biomolecules Article Modeling DNA Methylation Profiles through a Dynamic Equilibrium between Methylation and Demethylation 1, , 2,3, 4 Giulia De Riso * y , Damiano Francesco Giuseppe Fiorillo y, Annalisa Fierro , Mariella Cuomo 1,5, Lorenzo Chiariotti 1,5, Gennaro Miele 2,3 and Sergio Cocozza 1 1 Dipartimento di Medicina Molecolare e Biotecnologie Mediche, Università degli Studi di Napoli “Federico II”, Via S. Pansini 5, 80131 Naples, Italy; [email protected] (M.C.); [email protected] (L.C.); [email protected] (S.C.) 2 Dipartimento di Fisica “E. Pancini”, Università degli Studi di Napoli “Federico II”, 80126, Naples, Italy; dfgfi[email protected] (D.F.G.F.); [email protected] (G.M.) 3 Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, 80126 Naples, Italy 4 CNR-SPIN, c/o Complesso di Monte S. Angelo, via Cinthia, 80126 Naples, Italy; annalisa.fi[email protected] 5 CEINGE Biotecnologie Avanzate, via Gaetano Salvatore 482, 80145 Naples, Italy * Correspondence: [email protected] These authors contributed equally to the work. y Received: 9 July 2020; Accepted: 1 September 2020; Published: 3 September 2020 Abstract: DNA methylation is a heritable epigenetic mark that plays a key role in regulating gene expression. Mathematical modeling has been extensively applied to unravel the regulatory mechanisms of this process. In this study, we aimed to investigate DNA methylation by performing a high-depth analysis of particular loci, and by subsequent modeling of the experimental results. In particular, we performed an in-deep DNA methylation profiling of two genomic loci surrounding the transcription start site of the D-Aspartate Oxidase and the D-Serine Oxidase genes in different samples (n = 51). We found evidence of cell-to-cell differences in DNA methylation status. However, these cell differences were maintained between different individuals, which indeed showed very similar DNA methylation profiles. Therefore, we hypothesized that the observed pattern of DNA methylation was the result of a dynamic balance between DNA methylation and demethylation, and that this balance was identical between individuals. We hence developed a simple mathematical model to test this hypothesis. Our model reliably captured the characteristics of the experimental data, suggesting that DNA methylation and demethylation work together in determining the methylation state of a locus. Furthermore, our model suggested that the methylation status of neighboring cytosines plays an important role in this balance. Keywords: DNA methylation; DNA demethylation; mathematical modeling; statistical equilibrium; cell-to-cell heterogeneity; methylation profiles; epialleles 1. Introduction DNA methylation is a heritable epigenetic mark, consisting of the covalent binding of a methyl group to the 5th carbon of cytosines. In mammals, this modification mainly occurs at CpG dinucleotides, which are enriched at genomic regulatory regions, including gene promoters [1,2]. DNA methylation plays a key role in regulating gene expression by recruiting chromatin remodeling complexes or by regulating the binding of transcription factors to the DNA [3]. The methylation status of each CpG site is the result of two counteracting processes. Biomolecules 2020, 10, 1271; doi:10.3390/biom10091271 www.mdpi.com/journal/biomolecules Biomolecules 2020, 10, 1271 2 of 14 The gain of DNA methylation is due to the activity of the DNA methyltransferases (DNMTs), which transfer the methyl group from the S-Adenosyl L-Methionine (SAM) to unmethylated cytosines. In particular, DNMT1 is proposed as the maintenance methyltransferase, since it preferentially binds and modifies hemimethylated CpGs originating from DNA replication, thus ensuring the stable transmission of the DNA methylome during cell divisions. The de novo DNA methylation is instead mainly attributed to DNMT3a and DNMT3b, which bind both the hemimethylated and the unmethylated cytosines [2,3]. The methylated cytosines (5-methyl-cytosines; 5mC) can be reverted to their unmodified status through passive or active demethylation. The passive process is due to the occasional failure of methylation maintenance during DNA replication. In proliferating cells this can result in a slight, progressive DNA hypomethylation. The active demethylation involves the enzymes from the ten-to-eleven translocation (TET) family. Using Fe (II) and 2-oxoglutarate (2-OG) as cofactors, TETs sequentially oxidize the 5mC to 5-hydroxy-methyl-cytosine, 5-formyl-cytosine, and 5-carboxyl-cytosine. These modified bases are then excised from the DNA by the stepwise action of the thymine–DNA–glycosylase (TDG) and the Base Excision Repair (BER) [4–6]. Much attention has been dedicated in understanding how the methylation status of a CpG can be influenced by the status of the neighboring cytosines. Currently, DNA methylation is mainly considered a cooperative process, meaning that the higher the number of 5mCs in a region, the higher the probability is of a cytosine being methylated. In support of this hypothesis, it has been reported that nearby CpGs often share a similar methylation status [7–11]. This pattern of co-methylation has been attributed to the processivity of DNMT3s that, by binding to the DNA as oligomers, simultaneously methylate different nearby cytosines. Moreover, it has been proposed that the hemimethylated cytosines generated by DNMT3s can directly recruit DNMT1 during the de novo methylation, with a consequent spreading of methyl deposition on the surrounding cytosines [12]. Evidence of the cooperativity of DNA methylation can be also derived from mathematical models. Indeed, schemes that do not consider the methylation of a CpG to be dependent on the methylation of the surrounding sites are mostly unable to predict complex patterns of DNA methylation [13–15]. Whether DNA demethylation is a cooperative phenomenon is more controversial. It has been shown that TETs mostly oxidize 5mC in a non-processive way, stalling on the DNA after the formation of 5hmC. The resulting accumulation of this base prevents the de-novo DNA methylation and can lead to passive demethylation [4–6]. However, on a small fraction of genomic targets, mainly located in regulatory regions, TETs can oxidize 5mCs in a processive way, resulting in an active erasure of DNA methylation [4]. Whether TETs can be preferentially recruited at unmethylated regions is also unclear. Indeed, TETs are mostly indirectly recruited at specific target regions by interacting with other proteins, including transcription factors (TFs) [16]. Nonetheless, TFs can, in turn, bind the DNA in a methylation-sensitive way [17]. Furthermore, it has been proposed that some of the TETs can directly bind stretches of unmethylated cytosines via the CXXC domain. This is thought to be relevant for preventing aberrant DNA methylation at the CpG islands [18]. Recent evidence suggests that methylating and demethylating enzymes act synergistically in shaping the DNA methylation landscape. In particular, Gu et al. demonstrated that DNMTs and TETs contemporarily bind to the DNA, although in a complementary way. The binding of TETs to the gene promoters may avoid the spreading of DNA methylation to the active promoters by confining the DNMT3s outside these regulatory regions [19]. Recently, Rulands et al. provided evidence that DNA methylation and demethylation can occur sequentially on the same DNA molecule. By using a modeling approach, they showed that the co-expression of DNMTs and TETs in a cell can result in an oscillatory dynamic, with cytosines being continuously methylated and demethylated. The different kinetics of the methylation and demethylation reactions ultimately produce heterogeneous methylation profiles among cells [20]. Such heterogeneity, with different cells from the same tissues showing different methylation profiles at the same locus, has been extensively described in other studies [21–24]. Biomolecules 2020, 10, 1271 3 of 14 Despite the presence of this heterogeneity among cells, we and others described that the DNA methylation profiles are mostly conserved when comparing different individuals, suggesting that the cell population as a whole achieves a stable equilibrium in a tissue [25]. Mathematical modeling has been extensively applied to DNA methylation and has provided useful insights on the regulatory mechanisms of this process. In a previous study, we used Markov’s hidden chains to model the DNA methylation changes of the D-aspartate oxidase gene promoter during mouse development [26]. The model was, indeed, aimed at capturing the dynamic of DNA methylation over time. In this model, the methylation status of a CpG site was the result of both its intrinsic susceptibility to DNA methylation and of the methylation status of the surrounding cytosines. In the present study, we developed a new model aimed at analyzing the methylation dynamics, no longer as a function of time, but rather at the steady-state. The model was set up from experimental data obtained by in-depth DNA methylation profiling of 51 samples, using the D-Aspartate Oxidase (DAO) and the D-Serine Oxidase (DDO) as model genes. In this new mathematical model, we took into account both the contemporary effects of methylation and demethylation processes in a region and the influence of neighboring CpGs to these dynamics. 2. Materials and Methods 2.1. Ethical Approval C57BL/6J mice were purchased from the Jackson Laboratory (Bar Harbour, ME). All research involving animals was performed in accordance with the European directive 86/609/EEC governing