RESEARCH ARTICLE SUMMARY◥

EPIGENOMICS

Allele-specific epigenome maps revealsequence-dependent stochasticswitching at regulatory lociVitor Onuchic*, Eugene Lurie*, Ivenise Carrero, Piotr Pawliczek, Ronak Y. Patel,Joel Rozowsky, Timur Galeev, Zhuoyi Huang, Robert C. Altshuler, Zhizhuo Zhang,R. Alan Harris, Cristian Coarfa, Lillian Ashmore, Jessica W. Bertol, Walid D. Fakhouri,Fuli Yu, Manolis Kellis, Mark Gerstein, Aleksandar Milosavljevic†

INTRODUCTION: Amajority of imbalances inDNAmethylation between homologous chro-mosomes in humans are sequence-dependent;the DNA sequence differences between the twochromosomes cause differences in themethyla-tion state of neighboring cytosines on the samechromosome. The analyses of this sequence-dependent allele-specific methylation (SD-ASM)traditionally involvedmeasurement of averagemethylation levels across many cells. Detailedunderstanding of SD-ASM at the single-celland single-chromosome levels is lacking. Thisgap in understanding may hide the connection

between SD-ASM, ubiquitous stochastic cell-to-cell and chromosome-to-chromosome variationin DNA methylation, and the puzzling andevolutionarily conserved patterns of intermedi-ate methylation at gene regulatory loci.

RATIONALE:Whole-genome bisulfite se-quencing (WGBS) provides the ultimatesingle-chromosome level of resolution and com-prehensive whole-genome coverage required toexplore SD-ASM. However, the exploration ofthe link between SD-ASM, stochastic variationin DNA methylation, and gene regulation re-

quires deep coverage by WGBS across tissuesand individuals and the context of other epi-genomic marks and gene transcription.

RESULTS:We constructed maps of allelic im-balances in DNA methylation, histone marks,and gene transcription in 71 epigenomes from36 distinct cell and tissue types from 13 donors.Deep (1691-fold) combined WGBS read cover-age across 49methylomes revealed CpGmeth-ylation imbalances exceeding 30% differencesat 5% of the loci, which is more conservativethan previous estimates in the 8 to 10% range;a similar value (8%) is observed in our datasetwhen we lowered our threshold for detecting

allelic imbalance to 20%methylation difference be-tween the two alleles.Extensive sequence-

dependent CpGmethyla-tion imbalances wereobserved at thousands of

heterozygous regulatory loci. Stochastic switch-ing, defined as random transitions between fullymethylated and unmethylated states of DNA,occurred at thousands of regulatory loci boundby transcription factors (TFs). Our results ex-plain the conservation of intermediatemethyla-tion states at regulatory loci by showing that theintermediate methylation reflects the relativefrequencies of fully methylated and fully un-methylated epialleles. SD-ASM is explainableby different relative frequencies of methylatedand unmethylated epialleles for the two alleles.The differences in epiallele frequency spectra ofthe alleles at thousands of TF-bound regulatoryloci correlated with the differences in alleles’affinities for TF binding, which suggests amechanistic explanation for SD-ASM.We observed an excess of rare variants among

those showing SD-ASM, which suggests that anaverage human genome harbors at least ~200detrimental rare variants that also show SD-ASM. The methylome’s sensitivity to geneticvariation is unevenly distributed across thegenome, which is consistent with buffering ofhousekeeping genes against the effects of ran-dommutations. By contrast, less essential geneswith tissue-specific expression patterns showsensitivity, thus providing opportunity for evo-lutionary innovation through changes in generegulation.

CONCLUSION: Analysis of allelic epigenomemaps provides a unifying model that linkssequence-dependent allelic imbalances of theepigenome, stochastic switching at gene regu-latory loci, selective buffering of the regulatorycircuitry against the effects of randommutations,and disease-associated genetic variation.▪

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The list of author affiliations is available in the full article online.*These authors contributed equally to this work.†Corresponding author. Email: amilosav@bcm.eduCite this article as V. Onuchic et al., Science 361, eaar3146(2018). DOI: 10.1126/science.aar3146

SD-ASM

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SD-ASM is explainable by different frequencies of epialleles.Genetic variants affect the methylationstate of neighboring cytosines on the same chromosome. EveryWGBS readprovides a readout of both agenetic variant (G or T) at a heterozygous locus and the methylation state of neighboring cytosines(“epiallele”). Epiallele frequencies correlate with the affinity of TF binding at regulatory sites.

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RESEARCH ARTICLE◥

EPIGENOMICS

Allele-specific epigenome maps revealsequence-dependent stochasticswitching at regulatory lociVitor Onuchic1,2,3,4*†, Eugene Lurie1,3,4*, Ivenise Carrero1,3, Piotr Pawliczek1,3,Ronak Y. Patel1,3, Joel Rozowsky5,6, Timur Galeev5,6, Zhuoyi Huang1,7,Robert C. Altshuler4,8,9, Zhizhuo Zhang8,9, R. Alan Harris1,3,4, Cristian Coarfa1,3,4,Lillian Ashmore1,2,3, Jessica W. Bertol10, Walid D. Fakhouri10, Fuli Yu1,2,7,Manolis Kellis4,8,9, Mark Gerstein5,6, Aleksandar Milosavljevic1,2,3,4‡

To assess the impact of genetic variation in regulatory loci on human health, we constructed ahigh-resolution map of allelic imbalances in DNA methylation, histone marks, and genetranscription in 71 epigenomes from 36 distinct cell and tissue types from 13 donors. Deepwhole-genome bisulfite sequencing of 49 methylomes revealed sequence-dependent CpGmethylation imbalances at thousands of heterozygous regulatory loci. Such loci are enrichedfor stochastic switching, which is defined as random transitions between fully methylatedand unmethylated states of DNA.The methylation imbalances at thousands of loci areexplainable by different relative frequencies of the methylated and unmethylated states forthe two alleles. Further analyses provided a unifying model that links sequence-dependentallelic imbalances of the epigenome, stochastic switching at gene regulatory loci, anddisease-associated genetic variation.

Amajority of imbalances in DNA methyla-tion between homologous chromosomesin humans are associated with genetic var-iation in cis, in which the genetic variantsaffect the methylation state of neighboring

cytosines on the same chromosome (1, 2). Suchsequence-dependent allele-specific methylation(SD-ASM) affects at least 8 to 10% of the au-tosomal genome (3–5). SD-ASM is an ideally“controlled” natural experiment that providesinformation about consequences of genetic var-iation in cis because both “case” and “control”loci can be found within an individual on ho-mologous chromosomeswithin the same cellularand nuclear environment.

In contrast to association-based methods—such as expression quantitative trait loci (eQTLs)and methylation quantitative trait loci (mQTLs),used to establish the functional effects of com-mon (>5% minor allele frequency) noncodingvariants (6)—allelic imbalances (AIs) can beestablished by profiling a single sample, reveal-ing the functional effects in cis of both relativelylow-risk common variants and highly pene-trant disease-causing rare and de novo variants(1, 2, 5, 7–10).Although the analyses of SD-ASM traditionally

involved measurement of average methylationlevels across many cells, the epigenome is knownto exhibit stochastic cell-to-cell variation andeven variation between the two chromosomeswithin the same nucleus (11). Whole-genomebisulfite sequencing (WGBS) has the potentialto provide insights into stochastic variation atthe ultimate single-chromosome level of resolu-tion because it provides information about thegenetic variant and methylation of neighboringcytosines within the same sequencing read thatcomes from a single chromosome. Sequencing-based studies of DNAmethylation have revealedpervasive stochastic epigenetic polymorphismswithin autosomal loci (12, 13).Methylation patterns evolve along predictable

trajectories during normal development (14),being highly stochastic in earlymetastable stagesand stabilizing within differentiated tissues,which results inmosaicism (15). Themethylationpatterns are maintained in stem cells through adynamic stochastic epigenetic switching equilib-

rium (an ergodic process) that provides bothepigenetic buffering of environmental noise andresponsiveness to specific transcription factors(TFs) (12). By contrast, more differentiated cells(12) and tumor cells (13, 16) appear to use themore error-pronemechanism of direct replicationof CpG methylation patterns, which is associatedwith clonality and mosaicism. Despite the sto-chastic nature of DNAmethylation changes dur-ing development, in response to environmentalinput and in human diseases, the effects ofgenetic variation on stochasticity and mosaicismof the epigenome remain unexplored.

ResultsPatterns of AIs across epigenomic marks

To explore the effects of genetic variation on theepigenome, the National Institutes of Health(NIH) Roadmap Epigenomics Project (17 ) hasnow completedwhole-genome sequencing (WGS)on genomes of 13 donors and published NIHRoadmap reference epigenomes from 71 com-bined samples that collectively represent 27 dis-tinct tissue types and nine cell types (fig. S1). Foraccurate identification of heterozygous genomicloci, we sequenced the donor genomes (18). Eightassays were included in most of the samples andused for AI detection: WGBS, RNA sequencing(RNA-seq), and chromatin immunoprecipita-tion sequencing (ChIP-seq) for six differenthistonemarks (H3K4me3,H3K4me1,H3K36me3,H3K27me3,H3K9me3, andH3K27ac) (fig. S1).Weperformed allele-specific methylation (ASM) analy-sis at heterozygous single-nucleotidepolymorphism(SNP) loci within the 49 WGBS methylomesusing a threshold of absolute methylation dif-ference of >30% between alleles and by estimat-ing significance by means of Fisher’s exact teston the counts of methylated and unmethylatedcytosines observed on the same sequencing readwith each of the two SNP alleles (fig. S2A) (18).We performed the identification of AIs for his-tonemarks and transcription using the AlleleSeqpipeline (fig. S2B) (18, 19).Considering the AIs in all the marks, the im-

balances in DNA methylation were by far themost abundant (table S1 and fig. S3), largely be-cause of the genome-wide distribution of DNAmethylation, in contrast to the uneven genomicdistribution of other marks. Among the histonemarks, H3K27ac had more imbalance calls thanothers (table S1), in part owing to deeper ChIP-seq coverage for H3K27ac (table S1 and fig. S3).At promoters, H3K27ac and H3K4me3 markswere more abundant on the allele with less DNAmethylation (Fig. 1A). Conversely, H3K9me3 sig-nal was more abundant on the allele with moremethylation in promoters (Fig. 1A). At enhancers,H3K27ac tended to occur more often on the allelewith less DNA methylation (Fig. 1A). We alsodetected, at high specificity, enrichment ofAIs in methylation and coordinated changes intranscription and histone marks within a major-ity of those imprinted loci that included a het-erozygous SNP (figs. S4 and S5) (18).We next evaluated the extent of reported

SD-ASM. Consistent with genetic effects in cis

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1Molecular and Human Genetics Department, Baylor Collegeof Medicine, Houston, TX, USA. 2Program in Quantitative andComputational Biosciences, Baylor College of Medicine,Houston, TX, USA. 3Epigenome Center, Baylor College ofMedicine, Houston, TX, USA. 4NIH Roadmap EpigenomicsProject. 5Program in Computational Biology andBioinformatics, Department of Molecular Biophysics andBiochemistry, Yale University, New Haven, CT, USA.6Department of Computer Science, Yale University, New Haven,CT, USA. 7Human Genome Sequencing Center, BaylorCollege of Medicine, Houston, TX, USA. 8Computer Scienceand Artificial Intelligence Laboratory, Massachusetts Instituteof Technology, Cambridge, MA, USA. 9Broad Institute ofHarvard University and Massachusetts Institute ofTechnology, Cambridge, MA, USA. 10Center for CraniofacialResearch, Department of Diagnostic and BiomedicalSciences, School of Dentistry, University of Texas HealthScience Center at Houston, Houston, TX, USA.*These authors contributed equally to this work.†Present address: Illumina, San Diego, CA, USA.‡Corresponding author. Email: amilosav@bcm.edu

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(6, 20–22), co-occurrence of ASM at the sameheterozygous locus across different sampleswas higher than expected by chance under apermutation-based null model (fig. S6A). Thedegree of co-occurrence of ASM tended to behigher for pairs of samples across tissues ofthe same individual than between pairs fromthe same tissue across different individuals,which was higher than for samples withoutmatching tissue or individual (fig. S6B). Lowconcordance in ASM calls between individualsmay be due to local haplotype context, epigeneticdrift, or other nongenetic factors (3, 4, 6, 20, 22, 23).Gaussianmixturemodeling (18) showed that allelicdifferences in methylation (above the 30% thresh-old) at heterozygous SNPs had a tendency to occurin the same direction (the same allele showinghigher methylation than the other) across pairsof samples (fig. S6, C to E).In order to increase the power to detect SD-

ASM at high sensitivity, we pooled the readsacross all 49 methylomes and applied the samedetectionmethod as for individual samples (fig. S7A)(18). The deep coverage of the combined set(1691-fold total coverage in bisulfite sequencingreads in the combined set of 49 methylomes)increased our power to detect those sequence-associated AIs that were detectable across dif-ferent tissues and donors (fig. S7, B to D), whereasour power to detect tissue-dependent and donor-dependent SD-ASM was reduced (fig. S8, A andB). The number of accessible heterozygous loci(those having at least six counts per allele), forSD-ASM determination, after pooling rose to4,913,361, increasing our SD-ASM mappingresolution—measured as an average distancebetween “index hets”—to 600 base pairs (bp).At the 30% methylation difference defaultthreshold, AIs were detected at 5% of indexhets; lowering the threshold to 20%, a total of~8% index hets showed AIs.

Sensitivity of the methylome to geneticvariation varies across classes ofgenomic elements

We next explored whether SD-ASM had thetendency to occur within any particular typeof genomic element. Using the reads pooledacross the 49 methylomes, we observed deple-tion of SD-ASM within promoters containingCpG islands (Fig. 1B), as well as within CpGislands in general (Fig. 1C), which is consistentwith observations that ASM is depleted in CpGislands (4, 21) and that mQTLs are depletedwithin promoters of genes within CpG islands(24, 25) and that expression quantitative traitmethylation is enriched within CpG island shoresand not in CpG islands themselves (26). By con-trast, and mirroring previous mQTL patterns(25), promoters of genes not in CpG islandsshowed high levels of SD-ASM (Fig. 1D). Wealso observed enrichment of SD-ASM down-stream from the promoter and into the genebody (Fig. 1, B and D) and positive associationbetween allele-specific expression (ASE) andASM over exons (Fig. 1A), which is consistentwith higher methylation of actively transcribed

regions, including those on the X chromosome(27) and with the enrichment of mQTLs in re-gions flanking the transcription start site (TSS)(23, 28). One factor contributing to the ASM,particularly near the transcription start sites(Fig. 1D), may be the presence of transcriptionalregulatory signals (29).SD-ASM was also highly enriched within en-

hancers (Fig. 1E), which is consistent with pre-vious reports (24, 28). The abundance of TFbinding sites within enhancers suggests thatSD-ASM may result from disruption of TF bind-ing (23). Under that assumption, our data sug-gest that TF binding at CpG islands and CpG-richpromoters is buffered against genetic perturba-tions, whereas the TF binding to non-CpG pro-moters and enhancers is most sensitive.We alsoobserved a somewhat puzzling mild depletion

of SD-ASM in the flanking regions of enhancers(Fig. 1E), which also suggests buffering in thoseregions.

SD-ASM is attributable to differencesbetween allele-specific epiallelefrequency spectra

We next asked whether the lack of buffering atSD-ASM loci may result in excess stochasticityand metastability, which is defined by the pres-ence of more than one stable state, each stablestate corresponding to an epiallele (single-chromosome methylation pattern). To answerthis question, wemade use of the deep combinedWGBS read coverage across 49 methylomes(table S2) and that each read relates a singlevariant to a single epiallele. We assessed epi-alleles by scoring the methylation status of four

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Fig. 1. AIs vary depending on genomic region. (A) Number of AIs in histone marks and transcription,overlapping ASM loci, over classes of genomic elements. (B to E) Proportions of SD-ASM loci overtotal heterozygous loci in 200-bp bins near promoters, CpG islands, and enhancers.

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homozygous CpG sites (42 = 16 possible epi-alleles) that were the closest to each index het inindividual WGBS reads (13, 14) (Fig. 2A). [Ouruse of the term “epiallele” follows the most re-cent usage (12, 13) and does not comply with theoriginal definition (30), which implies intergen-erational inheritance. Our use of the term“metastability” is consistent with its use indynamical systems theory and does not implyinheritance of an epiallele during cell division.]To quantify the amount of stochasticity at

index het loci, we used Shannon entropy (18).The entropy values ranged from 0 to 4: An evendistribution of frequencies across the 16 possibleepiallele patterns produces a maximum entropyscore of 4 bits, whereas a complete absence ofstochasticity because of maximal “buffering” im-plies just one epiallele with nonzero frequencyand an entropy score of 0 bits. To assess quan-titatively any differences in buffering (lack ofsensitivity to genetic variation) between SD-ASMand control loci, we identified SD-ASM loci thathad sufficient coverage and a close index hetwithout ASM and compared entropies. A totalof 6619 (2.7%) of 241,360 loci with SD-ASMmetthe two criteria (18). We observed a strikingdifference in entropy, providing a quantitativeassessment of the higher stochasticity at theSD-ASM versus control loci (Fig. 2B).We next examined enrichment for epigenetic

polymorphisms at SD-ASM loci. We estimatedthe number of frequent epialleles for each locus

by sorting the epialleles from the most to theleast frequent and identified the minimal-size“top-list” of epialleles that accounted for at least60% of all the reads with ascertained epialleles.In contrast to the control loci, which typicallyhad only one high-frequency epiallele on the“top-list” and were therefore not epigeneticallypolymorphic, SD-ASM loci showed multiple fre-quent epialleles—in most cases, just two (Fig. 2C).By examining the top pairs of epialleles, we foundthat 71.7% of the pairs consisted of one that wascompletely methylated and another completelyunmethylated (Fig. 2C). This is concordant withprevious reports of biphasic (fully methylated andfully unmethylated) distributions of methylationin amplicons with high interindividual methyla-tion variance and in polymerase chain reactionclones with bimodalmethylation patterns (3, 31).AIs at SD-ASM loci could be traced to shifts inepiallele frequency spectra between alleles, typ-ically shifts in relative frequencies of the fullymethylated and fully unmethylated epialleles(Fig. 2C). We validated the observed excess ofstochasticity and the enrichment for the biphasicpattern at SD-ASM loci using an independentWGBS dataset from the Encyclopedia of DNAElements (ENCODE) (fig. S9, A to C) (18).We next quantified the relationship between

genetic variation and stochastic epialleles. Ateach locus, we estimated the probabilities ofepialleles for each allele (higher probabilities areindicated by thicker arrows in Fig. 2, C and D).

We then quantified the degree to which geneticalleles determine epiallele frequencies using acoefficient of constraint (18), an information-theoretic measure that is a generalization of theR2 coefficient of determination that is commonlyused in genetics and is more appropriate forquantifying genetic determination of stochasticphenotypes. A larger value for the coefficient ofconstraint value signifies that epigenetic variationismore constrained and determined by geneticvariation in cis. Intuitively, a larger coefficientof constraint indicates a larger difference in theepiallelic frequency spectra corresponding to thetwo alleles, implying a higher degree of deter-mination of epiallele frequency spectra by thegenetic alleles (Fig. 2D).There are two general mechanistic models

that could explain the effect of sequence varia-tion in cis on epiallele frequency spectra. Theergodic/periodicmodel stipulates ongoing switch-ing between metastable states, the transitionsbeing stochastic with a possible component ofperiodicity, such as circadian oscillations. If asufficient number of stochastic transitions fromone epiallele to another occur, that epiallele fre-quency spectrumdepends largely on the sequence-dependent shape of the current energy landscape(state transition probabilities) and not on theepigenetic memory of past events (Fig. 2E). Bycontrast, the mosaic model stipulates that epi-alleles are stably transmitted over time and evenduring cell division, being “frozen” after a period

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Fig. 2. Differences in epiallele frequency spectra causing SD-ASM.(A) Example of an epiallele frequency spectrum (bottom) derivedfrom observed epialleles in WGBS reads (top). (B) Histograms of Shannonentropy, in bits, for the epiallele frequency spectra for the hets showingSD-ASM (red) and the nearest (control) hets without SD-ASM (black).(C) Most heterozygous loci with two frequent epialleles show SD-ASM andhave entropy larger than 1.7 bits (red portion of the bar), the two epiallelesbeing biphasic (fully methylated or fully unmethylated) 71.7% of the

time. The callout on the right provides an example of a het in which thedifference between epiallele frequency spectra of allele 1 (A, orange) andallele 2 (G, blue) explains SD-ASM. (D) Histogram of coefficients ofconstraint for SD-ASM loci with two frequent epialleles. The calloutsillustrate an example het (T/C, top right callout) with a low coefficientof constraint, and another (G/C, bottom right callout) with a highcoefficient of constraint. (E) Illustration of buffering in contrast to ergodic/periodic and mosaic metastability.

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of initial metastability into one of the stablestates. Both models entail a period of meta-stability, whether past (mosaicism) or current(ergodic/periodic model).

CTCF binding loci showsequence-dependent stochasticswitching and looping

Because of its association with DNAmethylationat a large number of binding sites, we next ex-amined the role of CCCTC-binding factor (CTCF)in creating themetastable states that correspondto epialleles.Metastability is known to be createdby positive (including double-negative) feedbackloops (32) that in our case also include inter-actions in cis, such as the protection against DNAmethylation by CTCF binding and reciprocalpreference of CTCF for unmethylated DNA (33).The first indication of the role of CTCF bindingin metastability came from the observation thatthe heterozygote with the larger coefficient ofconstraint (G/C het) also showed larger differ-ences in predicted CTCF binding affinity be-tween the two alleles than the other (T/C het)(Fig. 2D). Considering that the coefficient ofconstraint is proportional to the differences inepiallele frequency spectra for the two alleles(identical epiallele frequency spectra resultingin coefficient of constraint value of 0), this ob-servation suggested a positive correlation betweenthe coefficient of constraint and the differencesinCTCFbinding affinity for the two genetic alleles,which was indeed observed (Fig. 3A). In terms ofthe epigenetic landscape distortion due to geneticvariation, we see that sequence variants that showlarger differences in CTCF binding affinity alsoshow greater differences in their epigenetic(energy) landscapes, as reflected in the moreprominent shifts between alleles in their oc-cupancy of metastable states (as measured byhigher values of coefficient of constraint) (Fig. 3A,top). Because CTCF binding and demethylationof its binding site aremutually reinforcing (form-ing a positive-feedback loop and a metastablestate), the model also predicts that the variantsassociated with higher CTCF binding affinitieswill show lowermethylation, which is indeed thecase (Fig. 3A, bottom) as previously observed(23, 24). Taken together, these results suggestsequence-dependent stochastic epigenetic switch-ing betweenmetastable states that is mediated byCTCF binding.Because the CTCF TF establishes chromatin

loops (34), we asked whether the allelic state ofmethylation also coincided with allelic looping.Toward this goal, we used a study (35) that re-ports heterozygous SNP loci that associate bothwith allelic CTCF binding and allelic chromatinlooping, as determined by means of chromatininteraction analysis by paired-end tag sequencing(ChIA-PET). Indeed, a total of 44 of those SNP lociwere also present in our dataset. Comparing oursignals for the methylation state of CTCF bindingsites with the predicted CTCF motif disruptionscores suggested that SD-ASM is a more accurateindicator of allelic CTCFbinding and looping thanthe motif disruption score (Fig. 3B) (18).

TF binding sites showsequence-dependent shiftsin epiallele frequency spectra and AIsAnalyses of ASM at regulatory elements andeQTLs revealed associations between ASM andallele-specific histone marks with downstreamallele-specific transcription (fig. S10, A to F) (18).These results complemented previous studies(22, 23) and suggested involvement of allele-specific TF binding and cofactors in ASM. Toexamine the role of allele-specific TF binding, wefocused on the set of 377 TFs assessed for bindingaffinity using the high-throughput systematicevolution of ligands by exponential enrichment(SELEX) method (36). As for CTCF, we identifiedthe subset of bindingmotif loci in a heterozygousstate with two frequent epialleles and examinedthe correlation between coefficient of constraintand difference in predicted allelic binding af-finities across these loci for each TF (table S3).Because of the relatively small number of suchloci per TF, only 13 showed significant individualP values (Student’s t test, P < 0.05), with onlyCTCF surviving Bonferroni correction (for test-ing 377 TFs) (table S3). However, a majority (11 of13) of the TFs that showed individually signif-icant correlation also showed positive correla-tion (P = 0.01, binomial test), which is consistentwith the pattern observed for CTCF where largerdifferences in TF binding affinities correspond tolarger distortions in the configuration of meta-stable states within the landscape (table S3).Likewise, we next examined for all 377 TFs

whether disruptions of their predicted bindingsites associated with methylation imbalances. Amajority (241) showed SD-ASM enrichment with-in their bindingmotifs compared with flankingloci (500 bp on each side) (Fig. 3C and table S4),suggesting that TF binding associates with allelicDNA methylation. The SD-ASM outside of theexaminedmotifsmay be attributable to sequencevariationwithin undiscovered binding loci, with-in motifs of noncoding RNAs, or within loci inphysical proximity or contact with regions ofperturbed TF activity.We then examined the relation between allelic

differences in motif strengths and methylationlevels at SD-ASM loci (18). We observed that formore than half of the TFs tested (207), there wasan association between motif strength and levelof methylation (Fig. 3C). Most TFs (159) showedgain in methylation on the allele with the dis-rupted motif, which is consistent with the TFbinding either protecting a region from passivemethylation (37) or causing active demethylation(Fig. 3C) (38). By contrast, a smaller number ofTFs (48), including members of TF familiesthat recruit methyltransferases such as the ETS-domain TF familymembers (39, 40), showed lossof methylation on the allele with the disruptedmotif (Fig. 3, C and D). About a quarter of TFsthat show enrichment for SD-ASM show no biasin directionality (table S4), the lack of bias beingexplainable by contextual behavior at differentbinding loci, such as for nuclear factor of ac-tivated T cells 1 (41) or because of competing TFsat overlapping motifs. Our results support that

TF motif sequences are predictive of proximalCpG methylation levels (23, 42, 43).We sought to validate the downstream func-

tional consequences of SD-ASM variants, withpredicted allelic differences in TF binding, usinga luciferase assay. We prioritized cis-overlappingmotifs (CisOMs), including those of c-MYCproto-oncogene (cMYC) and tumor suppressor p53(TP53) that show competitive binding at manyloci (44), because CisOMs provide one of themechanisms of metastability (Fig. 3E), and alsothose that may have consequences for humandisease (table S5). All four SNP validations showedallelic effects on luciferase expression, includingtwo SNPs within CisOMs for cMYC and TP53 andsome falling within disease-associated loci (fig. S11)(18),which suggests that SD-ASM helps identifythose disease-associated variants that also havefunctional consequences.

SD-ASM is enriched neardisease-associated loci

We observed that heterozygous variants withSD-ASM were enriched in the neighborhoodof variants previously reported as significant ingenome-wide association studies (GWASs) ofcommon disease (Fig. 4A) (22, 23, 45). The en-richment was stronger around GWAS variantsthat have been replicated in multiple studiesversus those that have not. To explore morespecifically the role of enhancers, we performed asimilar enrichment analysis focusing only onGWAS and SD-ASM variants overlapping en-hancer elements. Enhancers that contain replicatedGWAS variants were significantly (P < 0.0001, c2

test) more likely to also contain a variant withSD-ASM than enhancers that did not containreplicated GWAS variants (Fig. 4B). Taken to-gether, these results indicate that AIs provideinformation about the role of specific loci incommon diseases, pointing to the loci that aresensitive to the effects of genetic variation andhave functional effects. The enrichment of bothGWAS loci and AIs at enhancers, and sensitivityof TF binding to genetic variation discussed inprevious sections, provide a mechanistic linkbetween AIs and GWAS associations.

Variants showing SD-ASM are underpurifying selection

Because the variants with large effects are underpurifying selection, they tend to be rare, withfrequencies below the detection threshold ofassociation studies such as GWAS, mQTL, andeQTL. By contrast, AIs may provide evidence forfunctional effects even for rare variants that maybe detected in only one individual. On the basisof previous studies that have used signatures ofpurifying selection such as shifts toward smallerderived allele frequency (DAF) to identify func-tional variants (46, 47), we would expect thatASM variants would also tend to have a lowerDAF than those without ASM. Therefore, weobtained DAF estimates from the 1000 GenomesProject (48), ignoring variants that overlappedregions with low accessibility to variant calling.We observed that in nearly every sample in our

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dataset, heterozygous variants with ASM weresignificantly (P < 0.05, c2 test) more likely to haveDAF smaller than 1% than were those withoutASM (methylation difference between alleles <5%) (Fig. 4C). Overall, this analysis found ~130

(median) more rare (DAF < 1%) variants than ex-pected among those with ASM per individual met-hylome, providing a lower bound on the numberof those under purifying selection per individual.When we repeated the analysis for enhancer re-

gions, strong signal was again observed (Fig. 4D),suggesting amedian excess of at least 26 enhancervariants under purifying selection per individual.The lower bounds from individual samplesmay

underestimate the extent of purifying selection

Onuchic et al., Science 361, eaar3146 (2018) 28 September 2018 5 of 8

Fig. 3. Correlations between allelicdifferences in TF binding affinity,coefficient of constraint, and DNAmethylation. (A) (Top) Correlationbetween absolute CTCF binding affinitydifferences, based on position weightmatrix scores (PWMs), and thecoefficient of constraint for predictedCTCF binding sites with SD-ASM,two frequent epialleles, and a biphasicmethylation pattern. (Bottom)Correlation between CTCF bindingaffinity and DNA methylation atpredicted CTCF binding sites.(B) SD-ASM is more predictive ofallelic looping (28 true positive of44 predictions) than motif disruptionscores (1 true positive of 44 predic-tions). To control for specificity,thresholds were selected so thatboth methods predicted the samenumber of hets (44) to show alleliclooping. (C) SD-ASM at binding sites of377 TFs defined with the SELEXmethod. The pie chart (left) and thetable (right) indicate both enrichmentsand directionality trends using ashared color code. (D) (Top) Correla-tion between absolute ELK3 bindingaffinity differences and the coefficientof constraint for predicted bindingsites with SD-ASM, two frequentepialleles, and a biphasic methylationpattern. (Bottom) Correlation betweenELK3 binding affinity and DNAmethylation at predicted ELK3 bindingsites. (E) A mechanistic model of asequence-dependent energy land-scape with two metastable states:allele 1 (top row), correspondingto a landscape where the mostfrequently occupied metastablestate corresponds to a completelyunmethylated epiallele, and allele 2(bottom row), corresponding to alandscape where the most frequentlyoccupied metastable statecorresponds to a completelymethylated epiallele. Putativepositive-feedback loops involvinginteractions between TF binding andbinding site methylation are indicatedfor CTCF. An alternative modelinvolving competitive binding oftwo TFs is indicated on the right.Significance of correlations wastested by using Student’s t test.

A

r2 = 0.41

p-value = 0.00013

0.0

0.2

0.4

0.6

0.0 2.5 5.0 7.5 10.0

Coe

ffici

ent o

f Con

stra

int

Binding Likelihood Difference |Allele1-Allele2|

CTCF

−10 −5 0 5 10−100

−50

0

50

100

Binding Likelihood Difference (Allele 1− Allele 2)

% M

ethy

latio

n D

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ence

(A

llele

1−

Alle

le 2

)

High Density

LowDensity

44 hetSNPs in CTCF motifs exhibiting allelic looping in GM12878 cell line (Tang et al., 2015)

Prediction based onPWM scores between alleles

Prediction based on allelic imbalancein DNA methylation between alleles

Disruptive difference betweenalleles in PWM scoresNon-disruptive difference betweenalleles in PWM scores

43 1

28

16

Allele 1

Allele 2

G

hetSNPposition

UnmethylatedCpG

MethylatedCpG

CTCF

Methylation imbalance between alleles

No methylation imbalance between alleles

B

A

CSD-ASM enrichment & No correlation between motif score and direction of CpG methylation imbalance

No SD-ASM enrichment & No correlation between motif score and direction of CpG methylation imbalance

87

83

345

50

109

SD

-AS

M E

nric

hmen

tARNTLBARHL2BHLHB2BHLHB3BHLHE41CEBPBCEBPDCEBPECEBPGCENPBCREB3E2F1E2F2E2F3E2F4E2F7E2F8EGR1EGR2EGR3EGR4ELK1ELK3

ETV1ETV4ETV5GCM2GMEB2HOMEZHSFY2IRF4IRF5IRF7MLXMLXIPLMYBL1MYBL2NRF1OTX1PAX2VENTXXBP1YY1YY2ZBED1

ATF4CLOCKCTCFELF5EOMESESRRAESRRBESRRGETV2FIGLAFOXB1FOXC2FOXG1FOXO1FOXO3FOXO4FOXO6FOXP3GATA3GATA4GATA5HIC2HNF4A

IRX2IRX5JDP2KLF16MAFFMAFGMAFKMAXMEIS2MEIS3MEOX2MSCMYF6NEUROG2NFE2NFIANFIBNFIXNR2E1NR2F1NR2F6NR4A2PKNOX1

PKNOX2POU1F1POU2F1POU2F2POU2F3POU3F2POU3F4POU4F2POU5F1P1RARARFX2RFX3RFX4RFX5RXRARXRGSOX10SOX14SOX15SOX18SOX2SOX21SOX4

SOX7SOX8SOX9SP1SP3SP4SP8SPI1SPIBSPICSRFSRYTBX1TBX15TBX2TBX20TBX21TBX4TBX5TCF7L1TEAD1TEAD3TEAD4

TFAP4TFEBTFECTGIF1TGIF2TGIF2LXTP63ZIC1ZIC3ZIC4ZNF143ZNF232ZNF238ZNF435ZNF740ZNF75AZSCAN4

BARX1BHLHA15BSXCDX1CDX2DLX3DLX4EN1FOXC1FOXD2

FOXD3FOXJ2FOXJ3FOXL1GBX2HESX1HNF1AHNF1BHOXA1HOXA10

HOXA13HOXB13HOXB3HOXC10HOXC11HOXD11ISL2LHX9LMX1BMEF2A

MEF2BMEF2DMNX1MSX1MSX2NFAT5NKX2-3NKX2-8NKX6-1NKX6-2

OLIG2OLIG3PDX1POU3F1POU3F3POU4F1POU4F3POU6F2RARBZNF410

HINFP1ONECUT1ONECUT3

Motif disruption =Loss of CpG Methylation

Motif disruption =Gain of CpG Methylation

No

SD

-AS

M E

nric

hmen

t

r2 = 0.78p-value = 0.0082

0.0

0.1

0.2

0.3

2.5 5.0 7.5

Coe

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Binding Likelihood Difference |Allele1-Allele2|

D ELK3

−10 −5 0 5 10

−50

0

50

100

% M

ethy

latio

n D

iffer

ence

(A

llele

1−

Alle

le 2

)

Binding Likelihood Difference (Allele 1− Allele 2)

High Density

LowDensity

60

53 54

98

Alle

le 1

Alle

le 2

CTCF

CpG Methylation

Bound

CpG Methylation

NotBound

CpG Methylation

CompetitiveBinding

CpG Methylation

E

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because of underdetection of SD-ASM. We there-fore investigated whether an enrichment for rarevariants could also be seen for those variantsassociated with SD-ASM from the combineddataset, using neighboring variants as controls(18). We observed that the chance of a locushaving SD-ASM decreased as the derived allelefrequency increased (Fig. 4E; there were veryfew variants with DAF > 50%, causing high var-iance and large confidence intervals). We furthertested whether there was a significant enrich-ment for variants with DAF < 1% among thosewith SD-ASM and found that such enrichmentwas indeed significant (odds ratio 1.18; P < 0.0001,c2) (Fig. 4F). That enrichment represents anexcess of 2184 rare variants among those withSD-ASM compared with controls. Consideringthat this observed excess represents a set of 11genomes (nine individuals and two cell lines),we estimate at least ~200 variants with SD-ASMunder purifying selection per individual donor.

Discussion

Taken together, our findings suggest a mech-anistic link between sequence-dependent AIsof the epigenome, stochastic switching at generegulatory loci, and disease-associated geneticvariation. Our allelic epigenome map reveals CpGmethylation imbalances exceeding 30% differ-ences at 5% of the loci, which is more conserv-ative than previous estimates in the 8 to 10%range (3, 4); a similar value (8%) is observed inour dataset when we lowered our threshold fordetecting AI to 20% methylation difference be-tween the two alleles. We observed an excess ofrare variants among those showing ASM, sug-gesting that an average human genome harborsat least ~200 detrimental rare variants that alsoshow ASM.The methylome’s sensitivity to genetic varia-

tion is unevenly distributed across the genome.The higher buffering of CpG islands, and as-sociated promoters, may be due to their use byhousekeeping genes. Conversely, other promotersand enhancers may show lower buffering be-cause of their presence in tissue-specific genesthat tend not to be associated with CpG islands(49). Our findings are consistent with the evolu-tionary advantages that may stem from thebuffering of housekeeping genes against theeffects of random mutations—while still retain-ing the potential for evolutionary innovationthrough changes in the regulation of less es-sential genes with tissue-specific expressionpatterns—and refine reports that suggest that allpromoters show epigenetic buffering (50). High-est sensitivity to genetic variation at enhancers,and potentially perturbations in general, is con-sistent with observations of high cell-to-cellvariability of theirmethylation (28, 51).ValidatedGWAS loci, and the enhancers within those loci,show enrichment for AIs, suggesting that sen-sitivity of those loci to genetic variation, and po-tentially also to environmental influences, mayat least inpart explain their role in commondiseases.Overall, our results suggest an explanation for

the conservation of “intermediate methylation”

states at regulatory loci (52). These intermediatemethylation states reflect the relative frequenciesof fully methylated and fully unmethylated epi-alleles corresponding to biphasic on/off switchingpatterns (31) at regulatory loci marked with SD-

ASM.Moreover, our analyses reveal that the SD-ASM is explainable by allele-specific switchingpatterns at thousands of heterozygous loci.Waddington’s epigenetic landscape has served

as a guidingmetaphor for the emergence of cellular

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0.0 0.2 0.4 0.6 0.8 1.0

0.45

0.50

0.55

0.60

Pro

port

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of lo

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ith S

D-A

SM

Derived Allele Frequency0.0

0.1

0.2

0.3

0.4

0.5

13,877 / 24,91079,420 / 154,385

DAF< 1% DAF>1%

p-value = 6x10-36

Pro

port

ion

of lo

ci w

ith S

D-A

SM

ReplicatedGWAS

Not replicatedGWAS

0

500

1000

1500

2000

2500

3000p = 2x10-37 p = 0.002

# of

SD

-AS

M n

ear

GW

AS

SN

Ps

0

100

200

300

ReplicatedGWAS

Not replicatedGWAS

p = 1x10-5

p = 0.85

Enh

ance

rs w

ith G

WA

S a

nd S

D-A

SM

−1.0 −0.5 0.0 0.5 1.00

10

20

30

40

50

60

70

Log10 odds ratio

−Lo

g10

P−

Val

ueASM enrichment for DAF < 1%

Per sample - Genome Wide

Proportion of loci with SD-ASM vs DAFCombined set

−1.0 −0.5 0.0 0.5 1.0

0

5

10

15

Log10 odds ratio

−Lo

g10

P−

Val

ue

ASM enrichment for DAF < 1%Per sample - Over enhancers

A B

DC

E F SD-ASM enrichment for DAF < 1%Combined set - Genome Wide

observed expected observed expected

Fig. 4. Association of ASM with disease loci and purifying selection. (A and B) Enrichment ofASM in the proximity of GWAS loci. ASM hets within 1 kb of GWAS loci are compared with colocalized hetswithout ASM. (C to F) Evidence of purifying selection acting on rare variants with ASM. [(C) and (D)]Proportion of variants associatedwith ASMcomparedwith thosewithout ASMamong the rare (DAF< 1%)variants across individual methylomes. [(E) and (F)] Proportion of loci with ASM over total heterozygousloci over windows of increasing DAF in the combined set of methylomes. (F) This bar chart summaryof the data in (E) shows the excess of SD-ASMvariants among thosewith DAF < 1%. c2 tests were used forsignificance of enrichments.

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identities during development. The landscapehas until now been an abstract construct (53),disconnected from the mechanistic function ofgene regulation. Our energy landscapes (Figs. 2Dand 3E) may be interpreted as a special type ofepigenetic landscape model of gene regulatoryinteractions in cis in which epialleles correspondto metastable states (attractors) within the land-scape (30). As cells transition into a more dif-ferentiated state, the cellular epigenome enters abuffered “valley” at a bifurcation point in thelandscape (Fig. 2E). Because our current datasetis static, it precludes us from being able to dis-tinguish between the mosaic and stochastic/periodic models that characterize the more andless differentiated states, respectively.Consistent with proposed theoretical models

that define the landscape in terms of potentialenergy functions (53) and postulate local at-tractors created by positive-feedback loops (32),our model involves interactions between oneor more TFs, DNA methylation, and likely otherepigenomic marks. Competitive binding of TFsat CisOMs may be one of the mechanisms ofmetastability. By putting the metastable stateswithin the landscape in correspondence withepialleles and TF binding, we bringWaddington’slandscapes into correspondence with assayableand quantifiable epiallele frequency spectra andwith specific mechanisms of gene regulation.Our findings are consistent with the role for

bistable switching and stochasticity in bacterialgene regulation (54) and extend stochasticity toeukaryotic cells in vivo within their natural tissuecontext across a diversity of human tissues. Oneobvious question is the possible purpose of sto-chasticity at gene regulatory loci across bothdomains life. The sharp contrast between the“digital” nature of regulatory elements and the“analog” nature of concentrations of upstreamTFs, and downstream gene products, suggeststhat we may be observing a naturally evolvedsystem similar to von Neumann’s “stochasticcomputer,” an early hybrid analog-digital com-puter design that can implement regulatory cir-cuits within control systems in which analogquantities are not encoded by using the usualbinary or decimal system but are encoded asfractions of “on” states in a stochastic series ofon and off states (55). In contrast to a stand-alone stochastic computer, there is a multitudeof cells within a tissue, raising the question aboutthe role of intercellular communication withintissue microenvironment in the establishmentof a dynamic equilibrium that results in observedmethylation averages.To promote further data analyses and ex-

perimental work by the community, we providean Allelic Epigenome Atlas, a collection of an-notations, including AI scores, for all of the ~4.9million heterozygous loci analyzed here (18). Thebreadth of the genome-wide AI scores availablein the Allelic Epigenome Atlas, which includesthe multitude of different individual tissue andcell types profiled here, may serve as additionallayers of functional evidence for prioritizationof disease-causal candidate variants, including

subthreshold GWAS variants in implicated regionsand noncoding variants detected with clinicalwhole-genome sequencing.

Materials and methods

We identified heterozygous SNP loci using ajoint variant-calling pipeline on WGS datasetsfrom 13 donors from the NIH Roadmap Epige-nomics Project. We used ChIP-seq and RNA-seqdatasets from a total of 71 various tissues of thesedonors to detect AIs in histone marks and trans-cription as described (19). We detected allele-specific methylation using an in-house script on49 WGBS datasets to compare counts of methyl-ated and unmethylated cytosines proximal toeach allele. We tested different regulatory regionsand GWAS and eQTL loci for enrichment of AIsusing nearby heterozygous SNPs without AI ascontrols.We compared differences inmethylationbetween alleles with the alleles’ predicted TFmotif strengths. We analyzed epialleles by quan-tifying themethylation patterns of the four closestCpGs to the alleles in single WGBS reads andcomparing these patterns between alleles. Wecalculated Shannon entropy at different lociusing epiallele patterns to quantify stochastic-ity at SD-ASM loci. We calculated coefficient ofconstraints at SD-ASM loci to determine theconstraint of epiallele polymorphisms by geneticvariants.

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ACKNOWLEDGMENTS

We thank I. Golding for helpful comments and reviewing the paperand Y. Ruan for assisting with allelic looping datasets. Funding:A.M. acknowledges support from the Common Fund of theNational Institutes of Health (Roadmap Epigenomics Program,grant U01 DA025956). M.G. acknowledges support from the

National Human Genome Research Institute (grant5U24HG009446-02). W.D.F. acknowledges support from theNational Institute of General Medical Sciences (grant GM122030-01).M.K. acknowledges support from the National Instituteof Mental Health (grant R01 MH109978) and the National HumanGenome Research Institute (grants U01 HG007610 and R01HG008155). Author contributions: V.O., E.L., and A.M.conceptualized research goals and designed studies; R.A.H. andC.C. performed collection and organization of sequencing datasets;C.C., P.P., and R.Y.P. performed processing of sequencingdatasets; V.O., E.L., P.P., R.Y.P., J.R., T.G., Z.H., R.C.A., Z.Z., andL.A. performed data curation; Z.H. created and performed variant-calling pipelines with supervision from F.U.; J.R., T.G., R.C.A., andZ.Z. provided software and participated in allelic histone callingwith supervision from M.K. and M.G.; V.O., E.L., and I.C. performedbioinformatics, statistical analyses, and presentation of data withsupervision from A.M.; J.W.B. performed luciferase assay validationexperiments with supervision from W.D.F.; E.L. performedvalidation experiments on external datasets; L.A. developed theonline resource; V.O., E.L., and A.M. wrote the original draft; andE.L., M.K., and A.M. revised and edited the manuscript. Competinginterests: The authors declare no competing interests. Dataand materials availability: All allelic datasets are available onhttps://genboree.org/genboreeKB/projects/allelic-epigenome.Code used for bioinformatic analyses can be found at https://github.com/BRL-BCM/allelic_epigenome. The whole-genomesequencing, whole-genome bisulfite sequencing, and ChIP-sequencing reads that were used are stored on the RoadmapEpigenomics BioProject page (accession nos. PRJNA34535 andPRJNA259585) and dbGaP (accession nos. phs000791.v1.p1,phs000610.v1.p1, and phs0007000.v1.p1).

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/361/6409/eaar3146/suppl/DC1Materials and MethodsFigs. S1 to S12Tables S1 to S5References (56–78)

26 October 2017; resubmitted 7 May 2018Accepted 10 August 2018Published online 23 August 201810.1126/science.aar3146

Onuchic et al., Science 361, eaar3146 (2018) 28 September 2018 8 of 8

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regulatory lociAllele-specific epigenome maps reveal sequence-dependent stochastic switching at

Yu, Manolis Kellis, Mark Gerstein and Aleksandar MilosavljevicFuliRobert C. Altshuler, Zhizhuo Zhang, R. Alan Harris, Cristian Coarfa, Lillian Ashmore, Jessica W. Bertol, Walid D. Fakhouri,

Vitor Onuchic, Eugene Lurie, Ivenise Carrero, Piotr Pawliczek, Ronak Y. Patel, Joel Rozowsky, Timur Galeev, Zhuoyi Huang,

originally published online August 23, 2018DOI: 10.1126/science.aar3146 (6409), eaar3146.361Science 

, this issue p. eaar3146Sciencemay suggest a role in human disease.methylated chromosomes. This stochastic type of gene regulation was more common for rare genetic variants, which''off'' switches. Interestingly, methylation did not occur on each DNA molecule, resulting in a variable fraction of within individual chromosomal DNA molecules showed full or no methylation at specific sites corresponding to ''on'' andgenetic variation and sequence-dependent allele-specific methylation at gene regulatory loci. Regulatory sequences

examined disease-associatedet al.marks are poorly understood. Working with human-derived samples, Onuchic Genome-wide epigenetic marks regulate gene expression, but the amount and function of variability in these

Dissecting the epigenomic footprint

ARTICLE TOOLS http://science.sciencemag.org/content/361/6409/eaar3146

MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2018/08/22/science.aar3146.DC1

CONTENTRELATED http://science.sciencemag.org/content/sci/361/6409/1330.full

REFERENCES

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