Human epigenetic ageing is logarithmic with time across the entire lifespan

Abstract

Epigenetic changes during ageing have been characterized by multiple epigenetic clocks that allow the prediction of chronological age based on methylation status. Despite their accuracy and utility, epigenetic age biomarkers leave many questions about epigenetic ageing unanswered. Specifically, they do not permit the unbiased characterization of non-linear epigenetic ageing trends across entire life spans, a critical question underlying this field of research. Here we provide an integrated framework to address this question. Our model, inspired from evolutionary models, is able to account for acceleration/deceleration in epigenetic changes by fitting an individual's model age, the epigenetic age, which is related to chronological age in a non-linear fashion. Application of this model to DNA methylation data measured across broad age ranges, from before birth to old age, and from two tissue types, suggests a universal logarithmic trend characterizes epigenetic ageing across entire lifespans.

Keywords: Aging; DNA methylation.

Figure 1.

Site Selection Criterion . Scatter plots of inferred epigenetic age (e-age, y-axis) as a function of the chronological age (c-age, x-axis) as a result of applying the EPM algorithm to blood samples from data set GSE60132 (see more details in the Results sec.). Each point represents an individual. One thousand best sites were selected by the following three criteria. A: Sites are selected based on their variance, regardless of correlation to age. B: Sites are selected based on their covariance with age. C: Sites are selected by the (absolute) Pearson correlation coefficient.

Figure 2.

The trend function. Left: The trend function – Trend lines for four $tr$ values $tr=0.1,0.5,0.8,1$ in blue, red, green, and olive green colours respectively. Middle: Simulated actual noisy PM – Actual noisy e-ages (blue dots) values around the trend line (red) with specific $tr=0.5$ and ${\sigma }_p=.8$. The (green) ${45}^{\circ }$ line represents the c-age of each individual. Right: The values inferred by the EPM-CEM algorithm – green dots represent the inferred e-age by the algorithm. It should be compared to the real e-age (blue). While there is a gap, linear with time, between actual and inferred e-ages, the trend is captured.

Figure 3.

GSE40279 – Human blood data results I. (Top) E-age vs C-age in adults. Age is plotted in years. The left graph shows the best approximation to the data. The linear line is slightly and insignificantly inferior to the quadratic approximation and therefore is the best fit. (Bottom) Mann-Kendall test for monotonicity trend: c-age vs e-age ratio ordered from left to right according to c-age. If rate of ageing is decreasing, we expect to see a monotonic increase in the function. Indeed, the function is increasing but not in a significant manner.

Figure 4.

GSE87571 – Human blood data results II. (Top) E-age vs C-age in adults. Age is plotted in years. The left graph shows the best approximation to the data. The linear line is slightly and insignificantly inferior to the quadratic approximation. (Bottom) Mann-Kendall test for monotonicity trend: c-age vs e-age ratio ordered from left to right according to c-age. If rate of epigenetic ageing is decreasing with time, we expect to see a monotonic increase in the $\frac{\mathrm{c}-\mathrm{a}\mathrm{g}\mathrm{e}}{\mathrm{e}-\mathrm{a}\mathrm{g}\mathrm{e}}$-ratio function. Indeed, the function is significantly increasing.

Figure 5.

GSE36064 – Children blood data results . E-age vs C-age in young humans. Age is plotted in months. The left graph shows the best approximation to the data. The logarithmic approximation provides the best explanation.

Figure 6.

GSE60132 – Human, all ages, blood data results I. E-age vs C-age in wide age range . Age is plotted in years. The left graph shows the best trend line approximation to the data, which is the logarithmic trend function. At the right, the inferior trends – the quadratic and linear. The quadratic line is slightly and insignificantly inferior to the logarithmic approximation, buy also portrays a concave line due to negative first coefficient $-0.0078$.

Figure 7.

GSE64495 – Human, all ages, blood data results II. E-age vs C-age in kids and adults. Age is plotted in years. The left graph shows the best approximation to the data, obtained by the logarithmic trend line with $R^2=0.924$. On the right, the inferior trend lines, the linear line with $R^2=0.866$ and the quadratic line with $R^2=0.902$.

Figure 8.

GSE74193 – Brain development data results . E-age vs C-age in young humans. Age is plotted in years. The left graph shows the best approximation to the data. The logarithmic approximation provides the best explanation.

Figure 9.

EPM Hannum Horvath trend comparison. Top Left EPM and Horvath ageing trend. Top Middle EPM and Horvath (transformed ages) ageing trend. Top Right EPM and Hannum ageing trend.

Figure 10.

EPM Hannum Horvath rate coefficient comparison horvath and hannum site coefficients compared to the EPM initial methylation values $s_i^0$ and EPM rates $r_i$ for the CpG sites used in the Horvath and Hannun models, respectively. Left EPM and Horvath right EPM and Hannum.