribution, and the population average of the biological age.
