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Quantitative Biology

ISSN 2095-4689

ISSN 2095-4697(Online)

CN 10-1028/TM

邮发代号 80-971

Quantitative Biology  2013, Vol. 1 Issue (2): 156-174   https://doi.org/10.1007/s40484-013-0016-0
  本期目录
Understanding spatial organizations of chromosomes via statistical analysis of Hi-C data
Ming Hu1, Ke Deng1,2, Zhaohui Qin3, Jun S. Liu1()
1. Department of Statistics, Harvard University, Cambridge, MA 02138, USA
2. Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
3. Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, GA 30322, USA
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Abstract

Understanding how chromosomes fold provides insights into the transcription regulation, hence, the functional state of the cell. Using the next generation sequencing technology, the recently developed Hi-C approach enables a global view of spatial chromatin organization in the nucleus, which substantially expands our knowledge about genome organization and function. However, due to multiple layers of biases, noises and uncertainties buried in the protocol of Hi-C experiments, analyzing and interpreting Hi-C data poses great challenges, and requires novel statistical methods to be developed. This article provides an overview of recent Hi-C studies and their impacts on biomedical research, describes major challenges in statistical analysis of Hi-C data, and discusses some perspectives for future research.

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收稿日期: 2013-03-06      出版日期: 2013-06-05
Corresponding Author(s): Jun S. Liu   
 引用本文:   
. [J]. Quantitative Biology, 2013, 1(2): 156-174.
Ming Hu, Ke Deng, Zhaohui Qin, Jun S. Liu. Understanding spatial organizations of chromosomes via statistical analysis of Hi-C data. Quant. Biol., 2013, 1(2): 156-174.
 链接本文:  
https://academic.hep.com.cn/qb/CN/10.1007/s40484-013-0016-0
https://academic.hep.com.cn/qb/CN/Y2013/V1/I2/156
Fig.1  
Fig.2  
Fig.3  
Fig.4  
Fig.5  
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Fig.7  
Topics Methods Features Pros Cons References
Yaffe and Tanay Non-parametric bias correction Effective bias reduction Computationally intensive, difficult interpretation [73]
Bias reduction HiCNorm Parametric bias correction Computationally efficient, easy interpretation Rely on parametric assumption [87]
ICE Normalization method No assumption on any specific systemic biases Limited for equal-sized genome partition [74]
SCN Normalization method Effective removal of DNA circularization bias Limited for equal-sized genome partition [86]
PCA Chromosome-wide variance decomposition Discovery of two compartments based on spatial proximity Low resolution (several MBs) genome partition [34]
Dixon et al. Hidden Markov model Discovery of topological domain based on local chromatin interactions Two-step procedure of bias reduction and genome partition [45]
Genome partition Sexton el al. Local distance-scaling model Combining Yaffe and Tanay's bias correction model [73] with genome partition Computationally intensive [47]
Hou et al. Poisson mixture model Model intra-domain and inter-domain interactions via two Poisson distributions Two-step procedure of bias reduction and genome partition [48]
GeSICA Markov clustering algorithm Exploration of hierarchical sub-domain structures Lack of bias reduction [93]
Fractal globule model Model chromatin as a knot-free configuration NA* NA* [98,99]
Equilibrium globule model Model chromatin as a highly knotted configuration NA* NA* [100]
Polymer model Random loop model Looping is formed by random interaction between monomers NA* NA* [39]
Dynamic loop Looping is formed by diffusional motion of monomers NA* NA* [40]
Strings and binds switch Looping is affected by concentrations of binding molecules NA* NA* [41]
Inferring consensus
3D chromosomal
structure
Optimization-based methods Optimize a target function to measure the fitting of a 3D model Use biophysical constraints in 3D model reconstruction Local modes, fail to model experimental uncertainties [33,38,43]
MCMC5C Gaussian model First statistical model for Hi-C experimental uncertainties No bias removal, Gaussian variance estimate is ad hoc [42]
BACH Poisson model Combing bias removal with 3D model reconstruction Lack of biophysical constraints, computational intensive [103]
Evaluating structural variation of chromatin via statistical model Optimization-based methods Use multiple parallel runs to measure chromatin structural variation Explore all possible 3D models optimizing the target function Computationally intensive, sensitive to initialization [33,38,43]
Kalhor et al. Population-based approach Direct link Hi-C data to presence or absence of chromatin interaction Fail to model experimental uncertainties [37]
BACH-MIX Poisson mixture model Combing bias removal with evaluating chromatin structural variation Limited for studying local chromatin structural variation [103]
Tab.1  
1 N. Naumova, and J. Dekker, (2010) Integrating one-dimensional and three-dimensional maps of genomes. J. Cell. Sci., 123, 1979−1988.
pmid: 20519580
2 C. L. Woodcock, and R. P. Ghosh, (2010) Chromatin higher-order structure and dynamics. Cold Spring Harb Perspect Biol, 2, a000596.
pmid: 20452954
3 T. Misteli, (2004) Spatial positioning; a new dimension in genome function. Cell, 119, 153−156.
pmid: 15479633
4 J. Dekker, (2008) Gene regulation in the third dimension. Science, 319, 1793−1794.
pmid: 18369139
5 A. Miele, and J. Dekker, (2008) Long-range chromosomal interactions and gene regulation. Mol Biosyst, 4, 1046−1057.
pmid: 18931780
6 P. Fraser, and W. Bickmore, (2007) Nuclear organization of the genome and the potential for gene regulation. Nature, 447, 413−417.
pmid: 17522674
7 T. Misteli, (2007) Beyond the sequence: cellular organization of genome function. Cell, 128, 787−800.
pmid: 17320514
8 F. W. Alt,, Y. Zhang,, F. L. Meng,, C. Guo, and B. Schwer, (2013) Mechanisms of programmed DNA lesions and genomic instability in the immune system. Cell, 152, 417−429.
pmid: 23374339
9 F. Mitelman, (2000) Recurrent chromosome aberrations in cancer. Mutat. Res., 462, 247−253.
pmid: 10767636
10 J. D. Rowley, (1998) The critical role of chromosome translocations in human leukemias. Annu. Rev. Genet., 32, 495−519.
pmid: 9928489
11 B. van Steensel, and J. Dekker, (2010) Genomics tools for unraveling chromosome architecture. Nat. Biotechnol., 28, 1089−1095.
pmid: 20944601
12 T. Cremer,, et al. (2012) Chromosome Territory Organization within the Nucleus. Encyclopedia of Molecular Cell Biology and Molecular Medicine.
13 T. Cremer,, M. Cremer,, S. Dietzel,, S. Müller,, I. Solovei, and S. Fakan, (2006) Chromosome territories—a functional nuclear landscape. Curr. Opin. Cell Biol., 18, 307−316.
pmid: 16687245
14 M. R. Branco, and A. Pombo, (2007) Chromosome organization: new facts, new models. Trends Cell Biol., 17, 127−134.
pmid: 17197184
15 W. W. Wasserman, and A. Sandelin, (2004) Applied bioinformatics for the identification of regulatory elements. Nat. Rev. Genet., 5, 276−287.
pmid: 15131651
16 N. Gilbert,, S. Boyle,, H. Fiegler,, K. Woodfine,, N. P. Carter, and W. A. Bickmore, (2004) Chromatin architecture of the human genome: gene-rich domains are enriched in open chromatin fibers. Cell, 118, 555−566.
pmid: 15339661
17 E. de Wit, and W. de Laat, (2012) A decade of 3C technologies: insights into nuclear organization. Genes Dev., 26, 11−24.
pmid: 22215806
18 J. Dekker,, M. A. Marti-Renom, and L. A. Mirny, (2013) Exploring the three-dimensional organization of genomes: interpreting chromatin interaction data. Nat. Rev. Genet., 14, 390−403.
pmid: 23657480
19 J. Dekker,, K. Rippe,, M. Dekker, and N. Kleckner, (2002) Capturing chromosome conformation. Science, 295, 1306−1311.
pmid: 11847345
20 M. Simonis,, P. Klous,, E. Splinter,, Y. Moshkin,, R. Willemsen,, E. de Wit,, B. van Steensel, and W. de Laat, (2006) Nuclear organization of active and inactive chromatin domains uncovered by chromosome conformation capture-on-chip (4C). Nat. Genet., 38, 1348−1354.
pmid: 17033623
21 Z. Zhao,, G. Tavoosidana,, M. Sjölinder,, A. Göndör,, P. Mariano,, S. Wang,, C. Kanduri,, M. Lezcano,, K. S. Sandhu,, U. Singh,, et al. (2006) Circular chromosome conformation capture (4C) uncovers extensive networks of epigenetically regulated intra- and interchromosomal interactions. Nat. Genet., 38, 1341−1347.
pmid: 17033624
22 J. Dostie,, T. A. Richmond,, R. A. Arnaout,, R. R. Selzer,, W. L. Lee,, T. A. Honan,, E. D. Rubio,, A. Krumm,, J. Lamb,, C. Nusbaum,, et al. (2006) Chromosome Conformation Capture Carbon Copy (5C): a massively parallel solution for mapping interactions between genomic elements. Genome Res., 16, 1299−1309.
pmid: 16954542
23 J. Dostie, and J. Dekker, (2007) Mapping networks of physical interactions between genomic elements using 5C technology. Nat Protoc, 2, 988−1002.
pmid: 17446898
24 M. Simonis,, J. Kooren, and W. de Laat, (2007) An evaluation of 3C-based methods to capture DNA interactions. Nat. Methods, 4, 895−901.
pmid: 17971780
25 M. J. Fullwood, and Y. Ruan, (2009) ChIP-based methods for the identification of long-range chromatin interactions. J. Cell. Biochem., 107, 30−39.
pmid: 19247990
26 L. Handoko,, H. Xu,, G. Li,, C. Y. Ngan,, E. Chew,, M. Schnapp,, C. W. Lee,, C. Ye,, J. L. Ping,, F. Mulawadi,, et al. (2011) CTCF-mediated functional chromatin interactome in pluripotent cells. Nat. Genet., 43, 630−638.
pmid: 21685913
27 C. A. Espinoza, and B. Ren, (2011) Mapping higher order structure of chromatin domains. Nat. Genet., 43, 615−616.
pmid: 21709679
28 M. J. Fullwood,, M. H. Liu,, Y. F. Pan,, J. Liu,, H. Xu,, Y. B. Mohamed,, Y. L. Orlov,, S. Velkov,, A. Ho,, P. H. Mei,, et al. (2009) An oestrogen-receptor-alpha-bound human chromatin interactome. Nature, 462, 58−64.
pmid: 19890323
29 N. Rusk, (2009) When ChIA PETs meet Hi-C. Nat. Methods, 6, 863.
30 A. Miele,, K. Bystricky, and J. Dekker, (2009) Yeast silent mating type loci form heterochromatic clusters through silencer protein-dependent long-range interactions. PLoS Genet., 5, e1000478.
pmid: 19424429
31 B. Tolhuis,, R. J. Palstra,, E. Splinter,, F. Grosveld, and W. de Laat, (2002) Looping and interaction between hypersensitive sites in the active beta-globin locus. Mol. Cell, 10, 1453−1465.
pmid: 12504019
32 B. R. Lajoie,, N. L. van Berkum,, A. Sanyal, and J. Dekker, (2009) My5C: web tools for chromosome conformation capture studies. Nat. Methods, 6, 690−691.
pmid: 19789528
33 D. Baù, A. Sanyal,, B. R. Lajoie,, E. Capriotti,, M. Byron,, J. B. Lawrence,, J. Dekker, and M. A. Marti-Renom, (2011) The three-dimensional folding of the α-globin gene domain reveals formation of chromatin globules. Nat. Struct. Mol. Biol., 18, 107−114.
pmid: 21131981
34 E. Lieberman-Aiden,, N. L. van Berkum,, L. Williams,, M. Imakaev,, T. Ragoczy,, A. Telling,, I. Amit,, B. R. Lajoie,, P. J. Sabo,, M. O. Dorschner,, et al. (2009) Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science, 326, 289−293.
pmid: 19815776
35 N.L. van Berkum,, et al. (2010) Hi-C: a method to study the three-dimensional architecture of genomes. J. Vis. Exp., 39.
36 M. Baker, (2011) Genomics: Genomes in three dimensions. Nature, 470, 289−294.
pmid: 21307943
37 R. Kalhor,, H. Tjong,, N. Jayathilaka,, F. Alber, and L. Chen, (2012) Genome architectures revealed by tethered chromosome conformation capture and population-based modeling. Nat. Biotechnol., 30, 90−98 .
pmid: 22198700
38 Z. Duan,, M. Andronescu,, K. Schutz,, S. McIlwain,, Y. J. Kim,, C. Lee,, J. Shendure,, S. Fields,, C. A. Blau, and W. S. Noble, (2010) A three-dimensional model of the yeast genome. Nature, 465, 363−367.
pmid: 20436457
39 M. Rousseau,, J. Fraser,, M. A. Ferraiuolo,, J. Dostie, and M. Blanchette, (2011) Three-dimensional modeling of chromatin structure from interaction frequency data using Markov chain Monte Carlo sampling. BMC Bioinformatics, 12, 414.
pmid: 22026390
40 H. Tanizawa,, O. Iwasaki,, A. Tanaka,, J. R. Capizzi,, P. Wickramasinghe,, M. Lee,, Z. Fu, and K. Noma, (2010) Mapping of long-range associations throughout the fission yeast genome reveals global genome organization linked to transcriptional regulation. Nucleic Acids Res., 38, 8164−8177.
pmid: 21030438
41 M. A. Marti-Renom, and L. A. Mirny, (2011) Bridging the resolution gap in structural modeling of 3D genome organization. PLoS Comput. Biol., 7, e1002125.
pmid: 21779160
42 J. Mateos-Langerak,, M. Bohn,, W. de Leeuw,, O. Giromus,, E. M. Manders,, P. J. Verschure,, M. H. Indemans,, H. J. Gierman,, D. W. Heermann,, R. van Driel,, et al. (2009) Spatially confined folding of chromatin in the interphase nucleus. Proc. Natl. Acad. Sci. U.S.A., 106, 3812−3817.
pmid: 19234129
43 M. Bohn, and D. W. Heermann, (2010) Diffusion-driven looping provides a consistent framework for chromatin organization. PLoS ONE, 5, e12218.
pmid: 20811620
44 M. Barbieri,, M. Chotalia,, J. Fraser,, L. M. Lavitas,, J. Dostie,, A. Pombo, and M. Nicodemi, (2012) Complexity of chromatin folding is captured by the strings and binders switch model. Proc. Natl. Acad. Sci. U.S.A., 109, 16173−16178.
pmid: 22988072
45 J. R. Dixon,, S. Selvaraj,, F. Yue,, A. Kim,, Y. Li,, Y. Shen,, M. Hu,, J. S. Liu, and B. Ren, (2012) Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature, 485, 376−380.
pmid: 22495300
46 E. P. Nora,, B. R. Lajoie,, E. G. Schulz,, L. Giorgetti,, I. Okamoto,, N. Servant,, T. Piolot,, N. L. van Berkum,, J. Meisig,, J. Sedat,, et al. (2012) Spatial partitioning of the regulatory landscape of the X-inactivation centre. Nature, 485, 381−385.
pmid: 22495304
47 T. Sexton,, E. Yaffe,, E. Kenigsberg,, F. Bantignies,, B. Leblanc,, M. Hoichman,, H. Parrinello,, A. Tanay, and G. Cavalli, (2012) Three-dimensional folding and functional organization principles of the Drosophila genome. Cell, 148, 458−472.
pmid: 22265598
48 C. Hou,, L. Li,, Z. S. Qin, and V. G. Corces, (2012) Gene density, transcription, and insulators contribute to the partition of the Drosophila genome into physical domains. Mol. Cell, 48, 471−484.
pmid: 23041285
49 Z. Duan, and C. A. Blau, (2012) The genome in space and time: does form always follow function? How does the spatial and temporal organization of a eukaryotic genome reflect and influence its functions? Bioessays, 34, 800−810.
pmid: 22777837
50 X. Lan,, P. J. Farnham, and V. X. Jin, (2012) Uncovering transcription factor modules using one- and three-dimensional analyses. J. Biol. Chem., 287, 30914−30921.
pmid: 22952238
51 X. Lan,, H. Witt,, K. Katsumura,, Z. Ye,, Q. Wang,, E. H. Bresnick,, P. J. Farnham, and V. X. Jin, (2012) Integration of Hi-C and ChIP-seq data reveals distinct types of chromatin linkages. Nucleic Acids Res., 40, 7690−7704.
pmid: 22675074
52 E. E. Khrameeva,, A. A. Mironov,, G. G. Fedonin,, P. Khaitovich, and M. S. Gelfand, (2012) Spatial proximity and similarity of the epigenetic state of genome domains. PLoS ONE, 7, e33947.
pmid: 22496774
53 Y. C. Hwang,, Q. Zheng,, B. D. Gregory, and L. S. Wang, (2013) High-throughput identification of long-range regulatory elements and their target promoters in the human genome. Nucleic Acids Res., 41, 4835−4846.
pmid: 23525463
54 J. Wang,, X. Lan,, P. Y. Hsu,, H. K. Hsu,, K. Huang,, J. Parvin,, T. H. Huang, and V. X. Jin, (2013) Genome-wide analysis uncovers high frequency, strong differential chromosomal interactions and their associated epigenetic patterns in E2-mediated gene regulation. BMC Genomics, 14, 70.
pmid: 23368971
55 A. Baker,, B. Audit,, C. L. Chen,, B. Moindrot,, A. Leleu,, G. Guilbaud,, A. Rappailles,, C. Vaillant,, A. Goldar,, F. Mongelard,, et al. (2012) Replication fork polarity gradients revealed by megabase-sized U-shaped replication timing domains in human cell lines. PLoS Comput. Biol., 8, e1002443.
pmid: 22496629
56 B. Moindrot,, B. Audit,, P. Klous,, A. Baker,, C. Thermes,, W. de Laat,, P. Bouvet,, F. Mongelard, and A. Arneodo, (2012) 3D chromatin conformation correlates with replication timing and is conserved in resting cells. Nucleic Acids Res., 40, 9470−9481.
pmid: 22879376
57 S. Takebayashi,, V. Dileep,, T. Ryba,, J. H. Dennis, and D. M. Gilbert, (2012) Chromatin-interaction compartment switch at developmentally regulated chromosomal domains reveals an unusual principle of chromatin folding. Proc. Natl. Acad. Sci. U.S.A., 109, 12574−12579.
pmid: 22807480
58 G. Fudenberg,, G. Getz,, M. Meyerson, and L. A. Mirny, (2011) High order chromatin architecture shapes the landscape of chromosomal alterations in cancer. Nat. Biotechnol., 29, 1109−1113.
pmid: 22101486
59 S. De, and F. Michor, (2011) DNA replication timing and long-range DNA interactions predict mutational landscapes of cancer genomes. Nat. Biotechnol., 29, 1103−1108.
pmid: 22101487
60 R. Chiarle,, Y. Zhang,, R. L. Frock,, S. M. Lewis,, B. Molinie,, Y. J. Ho,, D. R. Myers,, V. W. Choi,, M. Compagno,, D. J. Malkin,, et al. (2011) Genome-wide translocation sequencing reveals mechanisms of chromosome breaks and rearrangements in B cells. Cell, 147, 107−119.
pmid: 21962511
61 Y. Zhang,, R. P. McCord,, Y. J. Ho,, B. R. Lajoie,, D. G. Hildebrand,, A. C. Simon,, M. S. Becker,, F. W. Alt, and J. Dekker, (2012) Spatial organization of the mouse genome and its role in recurrent chromosomal translocations. Cell, 148, 908−921.
pmid: 22341456
62 O. Elemento,, M. A. Rubin, and D. S. Rickman, (2012) Oncogenic transcription factors as master regulators of chromatin topology: a new role for ERG in prostate cancer. Cell Cycle, 11, 3380−3383.
pmid: 22918253
63 D. S. Rickman,, T. D. Soong,, B. Moss,, J. M. Mosquera,, J. Dlabal,, S. Terry,, T. Y. MacDonald,, J. Tripodi,, K. Bunting,, V. Najfeld,, et al. (2012) Oncogene-mediated alterations in chromatin conformation. Proc. Natl. Acad. Sci. U.S.A., 109, 9083−9088.
pmid: 22615383
64 J. M. Engreitz,, V. Agarwala, and L. A. Mirny, (2012) Three-dimensional genome architecture influences partner selection for chromosomal translocations in human disease. PLoS ONE, 7, e44196.
pmid: 23028501
65 M. Shugay,, I. Ortiz de Mendíbil,, J. L. Vizmanos, and F. J. Novo, (2012) Genomic hallmarks of genes involved in chromosomal translocations in hematological cancer. PLoS Comput. Biol., 8, e1002797.
pmid: 23236267
66 Z. Wang,, R. Cao,, K. Taylor,, A. Briley,, C. Caldwell, and J. Cheng, (2013) The properties of genome conformation and spatial gene interaction and regulation networks of normal and malignant human cell types. PLoS ONE, 8, e58793.
pmid: 23536826
67 E. V. Chambers,, W. A. Bickmore, and C. A. Semple, (2013) Divergence of Mammalian higher order chromatin structure is associated with developmental Loci. PLoS Comput. Biol., 9, e1003017.
pmid: 23592965
68 Z. Dai, and X. Dai, (2012) Nuclear colocalization of transcription factor target genes strengthens coregulation in yeast. Nucleic Acids Res., 40, 27−36.
pmid: 21880591
69 D. M. Witten, and W. S. Noble, (2012) On the assessment of statistical significance of three-dimensional colocalization of sets of genomic elements. Nucleic Acids Res., 40, 3849−3855.
pmid: 22266657
70 J. Paulsen,, T. G. Lien,, G. K. Sandve,, L. Holden,, O. Borgan,, I. K. Glad, and E. Hovig, (2013) Handling realistic assumptions in hypothesis testing of 3D co-localization of genomic elements. Nucleic Acids Res., (In press).
pmid: 23571755
71 J. M. Belton,, R. P. McCord,, J. H. Gibcus,, N. Naumova,, Y. Zhan, and J. Dekker, (2012) Hi-C: a comprehensive technique to capture the conformation of genomes. Methods, 58, 268−276.
pmid: 22652625
72 Z. Duan,, M. Andronescu,, K. Schutz,, C. Lee,, J. Shendure,, S. Fields,, W. S. Noble, and C. Anthony Blau, (2012) A genome-wide 3C-method for characterizing the three-dimensional architectures of genomes. Methods, 58, 277−288.
pmid: 22776363
73 E. Yaffe, and A. Tanay, (2011) Probabilistic modeling of Hi-C contact maps eliminates systematic biases to characterize global chromosomal architecture. Nat. Genet., 43, 1059−1065.
pmid: 22001755
74 M. Imakaev,, G. Fudenberg,, R. P. McCord,, N. Naumova,, A. Goloborodko,, B. R. Lajoie,, J. Dekker, and L. A. Mirny, (2012) Iterative correction of Hi-C data reveals hallmarks of chromosome organization. Nat. Methods, 9, 999−1003.
pmid: 22941365
75 H. Li, and R. Durbin, (2009) Fast and accurate short read alignment with Burrows-Wheeler transform. Bioinformatics, 25, 1754−1760.
pmid: 19451168
76 H. Li,, J. Ruan, and R. Durbin, (2008) Mapping short DNA sequencing reads and calling variants using mapping quality scores. Genome Res., 18, 1851−1858.
pmid: 18714091
77 B. Langmead,, C. Trapnell,, M. Pop, and S. L. Salzberg, (2009) Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biol., 10, R25.
pmid: 19261174
78 Tools: Novocraft.
79 Picard is avaible in the website of Github.
80 N. Servant,, B. R. Lajoie,, E. P. Nora,, L. Giorgetti,, C. J. Chen,, E. Heard,, J. Dekker, and E. Barillot, (2012) HiTC: exploration of high-throughput ‘C’ experiments. Bioinformatics, 28, 2843−2844.
pmid: 22923296
81 Y. Shavit, and P. Lio’, (2013) CytoHiC: a cytoscape plugin for visual comparison of Hi-C networks. Bioinformatics, 29, 1206−1207.
pmid: 23508968
82 X. Zhou,, R. F. Lowdon,, D. Li,, H. A. Lawson,, P. A. Madden,, J. F. Costello, and T. Wang, (2013) Exploring long-range genome interactions using the WashU Epigenome Browser. Nat. Methods, 10, 375−376.
pmid: 23629413
83 D. Aird,, M. G. Ross,, W. S. Chen,, M. Danielsson,, T. Fennell,, C. Russ,, D. B. Jaffe,, C. Nusbaum, and A. Gnirke, (2011) Analyzing and minimizing PCR amplification bias in Illumina sequencing libraries. Genome Biol., 12, R18.
pmid: 21338519
84 Y. Benjamini, and T. P. Speed, (2012) Summarizing and correcting the GC content bias in high-throughput sequencing. Nucleic Acids Res., 40, e72.
pmid: 22323520
85 D. K. Gascoigne,, et al. (2011) Reassessment of the Hi-C analysis of human genome architecture.
86 A. Cournac,, H. Marie-Nelly,, M. Marbouty,, R. Koszul, and J. Mozziconacci, (2012) Normalization of a chromosomal contact map. BMC Genomics, 13, 436.
pmid: 22935139
87 M. Hu,, K. Deng,, S. Selvaraj,, Z. Qin,, B. Ren, and J. S. Liu, (2012) HiCNorm: removing biases in Hi-C data via Poisson regression. Bioinformatics, 28, 3131−3133.
pmid: 23023982
88 W. A. Bickmore, and B. van Steensel, (2013) Genome architecture: domain organization of interphase chromosomes. Cell, 152, 1270−1284.
pmid: 23498936
89 A. Smallwood, and B. Ren, (2013) Genome organization and long-range regulation of gene expression by enhancers. Curr. Opin. Cell Biol., 25, 1−8.
pmid: 23352256
90 J. H. Gibcus, and J. Dekker, (2013) The hierarchy of the 3D genome. Mol. Cell, 49, 773−782.
pmid: 23473598
91 A. Tanay, and G. Cavalli, (2013) Chromosomal domains: epigenetic contexts and functional implications of genomic compartmentalization. Curr. Opin. Genet. Dev., 23, 1−7.
pmid: 23523342
92 G. Cavalli, and T. Misteli, (2013) Functional implications of genome topology. Nat. Struct. Mol. Biol., 20, 290−299.
pmid: 23463314
93 L. Liu,, Y. Zhang,, J. Feng,, N. Zheng,, J. Yin, and Y. Zhang, (2012) GeSICA: genome segmentation from intra-chromosomal associations. BMC Genomics, 13, 164.
pmid: 22559164
94 G. Fudenberg, and L. A. Mirny, (2012) Higher-order chromatin structure: bridging physics and biology. Curr. Opin. Genet. Dev., 22, 115−124.
pmid: 22360992
95 S. M. Gasser, (2002) Visualizing chromatin dynamics in interphase nuclei. Science, 296, 1412−1416.
pmid: 12029120
96 C. Lanctôt,, T. Cheutin,, M. Cremer,, G. Cavalli, and T. Cremer, (2007) Dynamic genome architecture in the nuclear space: regulation of gene expression in three dimensions. Nat. Rev. Genet., 8, 104−115.
pmid: 17230197
97 D. Gerlich,, J. Beaudouin,, B. Kalbfuss,, N. Daigle,, R. Eils, and J. Ellenberg, (2003) Global chromosome positions are transmitted through mitosis in mammalian cells. Cell, 112, 751−764.
pmid: 12654243
98 A. Y. Grosberg,, S. K. Nechaev, and E. I. Shakhnovich, (1988) The role of topological constraints in the kinetics of collapse of macromolecules. J. Phys., 49, 2095−2100.
99 A. Y. Grosberg,, et al. (1993) Crumpled globule model of the three-dimensional structure of DNA. Europhys. Lett., 23, 373.
100 C. Munkel, and J. Langowski, (1998) Chromosome structure predicted by a polymer model. Physcial Review E, 57, 5888−5896.
101 L. A. Mirny, (2011) The fractal globule as a model of chromatin architecture in the cell. Chromosome Res., 19, 37−51.
pmid: 21274616
102 D. Baù and M. A. Marti-Renom, (2011) Structure determination of genomic domains by satisfaction of spatial restraints. Chromosome Res., 19, 25−35.
pmid: 21190133
103 M. Hu,, K. Deng,, Z. Qin,, J. Dixon,, S. Selvaraj,, J. Fang,, B. Ren, and J. S. Liu, (2013) Bayesian inference of spatial organizations of chromosomes. PLoS Comput. Biol., 9, e1002893.
pmid: 23382666
104 J. S. Liu,, R. Chen, and W. H. Wong, (1998) Rejection control and sequential importance sampling. J. Am. Stat. Assoc., 93, 1022−1031.
105 J. Liu, (2001) Monte Carlo Strategies in scientific computing. New York: Springer-Verlag.
106 S. Duane,, et al. (1987) Hybrid Monte-Carlo. Phys. Lett. B, 195, 216−222.
107 T. Misteli, (2012) Parallel genome universes. Nat. Biotechnol., 30, 55−56.
pmid: 22231096
108 H. Akaike, (1974) A new look at the statistical model identification. IEEE Trans. Automat. Contr., 19, 716−723.
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