  The lengths of the telomere regions of chromosomes in a population of cells
are modelled using a chemical master equation formalism, from which the
evolution of the average number of cells of each telomere length is extracted.
In particular, the role of the telomere-elongating enzyme telomerase on these
dynamics is investigated. We show that for biologically relevant rates of cell
birth and death, one finds a critical rate, R_crit, of telomerase activity such
that the total number of cells diverges. Further, R_crit is similar in
magnitude to the rates of mitosis and cell death. The possible relationship of
this result to replicative immortality and its associated hallmark of cancer is
discussed.
