Long-lived mice
To study the effects of dwarfism, we studied 2- or 22-month-old male Ames Prop1df/df dwarf and wild-type mice livers [10], with four mice in each group. Mice were maintained under controlled conditions at the University of North Dakota (Grand Forks, ND, USA) with access to food ad libitum. To study the effects of calorie restriction and rapamycin treatment, we used female UM-HET3 mice livers aged to 22 months, where mice were subjected to calorie restriction (60% of food consumption relative to age-matched controls, gradually reduced over 2 weeks), subjected to 42 mg/kg dietary rapamycin treatment from 4 to 22 months, or left untreated, with four mice in each group. We also obtained livers from female untreated UM-HET3 mice aged to 2 months [12]. UM-HET3 mice were maintained at the University of Michigan (Ann Arbor, MI, USA). The weights of these mice are described in Additional file 6.
WGBS library preparation
DNA was isolated from mice livers using the DNeasy blood and tissue kit (Qiagen, Germantown, MD, USA). WGBS was carried out by the Beijing Genomics Institute (Shenzhen, China) following standard protocols [36]. Briefly, DNA was fragmented using sonication to an average fragment size of 100–300 bp, end-repaired, and ligated to methylated-sequencing adapters to generate sequencing libraries. Bisulfite conversion was performed on these sequencing libraries using the ZYMO EZ DNA Methylation-Gold kit (Irvine, CA, USA) and sequenced using 90 bp paired-end sequencing on an Illumina HiSeq-4000 (San Diego, CA, USA). Ames mice were sequenced to an expected 15× coverage; UM-HET3 mice were sequenced to an expected 5× coverage.
Data processing
For the WGBS study in long-lived mice, sequencing reads were trimmed using Trim Galore [37] and aligned to a bisulfite-converted mouse genome (mm9) obtained from UCSC [38] using bowtie [39]. Methylation states were called using bismark v0.10.0 [40]. The resulting sites were then converted to mm10 coordinates using liftOver [38] with default parameters.
In addition to the above data, public bisulfite sequencing data were downloaded from GEO [41] or the Sequence Read Archive (SRA) (accession numbers: [GEO: GSE60012] [19], [GEO: GSE52266] [42], [GEO: GSE67507] [43] and [SRA344045] [21]). Sequencing reads were trimmed using Trim Galore [37] with default parameters, aligned to bisulfite-converted Ensembl mmGRC38 version 84 [44] using bowtie2 [45] with parameters –N 1, and the methylation states were determined using Bismark v0.14.3 [40]. When multiple sequencing runs were associated with a single sample, the methylation states for each CpG were collapsed by summing the reads.
Human 450 K liver data were downloaded from GEO (accession numbers: [GEO: GSE61258] and [GEO: GSE48325]), corresponding to Horvath et al. [4] and Ahrens et al. [20] datasets. The data were processed in R using Minfi [46]. Missing data were imputed using impute package in R [47]. The data were then beta-mixture quantile normalized [48] using a gold reference distribution following the procedure provided by Horvath [2]. The gold reference distribution was set to the mean probe values from [GEO: GSE61258].
Evolutionary trends
To compare mice with humans, we wanted to maximize the number of mouse CpG markers that we could compare reliably across species. For this reason, we limited our analysis to RRBS datasets obtained from GEO. Specifically, we filtered Reizel et al. [19] with Cannon et al. [42] and Orozco et al. [43] to identify reproducible CpG sites. Sites were filtered according to the following criteria: ≥5 reads, <20% missing data across mice from all three studies, and distinct mapping onto chromosomes 1–19. We then removed individual mouse samples missing >40% of these sites. These filtering steps resulted in 97 samples profiled across 36,094 sites in Reizel et al. [19]. Missing data were imputed using the mean methylation value for that site.
To define a commonly–profiled set of orthologous CpG sites, we mapped the 36,094 sites profiled in mm10 to hg19 coordinates using liftOver [38], with -minMatch = 0.1. The resulting coordinates were intersected with the Illumina 450 K probes, as defined by their locations from the Illumina manifest (bedtools intersectbed [49]). Any mouse sites that mapped to the same human site were combined by taking the average value of these sites.
Annotation tracks were downloaded from Encode for human hepatocytes from UCSC [50]. The following data tracks were downloaded: DNASE-seq, H3K36me3, H3K4me1, H3K27ac, H3K9ac, H3K4me3 and H3K27me3. Enhancer regions were defined as the intersected regions between H3K27ac and H3K4me1. Bivalent regions were defined as the intersected regions between H3K4me3 and H3K27me3. Repeat elements were downloaded from UCSC for hg19 [51]. CpG sites were mapped to each feature by intersecting the site coordinates with each annotation using bedtools intersectbed. Annotations for transcription start site (TSS), 5′ untranslated region (UTR), body, exons, shelf, island and shore were defined by the Illumina 450 K manifest. Promoters were defined as CpG sites with TSS annotations. Similarly for mice, annotation tracks were downloaded from UCSC for the same marks from adult male mice liver. Gene features for mice were also downloaded from UCSC for mm10 or mm9 [51]. Coordinates for mm9 were translated to mm10 using liftOver (default parameters) and assigned to sites using bedtools intersectbed. Promoters in mice were defined as 2 kb upstream of protein-coding genes. We only considered annotations that fell within the orthologous-profiled set of CpGs. These annotations were used as genomic regions.
Odds ratios (ORs) were calculated by counting orthologous CpG sites annotated to different genomic regions and assessing whether they were age-associated or not age-associated. This formed a 2-by-2 contingency table for each genomic region, so we could assess whether age-associated sites were under-represented or over-represented in that particular genomic region. This process was repeated for each genomic region separately in both human and mouse. When there were overlapping genomic region annotations for sites, sites were counted only for the genomic region considered so that sites were not counted twice. Over-represented genomic regions were those with an OR > 1 and under-represented genomic regions were those with an OR < 1. p-values were calculated using Fisher’s exact test.
To identify age-associated sites, we built a multivariate linear model regressing each methylation site against treatment, gender and age in mice, or against body mass index, gender and age in humans. Then, we conducted a drop-one F-test to determine if age had a significant association with that site. For comparisons in the orthologous-profiled space between mice and humans, we conducted the drop-one F-test using Reizel et al. [19] for mice or all human samples, and we selected sites that had an age-association at a Benjamini-Hochberg 1% FDR. To calculate the significance of the overlap, we used a hypergeometric test.
To identify all age-associated sites, regardless of conservation, we conducted the same drop-one F-test, first using the 97 mice of Reizel et al. [19] for all 36,094 CpG sites, then selecting CpG sites that passed a Benjamini-Hochberg 1% FDR. We repeated this analysis using the 2.1-month-old mice from Cannon et al. [42] and 3.7-month-old mice from Orozco et al. [43], using the CpG sites identified in Reizel et al. [19], and selected sites that continued to have an age-association at a Benjamini-Hochberg 1% FDR. Using these criteria, we found 393 age-associated sites in mice. These sites were used to calculate entropy for Reizel et al. [19] (Fig. 1b). We identified age-associated CpG sites in humans similarly, using all 485,512 CpG sites on the 450 K Illumina chip, first in [GEO: GSE61258] [4] (79 samples), identifying CpG sites with an age-association at a Benjamini-Hochberg 1% FDR threshold. We repeated this analysis for the identified CpG sites in [GEO: GSE48325] [20] (85 samples), selecting CpG sites that passed a Benjamini-Hochberg 1% FDR threshold. Using these criteria, we found 322 age-associated CpG sites. These sites were used to calculate entropy (Fig. 1c) for [GEO: GSE61258] [4].
Entropy was calculated according to the formula described in [1]:
$$ E n t r o p y=\frac{1}{N\times log\left(\frac{1}{2}\right)}{\displaystyle {\sum}_i^N\left[ M{F}_i\times log\left( M{F}_i\right)+\left(1- M{F}_i\right)\times log\left(1- M{F}_i\right)\right]} $$
where MF
i
is the methylation fraction of the i
th methylation CpG site and N is the number of age-associated CpG sites (393 sites for mice and 322 sites for human, described above). Since the entropy approaches 0 when MF
i
approaches 0, the entropy for methylation sites with a value of 0 were set to 0.
Epigenetic clock data processing and data normalization
For construction of an epigenetic-aging model, we used [GEO: GSE60012] [19], [SRA344045] [21] and our own control mice, for a total of 124 mice liver/hepatocyte samples. Because RRBS is targeted towards CpG-rich regions of the genome, we included sites that were covered by ≥2 reads in 97% of mice, mapped to chromosomes 1–19 and had a standard deviation >0 and ≤20%. Mice missing over 30% of these sites were removed from further analysis. Missing data were imputed using the mean value of each site. These filtering steps resulted in 119 samples profiled across 7628 CpG sites. For studies profiling a single time point [42] and the long-lived mice, in order to maximize the overlap with the 7628 CpG sites selected above, we considered any site with ≥1 reads (bedtools intersectbed). Missing data were imputed by the mean methylation value for that site.
All data were then normalized using ComBat (nonparametric mode) from the SVA package in R [22, 23]. Ages (in days) were transformed to log2 scale, prior to normalization. The specific sequencing studies ([19, 21, 42], Ames and UM-HET3) were used to represent batch, and the model provided to ComBat included the covariates age, gender and treatment. After performing ComBat, we used PCA to verify that this normalization reduced the effects due to differences in sequencing technology or mouse strains (Additional file 1: Figure S2D,E). Bismark alignment reports, as well as average read depth per unique CpG called and per CpG used to construct the epigenetic-aging model, are shown in Additional file 2: Public data and Data here detailed.
Epigenetic-aging model construction
The normalized methylation values from [19, 21, 42] and data from wild-type, untreated UM-HET3 and Ames aged to 2 and 22 months (one from each group) (Additional file 2: Datasets used summary) were used as training data for ElasticNet regression [24] using the python scikit-learn package [52]. The normalized methylation values were used as features, and the log2-transformed ages (in days) were used as the predicted variable. Model fitting parameters were selected using 4-fold cross validation. The final model was trained on these training data with the most optimal regularization parameters when averaging the 4-fold cross-validation results. The model sites selected by ElasticNet, along with the associated weights and intercept, are shown in Additional file 3.
We assessed whether epigenetic ages were informative by comparing the epigenetic ages for untreated, wild-type mice from our study or mice from Cannon et al. [42]. We used either a t-test or an ANOVA to compare whether epigenetic ages were significantly different between 2- versus 22-month-old mice, and whether epigenetic ages of mice with similar chronological ages were affected by differences in genetic backgrounds (Additional file 4: Wild type stats). To assess the effect of normalization in addition to selection of regularization parameters or hidden biases correlated to aging signals, the covariates of each study were shuffled, ComBat normalization was repeated, and models were learned using the same strategy described above. This process was repeated 120 times and predictions between models generated from permuted data or actual data were compared using the residual (epigenetic age minus chronological age) for wild-type mice. The model learned from actual data minimized the residual for the wild-type mice (Additional file 1: Figure S2F–J).
We used the annotations for mouse (described above) to annotate the selected sites to genomic regions, considering only intronic, intergenic, exonic, promoter and enhancer regions. When there were overlapping annotations, we prioritized enhancer and promoter regions. We calculated under-representation of over-representation of these selected sites in these regions using a Fisher’s exact test, with significance defined as p < 0.01. We assigned nearest genes to these sites using closestBed and displayed this along with overlapping histone/chromatin state information in Additional file 3.
Assessing epigenetic age in long-lived mice
The epigenetic-aging model was applied to the methylation profiles of long-lived mice and the age-matched controls not used for training (Additional file 2: Datasets used summary). Reductions in age were calculated by subtracting the epigenetic ages of the untreated, wild-type mice from those of the treated mice of the same genetic background. To assess the significance, we used an ANOVA for all 22-month-old mice or only 22-month-old UM-HET3 mice. We also compared the epigenetic ages between treatments with their age-matched controls from the same genetic background using a t-test (Additional file 4: Treatment vs wild type stats).
Principal component analysis
PCA was conducted using scikit-learn package with the 148 CpG sites used in the epigenetic clock. The first two PCs separated age and treatment (Additional file 1: Figure S3A). We assessed the significance of variables that contributed to the variance along PC1 for each genetic background using a multivariate linear regression according to the following model:
$$ Principal\kern0.24em component\kern0.24em 1\sim age+ treatment $$
where treatment was modeled as a categorical variable. Results are shown in Additional file 5.
Hierarchical clustering
Hierarchical clustering was performed using python SciPy with linkage method “average” and Euclidean distance [53]. Methylation values were transformed using standard_scale = True and visualized using seaborn [54]. Hierarchical clustering was performed either using the top 20 most variable CpG sites (determined from the long-lived mice and wild-type mice) or all sites used by the epigenetic-aging model.