Effects of initial telomere length distribution on senescence onset and heterogeneity

Abstract

Replicative senescence, induced by telomere shortening, exhibits considerable asynchrony and heterogeneity, the origins of which remain unclear. Here, we formally study how telomere shortening mechanisms impact on senescence kinetics and define two regimes of senescence, depending on the initial telomere length variance. We provide analytical solutions to the model, highlighting a non-linear relationship between senescence onset and initial telomere length distribution. This study reveals the complexity of the collective behavior of telomeres as they shorten, leading to senescence heterogeneity.

Keywords: Replicative senescence; Stochastic model; Telomerase; Telomere; Yeast.

Fig. B.1

The expected length $\mathbb{E}(L_{\infty })$ as function of i_s.

Fig. 1

Scheme of a chromosome bearing two telomeres and undergoing replication. Telomeres end with a 3′ overhang of length a (measured to be 5–10 nucleotides in yeast (Soudet et al., 2014), chosen here as a=1 or 7 for theoretical or numerical purposes, respectively). After DNA replication, each telomere generates, through either the leading or the lagging strand replication machineries, two new telomeres of different lengths. The coupling effect between the two ends of the same chromosome imposes that only one of the two is shortened while the other retains the parental length.

Fig. 2

Steady-state telomere length distribution in the presence of telomerase. (a) and (b) Probability of recruitment and action of telomerase, as modeled from Teixeira et al. (2004) with a length threshold L_s or simplified with a sharp switch occurring at i_s. (c) Simulation of the steady-state distribution of telomere length using either (a) (black) or (b) (grey) to describe telomerase recruitment. i_s was set so as to reach the same mean in the steady-state distribution (Appendix B).

Fig. 3

Distinct effects of the mean and variance of the initial distribution on theoretical expressions and numerical simulations of the time of senescence. (a) Starting from a constant distribution $\mathbb{E}(L_{\infty })≔x_0$, the asymptotic expansion in Eq. (10) is computed and compared to numerical simulations (1000 independent simulations). (b) Starting from a uniform distribution of variance σ and mean $\mathbb{E}(L_{\infty })$, the time of senescence is computed using Eq. (11), which takes only the mean behavior of the initial shortest telomere into account, and compared to numerical simulations (1000 independent simulations).

Fig. 4

Comparison between simulated times of senescence (grey dots) and predictions from Eqs. (11) (dashed black lines) and (10) (black lines). (a) 32 telomere lengths are randomly drawn from a biologically relevant distribution with a high variance (Fig. 2c, grey distribution) and the time of senescence is simulated to give one data point (grey dot). This process is repeated 1000 times and compared to the two predictions. The grey line represents the average simulated time of senescence. (b) and (c): as in (a), but starting with an intermediate level of variance for the initial telomere length distribution or no variance at all, respectively.