The telomere lengthening conundrum - it could be biology

Abstract

Longitudinal studies of human leucocyte telomere length often report a percentage of individuals whose telomeres appear to lengthen. However, based on theoretical considerations and empirical data, Steenstrup et al. (Nucleic Acids Research, 2013, vol 41(13): e131) concluded that this lengthening is unlikely to be a real biological phenomenon and is more likely to be an artefact of measurement error. We dispute the logic underlying this claim. We argue that Steenstrup et al.'s analysis is incomplete because it failed to compare predictions derived from assuming a scenario with no true telomere lengthening with alternative scenarios in which true lengthening occurs. To address this deficit, we built a computational model of telomere dynamics that allowed us to compare the predicted percentage of observed telomere length gainers given differing assumptions about measurement error and the true underling dynamics. We modelled a set of scenarios, all assuming measurement error, but both with and without true telomere lengthening. We found a range of scenarios assuming some true telomere lengthening that yielded either similar or better quantitative fits to the empirical data on the percentage of individuals showing apparent telomere lengthening. We conclude that although measurement error contributes to the prevalence of apparent telomere lengthening, Steenstrup et al.'s conclusion was too strong, and current data do not allow us to reject the hypothesis that true telomere lengthening is a real biological phenomenon in epidemiological studies. Our analyses highlight the need for process-level models in the analysis of telomere dynamics.

Keywords: computational model; leucocyte telomere length; measurement error; telomere attrition; telomere dynamics; telomere lengthening.

Figure 1

The evidence presented by Steenstrup et al. (2013a) to support their claim that observed telomere lengthening is predominantly, if not entirely, an artefact of measurement error exacerbated by short follow‐up periods. (A) The predicted negative relationship between follow‐up period and percentage of TL gainers (n = 13 studies). The solid line shows the best‐fitting linear regression. (B) Agreement between theoretical predictions based on assuming constant telomere attrition and measurement error, and empirically observed percentage of TL gainers (n = 10 studies). The dotted line has a slope of 1 and shows the expectation if predictions were perfect. The solid line shows the best‐fitting line obtained from regression through the origin; the r‐squared value and slope of this line are given on the graph.

Figure 2

Simulations produce scenarios with differing telomere dynamics. Panels show examples of the true TL data (i.e. without added measurement error) produced by the computational model using the default values given in Table 2. True TL is plotted as a function of year for the nine scenarios obtained by combining three values of the standard deviation of annual attrition, σ_a (columns), with three values of the autocorrelation of annual attrition, r (rows). For clarity, each panel shows TL data from only 15 randomly chosen individuals from the 10 000 in each simulation.

Figure 3

Observed percentage of TL gainers always declines with follow‐up period independent of the telomere dynamics assumed. Panels show percentage of individuals showing a gain in TL from baseline in each follow‐up year for the same nine scenarios depicted in Fig. 2. The black lines show the percentage of true TL gainers from baseline. The grey lines show the percentage of observed TL gainers from baseline given different levels of measurement error at baseline and follow‐up (CVs of 2, 4 and 8%). Simulations assumed the default values in Table 2; TL was ‘measured’ only once at each time point.

Figure 4

Simulated scenarios with true TL lengthening provide the best fit to empirical data on the observed percentage of TL gainers. Panels explore how well our computational model predicts the empirical data from the same 10 studies analysed by Steenstrup et al. (2013a; see Table S1, Supporting information). (A) Correlation between predicted percentage of TL gainers derived from Steenstrup et al.'s analytical approach and from our computational model with no true TL gainers (i.e. σ_a = 0 and r = 0). The dotted line shows the expectation if the correlation is perfect. Results are based on assuming n = 10 000 individuals per study in the simulation. (B) The fit between the empirically observed percentage of TL gainers and the percentage of TL gainers predicted by the computational model for a range of different parameter value combinations. Results are based on simulations assuming the actual numbers of individuals in the empirical studies being modelled (n = 50–635) and the reported number of interassay replicates of TL measurement (1 or 2; see Table S1, Supporting information for details). The points show the mean r‐squared values derived from 100 replicates of the simulation, and the error bars show the 95% confidence intervals for these means. The dotted line shows the fit of Steenstrup et al.'s model; points above this line correspond to parameter combinations in the computational model that predict the observed data better than the latter scenario, and points below this line correspond to parameter combinations that predict the observed data worse. The best‐fitting parameter combination (σ_a = 50 and r = 0) is indicated with an asterisk (*). The range of values of the standard deviation of annual telomere attrition reported in papers from the Steenstrup et al.'s data set is shown with a bar; these comprise 14.3–14.9 (Kark et al., 2012), 29.4–53.2 (Chen et al., 2011), 27.4 (Steenstrup et al., 2013b) and 46.0 bp year⁻¹ (Aviv et al., 2009). (C) Fig 1B replotted using the predictions derived from the best‐fitting parameter combination in the computational model in place of Steenstrup et al.'s predictions. (D) The predicted measured percentage of TL gainers and the predicted true percentage of TL gainers derived for each of the studies in the Steenstrup et al.'s data set using the best‐fitting parameter combination in the computational model. Bars show the mean ± 95% confidence intervals from 100 replicates of the simulation.