Human data.

<p>(<b>a</b>) <i>Rate Acceleration/Deceleration under PM vs MC</i>: Curve indicates the MC/PM rates respectively at each site in the study. As can be seen, rates generally maintain their original sign under both MC and PM however some sites accelerate and others decelerate. (<b>b</b>) <i>Age Acceleration/Deceleration under PM vs MC</i>: Ages were sorted in ascending sequence. For every time, the ratio between the PM inferred time to real chronological time is plotted.</p

Performance of the identification under weaker PM signal (variance) .

<p><i>p</i>-value of the <i>χ</i>² is plotted versus the amount of noise. Each curve represent a different number of sites from {10, 20 30} (a) 50 individuals (b) 100 individuals.</p

The <i>mn</i> × 2<i>n</i> matrix <i>X</i> that is used in our closed form solution to the MC case.

<p>Every row corresponds to a component in the RSS polynomial and the corresponding entries (<i>i</i>th and <i>i</i> + <i>n</i>th) in that row are set to <i>t</i>_<i>j</i> and 1 respectively.</p

Molecular clock vs Universal PaceMaker.

<p>(<b>a</b>) Under the Molecular Clock (MC) model, methylation rates of sites differ among each other but are constant in time. (<b>b</b>) By contrast, under the Universal PaceMaker (UPM) model (right), rates may vary during with time but the pairwise ratio between sites rates remains constant.</p

A Statistical Framework to Identify Deviation from Time Linearity in Epigenetic Aging

<div><p>In multiple studies DNA methylation has proven to be an accurate biomarker of age. To develop these biomarkers, the methylation of multiple CpG sites is typically linearly combined to predict chronological age. By contrast, in this study we apply the Universal PaceMaker (UPM) model to investigate changes in DNA methylation during aging. The UPM was initially developed to study rate acceleration/deceleration in sequence evolution. Rather than identifying which linear combinations of sites predicts age, the UPM models the rates of change of multiple CpG sites, as well as their starting methylation levels, and estimates the age of each individual to optimize the model fit. We refer to the estimated age as the “epigenetic age”, which is in contrast to the known chronological age of each individual. We construct a statistical framework and devise an algorithm to determine whether a genomic pacemaker is in effect (i.e rates of change vary with age). The decision is made by comparing two competing likelihood based models, the molecular clock (MC) and UPM. For the molecular clock model, we use the known chronological age of each individual and fit the methylation rates at multiple sites, and express the problem as a linear least squares and solve it in polynomial time. For the UPM case, the search space is larger as we are fitting both the epigenetic age of each individual as well as the rates for each site, yet we succeed to reduce the problem to the space of individuals and polynomial in the more significant space—the methylated sites. We first tested our algorithm on simulated data to elucidate the factors affecting the identification of the pacemaker model. We find that, provided with enough data, our algorithm is capable of identifying a pacemaker even when a weak signal is present in the data. Based on these results, we applied our method to DNA methylation data from human blood from individuals of various ages. Although the improvement in variance across sites between the UPM and MC was small, the results suggest that the existence of a pacemaker is highly significant. The PaceMaker results also suggest a decay in the rate of change in DNA methylation with age.</p></div

Sample_Information

Sample information and genome-wide ancestry estimate

wyoteMeth_10x_3mil_sites_MF

This file contains the methylation frequency (MF, number of cytosines out of the total read coverage) per site for a coyote, wolves, and their hybrid offspring. This dataset contains ~3 million cytosines

Wyotes_15733_GBS_SNPs

This file contains SNP genotypes for 15,733 sites generated by GBS for a coyote, wolves, and their hybrid offspring

AIMS_delta

Genotypes for AIMs, delta values, outlier block detection, and population-specificit

nacanids_unrel_42Ksnps_CoatColor_wYNP_n33_white.tfam

PLINK formatted TFAM file with coat color genotype for each of 33 wolves. Individuals coded as a 2 are white, individuals coded as a 1 are not white (can be black or gray)