A population-epigenetic model to infer site-specific methylation rates from double-stranded DNA methylation patterns

Abstract

Cytosine methylation is an epigenetic mechanism in eukaryotes that is often associated with stable transcriptional silencing, such as in X-chromosome inactivation and genomic imprinting. Aberrant methylation patterns occur in several inherited human diseases and in many cancers. To understand how methylated and unmethylated states of cytosine residues are transmitted during DNA replication, we develop a population-epigenetic model of DNA methylation dynamics. The model is informed by our observation that de novo methylation can occur on the daughter strand while leaving the opposing cytosine unmethylated, as revealed by the patterns of methylation on the two complementary strands of individual DNA molecules. Under our model, we can infer site-specific rates of both maintenance and de novo methylation, values that determine the fidelity of methylation inheritance, from double-stranded methylation data. This approach can be used for populations of cells obtained from individuals without the need for cell culture. We use our method to infer cytosine methylation rates at several sites within the promoter of the human gene FMR1.

Fig. 1.

A double-stranded sequence from the promoter of the hypermethylated FMR1 of a normal human female recovered by using hairpin-bisulfite PCR. Unmethylated cytosines are converted to uracil during the bisulfite reaction and appear as thymine after PCR amplification. Methylated cytosines are not converted. Unconverted (methylated) CpGs are shown in black, and converted (unmethylated) CpGs are boxed. Among these 22 CpG/CpG dyads, 16 were methylated, 2 were hemimethylated, and 4 were unmethylated. The two sites labeled A and B are hemimethylated sites of opposed polarity, with the methylated cytosine on the top strand at one site and on the bottom strand at the other site. The 26-nucleotide hairpin linker is boxed at the far left, with the randomized 7-nucleotide variable barcode shaded. This double-stranded sequence has been separated into two halves for ease of presentation.

Fig. 2.

The transition from methylated and unmethylated single CpGs tallied at time t – 1, just before one round of DNA replication, to methylated, hemimethylated, and unmethylated CpG/CpG dyads tallied at time t, just before the next round of DNA replication. The transition probabilities are determined by the probabilities of maintenance (μ) and de novo (δ_p and δ_d) methylation events. De novo methylation probabilities are considered separately for parent (δ_p) and daughter (δ_d) strands, under the assumption that they are independently susceptible to de novo methylation. Unmethylated single CpGs entering the replication process are represented by white diamonds and u, and methylated single CpGs entering the replication process are represented by filled squares and m. Methylated CpG/CpG dyads produced by the replication process are represented by M, hemimethylated dyads are represented by H, and unmethylated dyads are represented by U.

Fig. 3.

Observed CpG/CpG dyad proportions and inferred methylation rates for seven CpG sites of the FMR1 promoter on the inactive X chromosome of a normal human female. (Lower) The bar graphs represent the proportions of methylated (black), hemimethylated (gray), and unmethylated (white) CpG/CpG dyads at each site; the horizontal line that divides each bar into two parts illustrates the frequency of methylated (below the line) and unmethylated (above the line) single CpGs at each site. (Upper) Maximum-likelihood point estimates for methylation rates. Triangles represent maintenance methylation rates (μ), and circles represent de novo methylation rates (δ). Open circles and triangles represent rates inferred under the assumption that parent and daughter strand de novo methylation rates are equal (δ_p = δ_d); filled circles and triangles represent rates inferred under the assumption that de novo methylation occurs only on the daughter strand (δ_p = 0). The inferred de novo methylation rate for site 16 is 1.0 under both assumptions, because the sampled sequences lacked CpG/CpG dyads of the unmethylated class. The values represented were calculated from the methylation patterns of 33 distinct hypermethylated sequences from different cells, as determined by their molecular barcodes. CpG site numbers correspond to those used in ref. .

Fig. 4.

Examples of maximum-likelihood estimates of site-specific methylation rates and their approximate 95% confidence regions. Point estimates of maintenance and de novo methylation rates were inferred by maximum likelihood under the model given in Fig. 2 by using the data on CpG/CpG dyad classes represented in Fig. 3 Lower. The estimates shown here are based on the assumption that parent and daughter strand de novo methylation rates are equal (δ_p = δ_d). The approximate 95% confidence regions are shown in white; the point estimates are indicated by gray dots. The four sites for which estimates are shown here represent the range of outcomes from the analysis of the seven CpG sites shown in Fig. 3.