Mutations accumulate as a result of DNA damage – an unavoidable byproduct of life: damage to DNA is caused by metabolic activity [1, 2], DNA replication [3], exposure to UV light, etc. Most of the damage is rapidly and successfully repaired by complex DNA repair pathways [4]. However the fidelity of the repair proteins and pathways is not perfect and erroneously repaired or unrepaired damage can result in mutations [5].

There exist two main ways to limit mutation accumulation in the population of cells: a) eliminate damaged cells or b) set a limit on the number of replications a cell can undergo. In the former case, a severely damaged cell can be removed form the pool of replicating cells in many ways: it can undergo cell-cycle arrest, autophagy, necrosis or activate pre-programmed suicidal program – apoptosis. This decision making is mediated at the level of a single cell and occurs within hours from the initial insult. Nearly all these processes involve p53 – a master regulator protein [6]. In the following sections, for simplicity, the combined effect of the p53 and other proteins regulating removal of severely damaged cells will be referred to as p53.

In an alternative scenario b) the spread of mutations in a lineage of proliferated cells is limited by telomeres and happens on the time-scale of weeks. The number of replications a given proliferated cell can undergo is given by the length of its telomeres – a stretch of (TTAGGG) DNA repeats at the chromosomal ends. Proliferated cells start with a wide distribution of telomere lengths (with the average about 15000 bp in e.g. human fibroblasts [7])) which progressively shorten at every cell division. Once the shortest telomere reaches the critical length (e.g. of about [8] 2000 bp in human fibrobasts), cells undergo replicative senescence – they stop dividing and in some cases undergo apoptosis.

It has been shown that the rate of telomere shortening is accelerated when cells are exposed to genotoxic stresses (e.g. reactive oxygen species (ROS)) [9]. These results shift the telomere paradigm from a simple clock counting cell divisions to a more sophisticated device recording the history of stress exposure within a cell lineage. While these results have opened a new perspective on replicative senescence, it is still unclear how and under what conditions can cells benefit from such a mechanism? As p53 already removes damaged cells that have a high chance to accumulate mutations, what does one gain by Stress-Induced Telomere Shortening (SITS) compared to classical view of Telomere Shortening (TS) at a constant rate?

To answer these questions we introduce a semi-quantitative model of replicating cells exposed to non-uniform genotoxic stresses.

The main objective of our model is to investigate the effect SITS has on mutation accumulation in a population of replicating cells. We hypothesized that the mechanism of SITS, which specifically accelerates senescence in more damaged progenies, will probably result in a slower mutation rate than in case of a constant, i.e. stress independent telomere shortening (TS). (In SITS the more damaged cells and thus ones with higher number of mutations, will be the first to undergo senescence. Thus SITS removes mutations from the population at a higher rate than TS.)

SITS increases longevity while minimizing mutation rate

In Figure 2 we show the dynamics of the three main characteristics: Number of dividing cells in population, N, telomere length, T and number of mutations, M averaged over all cells. When comparing the dynamics of SITS (Figure 2A-C) and TS models (Figure 2D-F) we find two remarkable results: a) SITS indeed decreases mutation rate but the effect is taking place at late time points (Figure 2 C and F) and b) SITS significantly increases the longevity of population, L, defined as number of replications after which the population drops below 200 (compare Figure 2A and D).

Both the increase in longevity and decrease in mutation rate are late events that take place when population of cells approaches a critical length in their telomeres (known as Hayflick limit [20]). The SITS produces wide distribution of telomere lengths. When average telomere length approaches the Hayflick limit cells with telomeres longer than the limit divide to compensate for dying cells with critically short telomeres, thus the average telomere length can be maintained above the limit for longer time. In Figure 2B this phenomena happens at around t = 150 cell divisions.

At early time points – when the mutation rate is determined only by the amount of DNA damage, <D>, in the population of cells and the apoptosis rate – there is no difference between the two scenarios. However at later time, when population starts approaching Hayflick limit (e.g. at t = 150), in SITS (but not in TS) a considerable amount of cells with short telomeres (i.e. stressed cells that accumulated many mutations) has been replaced by cells with longer telomeres and few mutations. Observe that the constant mutation rate over the whole life span would result in linear increase in number of mutations M with increasing longevity L. The SITS allows to break this linear dependence at late time points.

It is important to note that we have chosen the rate of telomere shortening to depend only linearly on the DNA damage, i.e. $\frac{d{T}_i}{\mathit{\text{dt}}}\sim D_i$, the effect on mutation rate would be even stronger if we use square or higher powers as this will make telomeres differentiate even more between damaged and non-damaged cells. Interestingly Zglinicki et al. [9] reported nearly square dependence of the rate of telomere shortening on the amount of ROS in different cell lines.

As the metabolic load varies widely from one cell type to another, as well as between individual cells in the population we wanted to investigate how our results depend on the mean DNA damage <D> and the cell-to-cell variability.

In Figure 3A we monitor the mutation rate, $<\frac{\mathit{\text{dM}}}{\mathit{\text{dt}}}>$ averaged over time and cells. Due to p53 mediated apoptosis, cells with DNA damage, D≫1 will be removed from population and thus the average of the assigned DNA damage, μ _D will differ from the actual average DNA damage, 〈D〉, averaged over replicating cells. We choose to use the latter as it allows us to focus on telomere effect alone.

While both SITS and TS mutation rates increase with increasing genotoxic load, 〈D〉, the SITS slows down the increase for the low and intermediate levels of 〈D〉∼0.025-0.375. The beneficial effect of SITS is maintained for all analyzed 〈D〉, but it saturates at higher levels of DNA damage, as p53 eliminates more and more cells.Remarkably, while in SITS case, longevity is decreasing with increasing DNA damage, it always remains above the TS values (see Figure 3B). The combined gain in increased longevity and decreased mutation rate is maximal at intermediate values of DNA damage, in the range between the “physiological” and apoptotic loads of DNA damage.

Cell-to-cell variability is required for SITS to take an effect

As we have seen in Figure 2B, both the increase in longevity as well as damped mutation rate rely on a wide distribution of telomere lengths. In our model the distribution of telomere lengths during SITS originates from the cell-to-cell variation in DNA damage. (If all cells were subject to the same level of DNA damage, all cells would have the same telomere length). Interestingly the wide distribution of telomere lengths can result from Telomeric Sister Chromatid Exchange (T-SCE) [21].

Antal et al., [22] have elegantly analyzed this phenomena treating it analytically as a diffusion-convection problem. They show that increasing the rate of T-SCE (while maintaining the same telomere attrition rate) will increase the mean proliferative potential (we refer to it as longevity) and widen distribution of telomere lengths and thus individual cell longevities. While the wide distribution of telomere lengths is a common explanation of how both SITS and T-SCE extend longevity of proliferating cells, they will have opposing effects on the accumulation of mutations. Under the assumption of constant mutation rate, the number of mutations in individual cells will increase linearly with their longevity and thus the distributions in number of mutations will match the distribution of longevities. This means that while SITS narrows the distribution of mutations by letting the less damaged cells live longer and removing highly mutated cells, the T-SCE widens the distribution of mutations as it both widens the distribution of cell longevities and at the same time recombination makes cells “forget” about their history of exposure to DNA damage. Widening of the distribution is a highly undesirable effect: The wider is the distribution, the higher is the chance to arrive to potential “cancer progenitors” – cells with many more mutations than on average in a given population. Interestingly higher eukaryotes have acquired a rather involved machinery, e.g. shelterins [23], to put T-SCE under tight control.

In Figure 4 we are investigating how the combined gain in mutation rate and longevity depends on the amount of cell-to-cell variability. To quantify the gain we have plotted the ratios of SITS to TS of mutation rates (R _M ) and longevities (R _L ), $R_M=\frac{<{\frac{\mathit{\text{dM}}}{\mathit{\text{dt}}}}_{\mathit{\text{SITS}}}>}{<{\frac{\mathit{\text{dM}}}{\mathit{\text{dt}}}}_{\mathit{\text{TS}}}>}$ and $R_L=\frac{<L_{\mathit{\text{SITS}}}>}{<L_{\mathit{\text{TS}}}>}$. (We choose normalized standard deviation, $\frac{{\sigma }_D}{<D>}$, also known as coefficient of variance, to quantify cell-to-cell variations.)

We find that the effect of SITS decreases as cells become more and more alike (decreasing $\frac{{\sigma }_D}{<D>}$). This suggests that stress induced telomere shortening and cell-to-cell variability in DNA damage inducing factors (e.g. metabolic load) are tightly interlinked.

Interestingly, the cells in in vitro cultures were shown to have widely variable doubling ability, even clonaly derived cells show distinct bi-modal distribution in number of doublings before senescence [24]. Passos et al. suggested that heterogeneity in telomere dependent senescence might stem from mitochondrial dysfunction [25].

Telomeres are perfect oxidative stress sensors as they are particularly sensitive to oxidative DNA damage. The reason is two fold: First, they acquire DNA damage at a faster rate then the rest of genome. This is due to triple-G structure – present in telomeres of all eukaryotes – which are exquisitely sensitive to oxidative damage. Second, the repair of the damage is less efficient at telomeres [26] probably due to telomere binding proteins that restrict access to telomeric DNA (e.g. TRF2). These D͡NA-based sensors work in parallel with a complex apparatus of protein-based DNA damage sensors. In response to DNA damage kinases ATM, ATR and MRN complex are rapidly recruited and activated at the site of damage. If the damage is persistent the signal by these protein-based sensors will arrest cell cycle and activate pro-apoptotic p53 thus leading to non-telomeric senescence. Why did these two mechanism evolve to parallel each other? Is it important for telomere-induced senescence to relate to oxidative stress?

A possible explanation is that the two carry complementary functions: While p53-mediated response is dealing with persistent and acute damage, telomeres work as sentinels [27] and track the history of transient and repairable damage. As repair is imperfect it sometimes results in mutations. The ability of SITS to sense stress and track cell’s history of stress exposure allows it to “estimate” the amount of these mutations in individual cells. Our model shows that without sensing and estimating (as it would have been in a classical mechanism of TS due to end-replication problem) the mutation rate remains unaffected and mutations can only be limited as a direct consequence of limiting the life-span of the population. However, SITS – through its sensing ability – does alter the mutation rate (as shown in Figure 2), thus softening the coupling between longevity and the amount of accumulated mutations. Furthermore, not only it affects the mutation rate, it also increases longevity in a heterogeneous population of cells.

We find that for the SITS to have an effect cells must differ from each other. An interesting physiologically relevant example of heterogeneity is reported for the insulin producing pancreatic beta cells. The pancreatic beta cells have a highly variable glucose-sensing thresholds at which they start synthesizing insulin [28]. Cells with lower thresholds will, on average, synthesize more insulin, resulting in a higher metabolic load and thus higher ROS production. Our findings suggest that such specialization into “hard working, heavily damaged” and “lazy, undamaged” cells should delay population senescence and decrease mutations (consequently decreasing the chance for tumor to originate).

It will be interesting to apply our model to the particular case when DNA damage has a bi-modal distribution as it is probably the case in pancreatic beta-cells.

Another example where cells might experience highly variable DNA damage is NF-kB induction by tumor necrosis factor (TNF). The activity of Nf-kB has been directly linked to oxidative DNA damage through Nitrogen Oxygen Species (NOS) [29]. It appears that similarly to pancreatic beta cells, there is a high cell-to-cell variability in TNF sensing thresholds which results in high variability in NF-kB induction [30] (and consequently NOS induced DNA damage). Furthermore, it has recently been argued that cell-to-cell heterogeneity is practically unavoidable and can come from a multitude of sources – from stochastic heterogeneity in oxidative DNA damage due to e.g. variations in metabolic loads to deterministic heterogeneity due to variations in cell size, cell density, stage in cell-cycle, etc. [31].

At this stage we chose not to include the effects of stem cells and telomerase. While telomerase will extend the longevity within our model, we expect it to counteract SITS in reducing mutations at late timepoints. Expanding the model to include these points will allow one to address a number of exciting questions e.g. relating aging and cancer originating from stem cells. Another interesting aspect is that replicative senescence caused by critically short telomeres in some cell types is mediated by p53, such that damage in p53 restores replicative capacity [32]. While in our presented model the two processes– senescence caused by short telomeres and p53 mediated cell cycle arrest and apoptosis– act independently, it will be interesting to investigate how the interdependence of the two influence the response.

Our findings highlight the unique features of telomeric versus p53-mediated stress response and suggest that telomere mediated stress-sensing and cell-to-cell heterogeneity are crucial for reducing mutations and extending longevity.

Ala Trusina, Center for Models of Life, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100, Denmark. Email: trusina@nbi.dk