Detection of allele-specific methylation through a generalized heterogeneous epigenome model

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1 BIOINFORMATICS Vol. 28 ISMB 2012, pages i163 i171 doi: /bioinfomatics/bts231 Detection of allele-specific methylation though a genealized heteogeneous epigenome model Qian Peng 1,2, and Joseph R. Ecke 2,3,4 1 Depatment of Compute Science and Engineeing, Univesity of Califonia-San Diego, 9500 Gilman Dive, La Jolla, CA and 2 Plant Biology Laboatoy, The Salk Institute fo Biological Studies, La Jolla, CA, 92037, USA. 3 Genomic Analysis Laboatoy, The Salk Institute fo Biological Studies, La Jolla, CA, 92037, USA. 4 Howad Hughes Medical Institute, The Salk Institute fo Biological Studies, Noth Toey Pines Road, La Jolla, Califonia 92037, USA ABSTRACT Motivations: High-thoughput sequencing has made it possible to sequence DNA methylation of a whole genome at the singlebase esolution. A sample, howeve, may contain a numbe of distinct methylation pattens. Fo instance, cells of diffeent types and in diffeent developmental stages may have diffeent methylation pattens. Alleles may be diffeentially methylated, which may patially explain that the lage potions of epigenomes fom single cell types ae patially methylated, and may have majo effects on tansciptional output. Appoaches elying on DNA sequence polymophism to identify individual pattens fom a mixtue of heteogeneous epigenomes ae insufficient as methylcytosines occu at a much highe density than SNPs. Results: We have developed a mixtue model-based appoach fo esolving distinct epigenomes fom a heteogeneous sample. In paticula, the model is applied to the detection of allele-specific methylation (ASM). The methods ae tested on a synthetic methylome and applied to an Aabidopsis single oot cell methylome. Contact: qpeng@cs.ucsd.edu 1 INTRODUCTION The advancement of high-thoughput sequencing has opened up many impotant aeas of applications, one of which is epigenome sequencing. DNA methylation may epess o activate tansciption, and is known to be involved in embyogenesis, genomic impinting and tumoigenesis in mammals, and tansposon silencing in plants (Besto, 2000; Li et al., 1992; Lippman et al., 2004; Rhee et al., 2002; Zhang et al., 2006; Zilbeman et al., 2007). To undestand the egulation and dynamics of DNA methylation, the locations of the modified cytosines need to be identified. The fist single-base esolution mappings of DNA methylation wee poduced fo the whole Aabidopsis thaliana genome (Cokus et al., 2008; Liste et al., 2008) and fo selected subsets of sites in the mouse genome (Meissne et al., 2008) using vaious bisulfite sequencing technologies. DNA methylation is the modification of DNA base cytosine (methylcytosine). A map of DNA methylation at single-base esolution is efeed to as methylome o epigenome. Cells of diffeent types and in diffeent developmental stages may have diffeent methylation pattens. It has been obseved that lage potions of the Aabidopsis methylomes ae patially methylated (Liste et al., 2008). This may be as a esult of the To whom coespondence should be addessed. sample containing a numbe of distinct methylomes. Abeant methylation is also a geneal featue of cance genomes. A bette undestanding of methylation pattens in cance genomes may lead to both new diagnostic makes and theapies based on the detection of methylation changes occuing ealy in tumoigenesis (Laid, 2003). In a tumo tissue paticulaly of an ealy stage, howeve, canceous cells and nomal cells ae often mixed togethe. DNA methylation pattens can also act as makes fo tacing stem cell expansion and tumo gowth (Kim et al., 2005; Shibata and Tavaé, 2006; Yatabe et al., 2001). Making use of methylation pattens in this way equies detemining methylation pattens associated with individual cells o cells fom the same clone. When compaing human fiboblast cell IMR90 and H1 embyonic stem cell (ESC) lines, it is obseved that IMR90 has a lowe level of methylation than H1 ESC (Liste et al., 2009). Both IMR90 and H1 ae of a single cell type. While it is expected that lage potions (80%) of the X chomosome ae patially methylated as the IMR90 cell line is fom a female and the DNA methylation is known to play an impotant ole in X chomosome inactivation (Riggs, 1975), it is unexpectedly obseved that aound 38% of IMR90 autosomes ae identified as patially methylated domains (PMD). What is the natue of patial methylations in a single cell type? Might allelic diffeences contibute to the patial methylations? Answeing these questions equies detecting allele-specific methylation (ASM) pattens. The methylcytosine is sometimes efeed to as the fifth DNA base (Liste and Ecke, 2009). Applying methods fo detection of single nucleotide polymophism (SNP) to methylation, howeve, may pesent difficulties. Methylcytosine is much moe dynamic than nucleotides and obsevations geneally suggest that methylation of a cytosine site is a statistical event. Unlike SNPs whee a nucleotide occus at a ate of 0, 50 o 100% in a diploid individual (if sequencing eos may be ignoed), the methylation level at a paticula site may fall anywhee in the ange fom 0% to 100%. Whethe a methylcytosine is allele-specific theefoe cannot be detemined by the site alone. It needs suppoting evidence fom the neighboing nucleotides. If a patially methylated cytosine is in the close vicinity of a SNP such that eads ae long enough to cove both sites, then it is staightfowad to detemine fom which allele the eads ae oiginated thus detemining the methylation level of the espective alleles. Some studies have shown that ASM is associated with SNPs (Kekel et al., 2008; Shoemake et al., 2010). The density of methylation acoss the whole genome, howeve, is much highe than that of DNA sequence polymophism. Fo instance, while thee ae close to 3 million SNPs discoveed in the human genome 62 million and 45 million methylcytosines wee detected in H1 and The Autho(s) Published by Oxfod Univesity Pess. This is an Open Access aticle distibuted unde the tems of the Ceative Commons Attibution Non-Commecial License ( by-nc/3.0), which pemits unesticted non-commecial use, distibution, and epoduction in any medium, povided the oiginal wok is popely cited.

2 Q.Peng and J.R.Ecke IMR90 cells (Liste et al., 2009). It has also been obseved that changes in cytosine methylation occu at a fequency much geate than that of the DNA sequence mutations (Ossowski et al., 2010; Schmitz et al., 2011). As a esult, SNPs ae absent in lage potions of the methylomes. We will descibe a method in this aticle that detects ASM without the assistance of SNPs. In addition, even though the functionalities of ASM ae not well undestood except that they play an impotant ole in impinting (Hellman and Chess, 2007; Kekel et al., 2008), it seems that the methylation level of an individual cytosine is less impotant than the oveall levels of methylations within a egion, which is also in contast to the SNPs. We, theefoe, focus ou effot in detecting egions of ASM. The emainde of the aticle is oganized as follows. A mixtue model is descibed in Section 2 fo modeling the outcome of a methylation sequencing expeiment whee the sample may contain a mixtue of heteogeneous epigenomes. It aims at pedicting methylation levels fo each cytosine in each individual epigenome. Section 3 lays out the details fo detecting egions of ASM based on the mixtue model and validates the methods on a synthetic methylome. The methods ae then applied to an Aabidopsis oot cell methylome and the esults ae listed in Section 4. Section 5 discusses the esults and offes some futue diections. 2 A MIXTURE MODEL FOR HETEROGENEOUS EPIGENOMES In bisulfite sequencing expeiments, DNA fagments ae teated with sodium bisulfite. The pocess convets unmethylated cytosines into uacils. The sequence of nucleotides (eads) in the conveted fagments ae subsequently detemined by a sequence. The eads poduced by the sequence ae aligned to a efeence genome. Usually only uniquely mapped eads ae etained. As a esult, what we have is a set of eads that ae most simila in sequence to thei espective mapped locations in the efeence genome, which ae pesumably the genomic oigins of the fagments that poduced the eads. In addition, each cytosine on evey mapped ead is labeled as eithe methylated o unmethylated. The methylation level of a paticula cytosine is computed as follows: if thee ae x eads that map to the position, and y out of the x eads have at this position a methylcytosine, then the methylation level is y/x. Note that if the ead depth at a cytosine position is below a cetain theshold, which is detemined by the allowed false positive ate, the methylation is not called, i.e. y =0. (Liste et al., 2008) If the oiginal sample is composed of a mixtue of epigenomes, be it fom a set of diffeent cell types, tissues o alleles, the mapped eads will eflect the mixtue. Ou goal is to infe the oiginal makeup of the mixtue fom the mapped eads. It should be noted that the attainment of the goal depends on whethe the oiginal epigenomes ae sufficiently heteogeneous so that we may distinguish them. As we ae only concened with methylation, we estict the eads to the genomic positions whee the methylation level is geate than zeo. The epigenomes and eads may be epesented as binay stings, whee methylcytosine is set to 1 and the emainde to 0. Let R be a set of binay stings, which we assume ae the eads poduced by a bisulfite sequencing expeiment futhe esticted to methylation sites. Fo sting R, let x i be the lette appeaing at position i fom ; let [ a, b ] be the positions that spans. Let C ={c j j =1 k} be the set of natual fequencies of epigenomes, whee c j is the fequency of the j-th epigenome, and k is the total numbe of epigenomes. When the model is used to detect the ASM of a diploid oganism, k equals to 2. Let M ={m ij i =1 n,j =1 k}, whee m ij is the pobability of methylation of epigenome j at position i, and n is the length of the epigenome. The pobability of obseving sting is k P()= c j p j, whee p j is the pobability that sting oiginates fom epigenome j, and b ( p j = mij x i +(1 m ij )(1 x i ) ). (1) i= a The pobability of obseving the set R is theefoe P(M,C,R)= RP(), o equivalently the log likelihood l(m,c,r)= RlogP(). The optimization goal is to detemine paametes C and M such that the pobability of obseving the set R is maximum, thus best explaining the eads. We estimate aay C and matix M by maximizing the likelihood l, agmax M,C logp(), R which can be solved by using the expectation-maximization (EM) algoithm (Dempste et al., 1977). Fist, we define a membeship matix A={a j R,j =1...k}, whee { 1 if j, a j = 0 if / j. As the membeship of sting with espect to epigenome j is unknown, it is estimated by its expected value as a j = c jp j j c j p. (2) j The likelihood can then be ewitten as l(m,c,r,a)= k a j log(c j p j ), (3) and the optimization becomes k agmax M,C a j log(c j p j ). Solving the maximization constained by k c j =1 yields the update equations at each M-step iteation of the EM algoithm as follows (see Appendix A fo the detailed deivation), c j = a j j a, m ij = j a jx i a. j When the algoithm conveges, the matix M contains the pedicted methylation levels fo each epigenome in the mixtue. i164

3 Detection of Allele-Specific Methylation 3 DETECTION OF ASM In this section, we descibe how the model is used to detect allele-specific methylated egions in a diploid oganism. Notice that ASM is not a pecisely defined tem. It geneally efes to a significant diffeence between the methylation levels of the two alleles. Fist, the methylome of a diploid individual is scanned fo patially methylated egions (PMRs) as candidates fo futhe analysis. Second, fo each candidate egion, the eads that align to this egion ae computationally assigned to the two alleles and the methylation levels of individual cytosines fom each allele ae estimated. Last, egions ae classified to allele-specific o nonspecific methylated egions, based on ead assignments and the pedicted methylation levels fom the pevious step. A synthetic methylome is used to test the model and to illustate the details of each step. We emak that detemining whethe a ead along with its methylcytosines has a highe pobability to oiginate fom one allele o the othe elies on the diffeences between the eads, i.e. the methylation states of the cytosines on the eads. The density of methylcytosines of a genome elative to the ead length in a sequencing expeiment is theefoe citical. Fo instance, if, on aveage, a ead coves at most one methylcytosine, then thee is vey little hope to deconvolve the allelic methylation states without additional infomation. While anticipating the apid gowth of the ead length in high-thoughput sequencing technology, we fist tested ou method on Aabidopsis thaliana, which has a easonably high methylation density. The median genomic distance, fo instance, between consecutive methylcytosines on Chomosome 1ofA. thaliana Col-0 is 15, while the typical ead length of an Illumina sequence is between 100 and 150 bp pesently. 3.1 Identify PMRs as candidates To detect ASM egions, the whole methylome is scanned fo PMRs as candidates, as thee is obviously not much diffeence between the two alleles if the methylation level of a egion is nea nil o complete. A contiguous methylated egion (CMR) efes to a genomic egion whee the genomic distance between any two consecutive methylcytosines is no lage than a sepaation theshold s, which is set at aound a width compaable to the ead length. Each CMR is scanned with a fixed-width sliding window whee the window width is the numbe of methylcytosines. A fixed-width window inside a CMR is classified as a PMR if no fewe than 90% of the methylcytosines ae at most 70% methylated (Liste et al., 2009). A PMR may be called with o without a specific lowe bound fo methylation levels. In the data we have analyzed, the aveage level of methylations in a CMR is at least 25%, due to that (i) the egion has contiguous methylcytosines; (ii) the allowed false positive ate fo calling a methylcytosine (Liste et al., 2008) in combination with the sequencing coveage dictates an implicit lowe bound on the methylation levels. Consecutive PMRs within the same CMR ae meged into a single egion. The dataset being tested is a synthetic methylome that is made up by combining the eads of two methylomes fom Aabidopsis oot cells: epidemis (We+) and endodemis (Sc+). The oot cells ae obtained by flow soting; thei methylomes by MethylC-Seq bisulfite sequencing (Liste et al., 2008). The genomic length of the eads is 83 bp. The eads fom one cell type in the mixtue ae teated as if they ae fom one allele of the synthetic methylome. The ASM Table 1. Samples of patially methylated egions fo classification 20 mc 35 mc 50 mc Samples CS NS CS NS CS NS Taining Testing mc: methylcytosine; CS: cell-specific; NS: non-specific of the synthetic methylome is, theefoe, simulated by cell-specific methylation in the mixtue. Fowad stand and evese stand ae pocessed sepaately. As ASM and cell-specific methylation aise fom diffeent biological pocesses, the pattens of diffeential methylations might, theefoe, cay signatues unique to each type. The afoementioned synthetic methylome is appopiate fo testing cellspecific methylations; yet whethe it is a good suogate fo testing ASMs may be questioned. We ague that since the classification is lagely based on oveall methylation levels within a egion athe than elations among methylation levels of individual cytosine sites, the citeia similaly apply to both cell-specific methylation and ASM. The sepaation theshold s is set to 100 bp. Each CMR is scanned with a sliding window of width 20, 35 and 50 methylcytosines espectively. Each PMR in the synthetic methylome is labeled as eithe cell-specific (allele-specific), if no fewe than 90% cytosines in the egion ae methylated in only one of the two cells, o nonspecific othewise. Fo the pupose of leaning, consecutive windows within the same CMR ae meged into one egion only if they ae labeled as the same type. Fo a sliding window of width 20, both cell-specific egions and non-specific egions have a median width of 23 methylcytosines. All of the cell-specific egions and aound the same numbe of andomly selected non-specific egions ae kept as samples fo futhe analysis. The samples ae divided into taining and testing samples (Table 1). 3.2 Pedict allelic methylation levels Fo each PMR, the algoithm descibed in Section 2 is applied with k =2. Fo each sample of the synthetic methylome, the eads fom the two individual methylomes ae mixed togethe. One potential poblem with the EM algoithm is that it may convege to a local optimum. Thee ae vaious ways to initialize the paametes. One initialization is to andomly assign each ead to a cluste, i.e. set a j =1 at pobability 1/k. Anothe option is to set c j =1/k, and then andomize matix M. A thid option is to andomize the membeship matix A, which appeas to be the best option afte testing with simulated data. We un the algoithm L times, each with a new andom matix A as the initialization. Let A 1, A 2,...,A L be the membeship matix when each individual un conveges, fom which two new initializations ae deived: A L+1 and A L+2, fo two additional uns. 1 They ae defined as 1 A subtlety hee concens the odeing of the clustes at the end of each un. The details ae omitted. i165

4 Q.Peng and J.R.Ecke Fig. 1. Expeimental (a and b) vesus pedicted (c and d) methylation levels of the synthetic methylome. Expeimental methylation levels fom We+ ae shown in cicles, Sc+ in stas. Two symbols in the bottom figues (c and d) indicate two pedicted individual methylomes fo the synthetic methylome. The left (a and c) is of an allele-specific egion: chomosome 1: [ , ] on fowad stand. The egion contains 50 methylcytosines (mc); 160 eads ae aligned to this egion. The ight (b and d) is of a non-specific egion: chomosome 3: [ , ] on fowad stand. The egion contains 42 mc; 367 eads ae aligned to the egion follows: fo R, j =1...k, a L+1 j a L+2 j = = 1 L a L j i ; i=1 { 1 if j =agmax k j =1 (al+1 j ) 0 othewise. Of the total L+2 uns, the one that conveges to the lagest likelihood is selected. The matix M yields a pedicted level of methylations at each cytosine site. Figue 1 illustates two samples of PMRs fom the synthetic methylome: one cell-specific and the othe non-specific. Both expeimental and pedicted methylation states ae shown. The expeimental data ae fom the individual methylomes and ae thus teated as golden. The pedicted methylation states ae used fo futhe classification. 3.3 Classify candidate egions with a suppot vecto machine classifie Once the methylation levels of individual methylcytosines in each allele ae estimated and the membeship of eads pedicted by the model, what emains is to chaacteize and classify each egion based on the estimations. Recall that we used a athe simplistic ule to automatically label the samples in the synthetic methylome when pepaing the taining and testing samples. The labels ae deived fom the knowledge of the two individual methylomes making up the synthetic methylome, and theefoe ae independent of the pedictions made by the mixtue model. One option is to use the same ule to classify a egion fom pedicted methylation levels. We hope to captue moe chaacteistics of the two classes, howeve, so multiple measues ae employed fo this task when it is applied to the eal epigenome. We also use the synthetic methylome to tain a suppot vecto machine (SVM) classifie that is late used fo a eal single cell methylome. Notice that the value a j gives the pobability that the ead is fom allele j. If a ead needs to be assigned to a single allele, it should be assigned to the j that has the lage value of a j, o fomally, to cluste j =agmax j (a j ). The featues fo SVM ae extacted fom the estimated methylation levels (M ) and allele fequencies (C). A total of nine featues ae used (details omitted due to exigencies of space). Both linea and adial basis function (RBF) kenels ae tested; the latte yield bette pefomance. Five-fold coss-validation is used to select the best paametes fo the kenel function fom each taining set. The testing esults ae shown in Table 2. In some of the false positive (FP) samples, both cells have completely unmethylated eads and these eads ae clusteed togethe in the synthetic methylome, which ae then classified as allele-specific (cell-specific). We hypothesize that these egions have ASM in both individual cell types. i166

5 Detection of Allele-Specific Methylation Table 2. Testing esults fo classification of patially methylated egions 20 mc 35 mc 50 mc Samples CS NS CS NS CS NS Pedicted CS 88 (TP) 13 (FP) Pedicted NS 12 (FN) 87 (TN) Accuacy 87.5% 87.5% 83.3% CS: cell-specific; NS: non-specific Table 3. Classes based on diffeential aveaged methylation d Class name Label [0.0,0.2] Similaly methylated d s (0.2,0.9) Modeately diffeentially methylated d m [0.9,1.0] Highly diffeentially methylated d h Table 4. Pedicted ASM egions Method svm lm dm mww Intesection Regions d h : (1) d m : (2) d m 192 (3) 3.4 Identify ASM egions with multiple filtes Using an SVM classifie has its limitations. A classifie tained on one oganism will cetainly not be appopiate fo othe oganisms. A classifie tained on one cell type may be questionable fo anothe vey diffeent type. When paametes fo the sequencing expeiment change, the classifie should be etained. In addition, thee may not be sufficient data samples fo leaning at all. Additional measues ae theefoe necessay fo eal data. The Mann Whitney Wilcoxon (mww) test is pefomed on the two clustes esulting fom the mixtue model. If the null hypothesis is ejected, one cannot eadily claim that the methylations ae allelespecific. But if on the othe hand the null hypothesis is not ejected, it is unlikely that the methylations ae allele-specific. Two additional filtes ae based on methylation ates. One filte is called low methylation ate (lm). It computes whethe one of the two clustes is 10% methylated at 80% sites. The othe is called diffeential aveaged methylation ate (dm). The aveaged methylation ate fo each cluste in the egion is defined as j = 1 n m ij, n m i=1 i1 +m i2 and the diffeential aveaged methylation as d = 1 2. We define thee classes based on this measue shown in Table 3. 4 DETECT ASM REGIONS FOR ARABIDOPSIS EPIDERMIS METHYLOME The methods ae applied to the methylome of a single cell type, a oot epidemis (We+) cell fom A. thaliana Col-0. Thee ae a total of 452 patially methylated egions as defined in Section 3.1. The total genomic length of the egions is bp, coveing 9980 methylcytosines. The eads ae aligned to these egions. Once the methylation levels of the two alleles and the membeship of all eads ae pedicted by the models, the esults ae subject to fou methods fo classification as mentioned in Sections 3.3 and 3.4. Recall that the SVM model is tained on the synthetic methylome made up of two Aabidopsis oot methylomes, We+ being one of them. Table 4 shows the numbe of PMRs pedicted to be allelespecific by each method and the intesection is taken so as to obtain the most consevative pedictions. The fist two ows of the table eflect the intesections taken between the d h class and all othe citeia, and d m class and othe citeia, espectively, totaling 34 egions. Table 5 lists the details and annotations fo goup (1), and Table 6 fo goup (2). Based on the pedicted methylation levels, both goups ae highly allele-specific. While one of the two alleles has nealy no methylation, in the fist goup of 18 egions, the othe allele is in geneal highly methylated; and in the second goup of 16 egions, the methylated allele is moe patially methylated. An example fom each goup is shown in Figue 2. If the citeia fo ASM ae elaxed a bit by emoving the athe stingent filte lm, many moe egions [the last ow (3) in Table 4] ae admitted Table 5. Pedicted ASM egions, goup (1) in Table 4 ch Cood stat Cood end No. of mc st Gene model < AT1G AT1TE AT1TE AT1TE > AT1G59660 < AT1G AT2G UTR AT2TE29970 < AT2G > AT2G34060 > AT2G AT3TE < AT3G45570 AT3TE < AT4G > AT4G20210 AT4TE AT4TE55215 > AT4G22690 < AT4G AT4TE AT5TE18530 > AT5G AT5TE AT5TE < AT5G AT5TE94040 ch: chomosome; st: stand; <: upsteam; >: downsteam; Signs in the last column indicate opposite stands. i167

6 Q.Peng and J.R.Ecke Table 6. Pedicted ASM egions, goup (2) in Table 4 ch Cood stat Cood end No. of mc st Gene model < AT1G < AT1G AT1TE70195 AT1TE < AT1G AT2TE09960 > AT2G AT2TE51520 > AT2G AT2TE51520 > AT2G > AT3TE AT3TE AT3TE65915 < AT3G AT3TE > AT3G > AT4TE AT4TE19110 < AT4G AT5TE AT5TE AT5TE55235 < AT5G AT5TE62865 ch: chomosome; st: stand; <: upsteam; >: downsteam; Signs in the last column indicate opposite stands. Fig. 2. Read assignments (a and b) and methylation levels (c and d) of the pedicted ASM egions of Aabidopsis We+ cell. Cicle and sta symbols in c and d epesent two alleles. Lines in top (a and b) figues ae esticted eads (solid and dotted lines epesent two alleles); small diamonds on lines ae methylations. Left (a and c) : a egion of Table 4(1): chom 4: [ , ] stand. Right (b and d) : a egion of Table 4(2): chom 5: [ , ] + stand i168

7 Detection of Allele-Specific Methylation Table 8. GO annotation summay fo potein coding genes in Table 7 Functional categoy Gene body Upsteam Downsteam Unknown cellula components Chlooplast Othe intacellula components Othe cellula components 7 6 Othe cytoplasmic components Othe membanes Nucleus Plastid Plasma membane Unknown molecula functions Othe enzyme activity Othe binding Potein binding Tansfease activity 2 4 Othe molecula functions 4 2 Tansfease activity 5 Tanspote activity 1 4 Hydolase activity 3 DNA o RNA binding 3 Nucleotide binding 3 Fig. 3. An example fom Table 4 goup (3): egion: chom 1: [77393, 77508] stand, 20 mc. (a) eads assignments. (b) pedicted methylation levels Othe metabolic pocesses Unknown biological pocesses Othe cellula pocesses Response to stess Response to abiotic o biotic stimulus 5 6 Tansciption,DNA-dependent Potein metabolism 5 1 Tanspot 1 4 Othes Table 7. Annotation summay of all ASM egions in Table 4 Annotation Ovelap Upsteam Downsteam Potein coding gene 4 (4) exon 50 (24) 56 (25) 9 (7) inton 1 (1) 3 UTR TE gene 19 (8) 11 (3) 4 (1) Pseudogene mi, t, othe RNA 1 5 (2) 3 Tansposon (only) 66 (39) Numbes in paenthesis ae on the opposite stands. Upsteam and downsteam ae within 1kb. fo futhe examination. An example fom this goup is shown in Figue 3. Table 7 summaizes the TAIR9 annotations (TAIR, 2009) fo all thee goups of a total of 226 pedicated ASM egions. Many egions ovelap with natual tansposons as expected; the last ow in the table epots the numbe of egions that have no othe annotation than tansposon. Fo the potein coding genes, the gene ontology annotations ae summaized in Table 8. One egion fom goup (3), on fowad stand of chomosome 1: , is on the antisense of an exon of potein coding gene AT3G29360, an impinted gene in A. thaliana seed epoted by McKeown et al. (2011). The egion has 26 methylcytosines. 5 CONCLUSION AND DISCUSSION We have descibed a computational model fo esolving distinct epigenomes fom a heteogeneous sample. In paticula, we applied this model to identify allele-specific methylated egions. The eads fom potentially multiple epigenomes ae mapped to a common efeence genome. The goal is essentially to infe the distinct methylation pattens fom the mapped eads. Ou appoach is diffeent fom pevious attempts in that it does not ely on SNPs, which ae few and fa between when compaed with methylcytosines. The model was tested on a synthetic methylome. The classification based on the mixtue model in conjunction with an SVM classifie yielded an accuacy of 87.5%. Even though the SVM appoach is not always applicable to eal methylomes, since all the featues ae deived fom the pedicted methylation levels and cluste fequencies, the test esults eflect the eliability of the pedictions made by the model. Additional multiple filtes fo ASMs may futhe educe the numbe of false positives. Additional appoaches may be employed to validate the methods fo ASM detection. One appoach is to use ASMs detemined with SNP data as gound tuth, although such data ae pesently spase and anecdotal. Anothe appoach to validate ASM is to use heitable epi-alleles in combination with phasing infomation obtained fom cossing of plants. i169

8 Q.Peng and J.R.Ecke We applied the methods to egions of the genome with elatively high density of methylcytosines with each egion being teated independently. By taking advantage of pai-end eads and othe infomation, it will also be possible to do phasing and extend and connect the egions. Ou model assumes that methylations ae independent of each othe. Methylations in some egions have a tendency to occu in clustes, which indicates a cetain dependency. While ou model gives a easonably good fist-ode appoximation, Makov chain-based models pehaps may be exploed to take the dependency into consideation. Identifying ASM is still only at initial eseach stages. Anothe diection fo futue eseach is to focus on undestanding the functionalities of ASM, fo instance, how they ae elated to allele-specific expession. Moe complicated heteogeneous epigenome samples may aise fom a mixtue of vaious cell types, o a mixtue of canceous cells at vaious stages, which pesent yet moe and geate challenges than the allelic methylations of a diploid cell. Such samples will enable an ultimate test fo the powe of the methods. The initial steps ae to develop scenaios and citeia fo validation as it becomes less obvious what defines cell-specific methylations in the context of multiple cell types. ACKNOWLEDGEMENT We would like to thank Ds Ryan Liste and Ronan O Malley fom the Salk Institute fo poviding the expeimental data, and Pofesso Sanjoy Dasgupta fom UC-San Diego fo insightful discussions. Funding: This wok was suppoted by the Howad Hughes Medical Institute and the Godon and Betty Mooe Foundation to JRE. JRE is an HHMI-GBMF Investigato. Conflict of Inteest: none declaed. REFERENCES Besto,T.H. (2000) The DNA methyltansfeases of mammals. Hum. Mol. Genet., 9, Cokus,S.J. et al. 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Genet., 39, APPENDIX A Section 2 descibed the model fo a mixtue of epigenomes. This section details the deivation of the update equations at each M-step iteation fo the EM algoithm. Recall fom Section 2 that the optimization goal is to detemine the methylation pobability matix M and the epigenome fequency aay C such that the likelihood l(m,c,r,a) as defined by Equation (3) is maximized given the set of obseved esticted eads R. The membeship matix A is estimated by Equation (2) at each iteation. As the maximization of likelihood l(m,c,r,a) is constained by k c j =1, i.e. the epigenome fequencies sum up to 1, we will intoduce Lagange multiplie λ and maximize the unconstained function l(m,c,r,a,λ)= k k a j log(c j p j ) λ c j 1. Substituting in p j given by Equation (1), we have l = k k (a j logp j +a j logc j ) λ c j 1 = k b ( a j log mij x i +(1 m ij )(1 x i ) ) i= a + k k a j logc j λ c j 1 = k b ( a j xi logm ij +(1 x i )log(1 m ij ) ) i= a + k k a j logc j λ c j 1. i170

9 Detection of Allele-Specific Methylation Maximizing l with espect to M,C,λ by setting the espective patial deivatives to zeo yields the following set of equations l =0 ( ) x i a j 1 x i =0 m ij m ij 1 m ij a j (x i m ij )=0, l =0 a j λ=0 c j c j c j = 1 a j, λ l λ =0 ( 1 a j )=1 λ j λ= a j. j Solving fo m ij and substituting in λ fo c j lead to the update equations at each M-step iteation of the EM algoithm as follows, m ij = a jx i a, c j = a j j j a. j i171