Motivation: How chromatin folds in three-dimensional (3D) space is closely related to transcription regulation. As powerful tools to study such 3D chromatin conformation, the recently developed Hi-C technologies enable a genome-wide measurement of pair-wise chromatin interaction. However, methods for the detection of biologically meaningful chromatin interactions, i.e. peak calling, from Hi-C data, are still under development. In our previous work, we have developed a novel hidden Markov random field (HMRF) based Bayesian method, which through explicitly modeling the non-negligible spatial dependency among adjacent pairs of loci manifesting in high resolution Hi-C data, achieves substantially improved robustness and enhanced statistical power in peak calling. Superior to peak callers that ignore spatial dependency both methodologically and in performance, our previous Bayesian framework suffers from heavy computational costs due to intensive computation incurred by modeling the correlated peak status of neighboring loci pairs and the inference of hidden dependency structure

Hu, Ming

Li, Yun

Wu, Cong

Xu, Zheng

Zhang, Guosheng

English

PubMed

Carolina Digital Repository

Genome analysisFastHiC: a fast and accurate algorithmto detect long-range chromosomalinteractions from Hi-C dataZheng Xu1,2,3, Guosheng Zhang2,4, Cong Wu5, Yun Li1,2,3,* andMing Hu6,*1Department of Biostatistics, 2Department of Genetics, 3Department of Computer Science, 4Curriculum inBioinformatics and Computational Biology, University of North Carolina, Chapel Hill, NC 27599, USA, 5College ofVeterinary Medicine, Nanjing Agricultural University, Nanjing, Jiangsu 210095, China and 6Division of Biostatistics,Department of Population Health, New York University School of Medicine, New York, NY 10016, USA*To whom correspondence should be addressed.Associate Editor: Inanc BirolReceived on January 20, 2016; revised on April 4, 2016; accepted on April 25, 2016AbstractMotivation: How chromatin folds in three-dimensional (3D) space is closely related to transcriptionregulation. As powerful tools to study such 3D chromatin conformation, the recently developedHi-C technologies enable a genome-wide measurement of pair-wise chromatin interaction.However, methods for the detection of biologically meaningful chromatin interactions, i.e. peakcalling, from Hi-C data, are still under development. In our previous work, we have developed anovel hidden Markov random field (HMRF) based Bayesian method, which through explicitly mod-eling the non-negligible spatial dependency among adjacent pairs of loci manifesting in high reso-lution Hi-C data, achieves substantially improved robustness and enhanced statistical power inpeak calling. Superior to peak callers that ignore spatial dependency both methodologically and inperformance, our previous Bayesian framework suffers from heavy computational costs due to in-tensive computation incurred by modeling the correlated peak status of neighboring loci pairs andthe inference of hidden dependency structure.Results: In this work, we have developed FastHiC, a novel approach based on simulated field ap-proximation, which approximates the joint distribution of the hidden peak status by a set of inde-pendent random variables, leading to more tractable computation. Performance comparisons inreal data analysis showed that FastHiC not only speeds up our original Bayesian method by morethan five times, bus also achieves higher peak calling accuracy.Availability and Implementation: FastHiC is freely accessible at:http://www.unc.edu/yunmli/FastHiC/Contacts: yunli@med.unc.edu or ming.hu@nyumc.orgSupplementary information: Supplementary data are available at Bioinformatics online.1 IntroductionThe spatial organizations of chromosomes play a critical role intranscription regulation. In particular, regulatory elements such asenhancers, often contact with the promoters of targeted genes byforming long-range DNA looping. Understanding such 3D chroma-tin conformation provides novel insights into the regulation mechan-isms of gene expression (Gorkin et al., 2014). The recentlydeveloped Hi-C technologies enable a genome-wide measurement ofVC The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com 2692Bioinformatics, 32(17), 2016, 2692–2695doi: 10.1093/bioinformatics/btw240Advance Access Publication Date: 3 May 2016Applications Notechromatin interaction (Lieberman-Aiden et al., 2009). In the Hi-Cdata, the contact frequency between any two chromatin loci is meas-ured by the number of paired-end reads spanning across them.Higher read count indicates more frequent chromatin interactionand closer spatial proximity.The rapid accumulation of Hi-C data with high sequencingdepth enables the study of chromatin interaction at the unprece-dented resolution (Jin et al., 2013; Rao et al., 2014). However, thedetection of biologically meaningful long-range chromatin inter-actions poses great challenges. Most existing methods (Ay et al.,2014; Jin et al., 2013; Rao et al., 2014) assume that the chromatininteraction frequencies for different loci pairs are independent,which is clearly invalid. If two loci show high interaction frequency,their adjacent loci will be more likely to interact with each other. Tofill in this gap, we have recently developed a novel hidden Markovrandom field based Bayesian (HMRFBayes) method to explicitlymodel the spatial dependency among adjacent loci (Xu et al., 2016).By borrowing information across neighborhood loci, HMRFachieves substantially improved robustness and enhanced statisticalpower.While extremely promising, HMRFBayes is based on a Bayesianframework which requires intensive computation. The key challengeis to efficiently and effectively infer the dependency structure under-lying the hidden peak status. To address this challenge, we de-veloped a novel algorithm named FastHiC, which approximates thejoint distribution of the hidden peak status by a set of independentrandom variables. Under such approximation, we adopted an EMalgorithm for statistical inference. Compared with HMRFBayes,FastHiC not only speeds up by more than five times, but alsoachieves higher peak calling accuracy.2 Statistical modelWe use the same HMRF model as in our previous work (Xu et al.,2016). Our goal is to detect biologically meaningful chromatin inter-actions among N loci. Let xij and eij represent the observed and ex-pected chromatin contact frequency between loci i and j,respectively ð1  i < j  NÞ. Here, eij is known based on the pre-specified background model (Ay et al., 2014; Jin et al., 2013). Let zijbe the hidden peak status: zij ¼ 1 indicates a biologically meaningfulinteraction, while zij ¼ 1 indicates a random collision. We furtherassume that xij follows a negative binomial distribution with meaneij expfhðzij þ 1Þ=2g and over-dispersion /. Here, expfhg is thesignal-noise-ratio of the peak over the background. In the HMRFmodel, we assume that xij’s are conditionally independent given thehidden peak status zij, where zij follows an Ising distribution (Besag,1974):p zij jw  ¼ 1WðwÞ exp wXii0j jþ jj0j j¼1zijzi0 j08<:9=;:Here, w is the parameter accounting for spatial dependency. Largerw indicates higher spatial dependency. WðwÞ is the normalizationconstant without explicit expression form.The key challenge is the efficient and effective inference ofthe spatial dependency parameter w. In our previous work (Xuet al., 2016), we used the pseudo-likelihood (PL) to approximate theIsing distribution, and devised a Gibbs sampler for statisticalinference.PL zij jw  ¼Y1 i< jNpðzijjzi0j0 ; i i0j j þ j j0j j ¼ 1; wÞ:However, in the PL approximation, the neighborhood of eachloci pair can still fluctuate, resulting in intractable computation ofw. To solve this problem, we developed a novel algorithm namedFastHiC, which uses the simulated field mij ¼ Eðzijjzi0 j0 ; i i0 þj j0  ¼ 1Þ to approximate the joint distribution of the peak statusimplicated by the Ising distribution (Celeux et al., 2003), leading toa modified pseudo-likelihood (MPL):MPL zij jw  ¼Y1 i< jNpðzijjmi0 j0 ; i i0j j þ j j0j j ¼ 1; wÞ:This MPL approximates the Ising distribution by a set of inde-pendent random variables, enabling tractable computation of w.FastHiC then adopts an EM algorithm for inference. Details of thesimulated field approximation and EM algorithm can be found inSupplementary Material Section S1.3 ResultsWe first conducted simulation study to compare the performance ofFastHiC with HMRFBayes (Supplementary Material Section S2).These two methods achieved comparable statistical efficiency in par-ameter estimations (Supplementary Table S1) and peak calling ac-curacy (Supplementary Fig. S1 and Table S2). Noticeably, FastHiCran more than five times faster than HMRFBayes (SupplementaryTable S3), due to the novel implementation of simulated fieldapproximation.Next, we re-analyzed the Hi-C data in human IMR90 cells (Jinet al., 2013) where 2262 topological associated domains (TADs) wereidentified (Dixon et al., 2012). We analyzed each TAD separately todetect intra-TAD chromatin interactions at 4Kb resolution. Wedidnot analyze inter-TAD chromatin interactions because lowsequencing depth for inter-TAD reads (the average number of intra-TAD and inter-TAD reads are 58.91 and 1.57, respectively). Since wehave shown that HMRFBayes (Xu et al., 2016) outperforms AFC (Jinet al., 2013) and Fit-Hi-C (Ay et al., 2014), in this work, we onlycompared the performance of FastHiC and HMRFBayes(Supplementary Table S4). We did not compare with HiCCUPS (Raoet al., 2014) since its software is not publicly available. Overall,FastHiC and HMRFBayes obtained highly similar peak calling re-sults. The Spearman correlation coefficient of peak probabilities be-tween FastHiC and HMRFBayes within each TAD has median 0.934and standard deviation 0.121. In addition, we compared the peakcalling results from FastHiC and HMRFBayes with the chromatinloops identified from the in situ Hi-C data (Rao et al., 2014). Figure1A shows that peaks identified by FastHiC have slightly higher over-lap with chromatin loops than peaks identified by HMRFBayes.Overall, FastHiC and HMRFBayes achieved highly similar peak call-ing accuracy in real Hi-C data in human IMR90 cells.Next, we compared the computational time of four differentpeak callers with different TAD sizes (Fig. 1B). In general, the run-ning time increases quadratically with the TAD size. For all 2262TADs, the average running time for FastHiC, HMRFBayes, AFCand Fit-Hi-C are 428, 4134, 2605 and 19 s, respectively. FastHiCruns much faster than HMRFBayes and AFC. Although Fit-Hi-Cruns faster than FastHiC, we have showed that the HMRF-based ap-proach outperformed Fit-Hi-C in peak calling accuracy (Xu et al.,2016). Compared with Fit-Hi-C, we believe that FastHiC achieves areasonable balance between speed and accuracy.To further compare the performance of FastHiC andHMRFBayes, we analyzed two additional Hi-C datasets in humanH1 embryonic stem cells (Dixon et al., 2015) and human GM12878FastHiC 2693lymphoblastic cells (Selvaraj et al., 2013). We detected intra-TADchromatin interactions at 40 kb resolution. To evaluate peak callingaccuracy, we compared the peak calling results from FastHiC andHMRFBayes with the recently published ChIA-PET data on H1 (Jiet al., 2015) and GM12878 cells (Tang et al., 2015). We found thatpeaks identified from FastHiC show much higher overlap with chro-matin loops detected from ChIA-PET data than those identifiedfrom HMRFBayes, in both H1 (Fig. 1C and Supplementary Fig. S2)and GM12878 cells (Fig. 1D). These results demonstrate thatFastHiC achieves higher peak calling accuracy than HMRFBayes.In addition, we explored modeling the dependency structurewith broader neighborhood, but neither simulation studies nor realdata analysis showed performance improvement (SupplementaryMaterial Section S4).4 ConclusionIn summary, we have developed FastHiC, a fast and accurate algorithmto detect long-range chromatin interactions from Hi-C data. FastHiCutilized the same hidden Markov random field model as in our previouswork (Xu et al., 2016), but with a novel implementation of the simu-lated field approximation, leading to more than five times speed-up andhigher peak calling accuracy. We believe that FastHiC has potential tobecome a useful tool in studying chromatin spatial organization.FundingThis research was supported by the National Institute of Health grants R01-HG006292 and R01-HG006703 (awarded to YL), and 1U54DK107977-01(awarded to MH).Fig. 1. (A) The overlap between in-situ Hi-C loops (Rao et al., 2014) and peaks identified by FastHiC and HMRFBayes. (B) Computational time of four peak callers.(C) The overlap between ChIA-PET loops (Ji et al., 2015) and peaks identified by FastHiC and HMRFBayes in primed H1 cells. (D) The overlap between ChIA-PETloops (Tang et al., 2015) and peaks identified by FastHiC and HMRFBayes in GM12878 cells2694 Z.Xu et al.Conflict of Interest: none declared.ReferencesAy,F. et al. (2014) Statistical confidence estimation for Hi-C data reveals regu-latory chromatin contacts. Genome Res., 24, 999–1011.Besag,J. (1974) Spatial interaction and the statistical analysis of lattice systems(with Discussion). J. R. Stat. Soc. Ser. B, 36, 192–236.Celeux,G. et al. (2003) EM procedures using mean field-like approximationsfor Markov model-based image segmentation. Pattern Recognit., 36,131–144.Dixon,J.R. et al. (2012) Topological domains in mammalian genomes identi-fied by analysis of chromatin interactions. Nature, 485, 376–380.Dixon,J.R. et al. (2015) Chromatin architecture reorganization during stemcell differentiation. Nature, 518, 331–336.Gorkin,D.U. et al. (2014) The 3D genome in transcriptional regulation andpluripotency. Cell Stem Cell, 14, 771–775.Ji,X. et al. (2015) 3D chromosome regulatory landscape of human pluripotentcells. Cell Stem Cell, 18, 262–275.Jin,F. et al. (2013) A high-resolution map of the three-dimensional chromatininteractome in human cells. Nature, 503, 290–294.Lieberman-Aiden,E. et al. (2009) Comprehensive mapping of long-range inter-actions reveals folding principles of the human genome. Science, 326,289–293.Rao,S.S.P. et al. (2014) A 3D map of the human genome at kilobase resolutionreveals principles of chromatin looping. Cell, 159, 1665–1680.Selvaraj,S. et al. (2013) Whole-genome haplotype reconstruction usingproximity-ligation and shotgun sequencing. Nat. Biotechnol., 31,1111–1118.Tang,Z. et al. (2015) CTCF-mediated human 3D genome architecture revealschromatin topology for transcription. Cell, 163, 1611–1627.Xu,Z. et al. (2016) A hidden Markov random field based Bayesian method forthe detection of long-range chromosomal interactions in Hi-C Data.Bioinformatics, 32, 650–656.FastHiC 2695

FastHiC: a fast and accurate algorithm to detect long-range chromosomal interactions from Hi-C data

http://dx.doi.org/10.1093/bioinformatics/btw240

FastHiC: a fast and accurate algorithm to detect long-range chromosomal interactions from Hi-C data

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