Computing the length of the shortest telomere in the nucleus

The telomere length can either be shortened or elongated by an enzyme called telomerase after each cell division. Interestingly, the shortest telomere is involved in controlling the ability of a cell to divide. Yet, its dynamics remains elusive. We present here a stochastic approach where we model this dynamics using a Markov jump process. We solve the forward Fokker-Planck equation to obtain the steady state distribution and the statistical moments of telomere lengths. We focus specifically on the shortest one and we estimate its length difference with the second shortest telomere. After extracting key parameters such as elongation and shortening dynamics from experimental data, we compute the length of telomeres in yeast and obtain as a possible prediction the minimum concentration of telomerase required to ensure a proper cell division.