Critical telomerase activity for uncontrolled cell growth.

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.