2015
Journal article
Open Access
Inferring 3D chromatin structure using a multiscale approach based on quaternions
Caudai C., Salerno E., Zoppè M., Tonazzini A.
Quaternions Computer Science Applications Molecular Biology Structural Biology Multiscale approach Chromatin structure Chromosome conformation capture Biochemistry 3d chromatin structure Applied Mathematics Methodology Article Computational biology
Background: The knowledge of the spatial organisation of the chromatin fibre in cell nuclei helps researchers to understand the nuclear machinery that regulates DNA activity. Recent experimental techniques of the type Chromosome Conformation Capture (3C, or similar) provide high-resolution, high-throughput data consisting in the number of times any possible pair of textsc{dna} fragments is found to be in contact, in a certain population of cells. As these data carry information on the structure of the chromatin fibre, several attempts have been made to use them to obtain high-resolution 3D reconstructions of entire chromosomes, or even an entire genome. The techniques proposed treat the data in different ways, possibly exploiting physical-geometric chromatin models. One popular strategy is to transform contact data into Euclidean distances between pairs of fragments, and then solve a classical distance-to-geometry problem. Results: We developed and tested a reconstruction technique that does not require translating contacts into distances, thus avoiding a number of related drawbacks. Also, we introduce a geometrical chromatin chain model that allows us to include sound biochemical and biological constraints in the problem. This model can be scaled at different genomic resolutions, where the structures of the coarser models are influenced by the reconstructions at finer resolutions. The search in the solution space is then performed by a classical simulated annealing, where the model is evolved efficiently through quaternion operators. The presence of appropriate constraints permits the less reliable data to be overlooked, so the result is a set of plausible chromatin configurations compatible with both the data and the prior knowledge. Conclusions: To test our method, we obtained a number of 3D chromatin configurations from Hi-C data available in the literature for the long arm of human chromosome 1, and validated their features against known properties of gene density and transcriptional activity. Our results are compatible with biological features not introduced {em a priori} in the problem: structurally different regions in our reconstructions highly correlate with functionally different regions as known from literature and genomic repositories.
Source: BMC bioinformatics 16 (2015). doi:10.1186/s12859-015-0667-0
Publisher: BioMed Central,, [London] , Regno Unito
Fussner, E, Strauss, N, Djuric, U, Li, R, Ahmed, K, Hart, M. Open and closed domains in the mouse genome are configured as 10 nm chromatin fibres. EMBO reports. 2012; 13 (11): 992-6
Quenét, D, MCNally, JG, Dalal, Y. Through thick and thin: the conundrum of chromatin fibre folding in vivo. EMBO reports. 2012; 13 (11): 943-4
Lamond, AI, Earnshaw, WC. Structure and function in the nucleus. Science. 1998; 280: 547-53
Langer-Safer, PR, Levine, M, Ward, DC. Immunological method for mapping genes on drosophila polytene chromosomes. Proc Natl Acad Sci USA. 1982; 79: 4381-385
Amann, R, Fuchs, BM. Single-cell identification in microbial communities by improved fluorescence in situ hybridization techniques. Nat Rev Microbiol. 2008; 6: 339-48
Dekker, J, Rippe, K, Dekker, M, Kleckner, N. Capturing chromosome conformation. Science. 2002; 295: 1306-1311
Zhao, Z. Circular chromosome conformation capture (4c) uncovers extensive networks of epigenetically regulated intra- and interchromosomal interactions. Nat Genet. 2006; 38: 1341-1347
Dostie, J, Dekker, J. Mapping networks of physical interactions between genomic elements using 5c technology. Nat Protoc. 2007; 2: 988-1002
Lieberman-Aiden, E, van Berkum, NL, Williams, L, Imakaev, M, Ragoczy, T, Telling, A. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science. 2009; 326: 289-93
van Berkum, NL, Lieberman-Aiden, E, Williams, L, Imakaev, M, Gnirke, A, Mirny, LA. Hi-c: a method to study the three-dimensional architecture of genomes. J Vis Exp. 2010; 39: 1869-1875
Nagano, T, Lubling, Y, Stevens, TJ, Schoenfelder, S, Yaffe, E, Dean, W. Single-cell hi-c reveals cell-to-cell variability in chromosome structure. Nature. 2013; 502: 59-64
Fraser, J, Rousseau, M, Shenker, S, Ferraiuolo, MA, Hayashizaki, Y, Blanchette, M. Chromatin conformation signatures of cellular differentiation. Genome Biol. 2009; 10: 37
Duan, Z, Andronescu, M, Schutz, K, McIlwain, S, Kim, YJ, Lee, C. A three-dimensional model of the yeast genome. Nature. 2010; 465: 363-7
Zhang, ZZ, Li, G, Toh, KC, Sung, WK, Deng, M. Inference of spatial organizations of chromosomes using semi-definite embedding approach and hi-c data. Research in Computational Molecular Biology. 2013
Rippe, K. Making contacts on a nucleic acid polymer. Trends Biochem Sci. 2001; 26: 733-40
Tanizawa, H, Iwasaki, O, Tanaka, A, Capizzi, JR, Wickramasinghe, P, Lee, M. Mapping of long-range associations throughout the fission yeast genome reveals global genome organization linked to transcriptional regulation. Nucleic Acids Res. 2010; 38: 8164-177
Kalhor, R, Tjong, H, Jayathilaka, N, Alber, F, Chen, L. Genome architectures revealed by tethered chromosome conformation capture and population-based modeling. Nature Biotechnol. 2012; 30: 90-100
Baù, D, Sanyal, A, Lajoie, BR, Capriotti, E, Byron, M, Lawrence, JB. The three-dimensional folding of the alpha-globin gene domain reveals formation of chromatin globules. Nat Struct Mol Biol. 2011; 18: 107-14
Baù, D, Marti-Renom, MA. Structure determination of genomic domains by satisfaction of spatial restraints. Chromosome Res. 2011; 19: 25-35
Langowski, J, Heermann, DW. Computational modeling of the chromatin fiber. Semin Cell Dev Biol. 2007; 18: 659-67
Tark-Dame, M, van Driel, R, Heermann, DW. Chromatin folding–from biology to polymer models and back. J Cell Sci. 2011; 124: 839-45
Tokuda, N, Terada, TP, Sasai, M. Dynamical modeling of three-dimensional genome organization in interphase budding yeast. Biophys J. 2012; 102: 296-304
Iyer, BVS, Kenward, M, Arya, G. Hierarchies in eukaryotic genome organization: insights from polymer theory and simulations. BMC Biophys. 2011; 4: 8
Marti-Renom, M, Mirny, LA. Bridging the resolution gap in structural modeling of 3d genome organization. PLOS Comput Biol. 2011; 7: 1002125
Gehlen, LR, Gruenert, G, Jones, MB, Rodley, CD, Langowski, J, O’Sullivan, JM. Chromosome positioning and the clustering of functionally related loci in yeast is driven by chromosomal interactions. Nucleus. 2012; 3: 370-83
Meluzzi, D, Arya, G. Recovering ensembles of chromatin conformations from contact probabilities. Nucleic Acid Res. 2013; 41: 63-75
Giorgetti, L, Galupa, R, Nora, EP, Piolot, T, Lam, F, Dekker, J. Predictive polymer modeling reveals coupled fluctuations in chromosome conformation and transcription. Cell. 2014; 157: 950-63
Rousseau, M, Fraser, J, Ferraiuolo, MA, Dostie, J, Blanchette, M. Three-dimensional modeling of chromatin structure from interaction frequency data using markov chain monte carlo sampling. BMC Bioinf. 2011; 12: 414-29
Yaffe, E, Tanay, A. Probabilistic modeling of hi-c contact maps eliminates systematic biases to characterize global chromosomal architecture. Nat Genet. 2011; 43: 1059-1067
Hu, M, Deng, K, Qin, Z, Dixon, J, Selvaraj, S, Fang, J. Bayesian inference of spatial organizations of chromosomes. PLOS Comp Biol. 2013; 9: 1002893
Varoquaux, N, Ferhat, A, Stafford Noble, W, Vert, JP. A statistical approach for inferring the 3d structure of the genome. Bioinformatics. 2014; 30: 26-33
32 Caudai C. Ricostruzione tridimensionale della struttura della cromatina da dati tipo chromosome conformation capture. Technical Report 2014-PR-003, National Research Council of Italy - ISTI, Pisa, Italy (January 2014).
Duggal, G, Patro, R, Sefer, E, Wang, H, Filippova, D, Khuller, S. Resolving spatial inconsistencies in chromosome conformation measurements. Algorithms Mol Biol. 2013; 8: 8
Hu, M, Deng, K, Qin, Z, Liu, JS. Understanding spatial organizations of chromosomes via statistical analysis of hi-c data. Quant Biol. 2013; 1: 156-74
Dixon, JR, Selvaraj, S, Yue, F, Kim, A, Li, Y, Shen, Y. Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature. 2012; 485: 376-80
Vince, JA. Geometric Algebra for Computer Graphics. 2008
Olins, AL, Olins, DE. Spheroid chromatin units (v bodies). Science. 1974; 183: 330-2
Imakaev, M, Fudenberg, G, Patton McCord, R, Naumova, N, Goloborodko, A, Lajoie, BR. Iterative correction of hi-c data reveals hallmarks of chromosome organization. Nat Methods. 2012; 9: 999-1003
Kirkpatrick, S, Gellatt, CDJ, Vecchi, MP. Optimization by simulated annealing. Science. 1983; 229: 671-80
Metropolis, N, Rosenbluth, AW, Rosenbluth, MN, Teller, E. Equations of state calculations by fast computing machines. J Chem Phys. 1953; 21: 1087-1091
Grassia, FS. Practical parameterization of rotations using the exponential map. J Graph Tools. 1998; 3: 29-48
Karney, CF. Quaternions in molecular modeling. J Mol Graph Model. 2007; 25: 595-604
Hanson, AJ, Thakur, S. Quaternion maps of global protein structure. J Mol Graph Model. 2012; 38: 256-78
Magarshak, Y. Quaternion representation of rna sequences and tertiary structures. Biosystems. 1993; 30: 21-9
Consortium, TEP. A user’s guide to the encyclopedia of dna elements (encode). PLoS Biol. 2011; 9 (4): 1001046-1013711001046
Kent, WJ, Sugnet, CW, Furey, TS, Roskin, KM, Pringle, TH, Zahler, AM. The human genome browser at ucsc. Genome Res. 2002; 12: 996-1006
Versteeg, R, van Schaik, BDC, van Batenburg, MF, Roos, M, Monajemi, R, Caron, H. The human transcriptome map reveals extremes in gene density, intron length, gc content, and repeat pattern for domains of highly and weakly expressed genes. Genome Res. 2003; 13: 1998-2004
Mateos-Langerak, J, Bohn, M, de Leeuw, W, Giromus, O, Manders, EMM, Verschure, PJ. Spatially confined folding of chromatin in the interphase nucleus. PNAS. 2009; 106: 3812-817
1. Fussner E, Strauss N, Djuric U, Li R, Ahmed K, Hart M, et al. Open and closed domains in the mouse genome are configured as 10 nm chromatin fibres. EMBO reports. 2012;13(11):992-6.
2. Quenét D, MCNally JG, Dalal Y. Through thick and thin: the conundrum of chromatin fibre folding in vivo. EMBO reports. 2012;13(11):943-4.
3. Lamond AI, Earnshaw WC. Structure and function in the nucleus. Science. 1998;280:547-53.
4. Langer-Safer PR, Levine M, Ward DC. Immunological method for mapping genes on drosophila polytene chromosomes. Proc Natl Acad Sci USA. 1982;79:4381-385.
5. Amann R, Fuchs BM. Single-cell identification in microbial communities by improved fluorescence in situ hybridization techniques. Nat Rev Microbiol. 2008;6:339-48.
6. Dekker J, Rippe K, Dekker M, Kleckner N. Capturing chromosome conformation. Science. 2002;295:1306-1311.
7. Zhao Z. Circular chromosome conformation capture (4c) uncovers extensive networks of epigenetically regulated intra- and interchromosomal interactions. Nat Genet. 2006;38:1341-1347.
8. Dostie J, Dekker J. Mapping networks of physical interactions between genomic elements using 5c technology. Nat Protoc. 2007;2:988-1002.
9. Lieberman-Aiden E, van Berkum NL, Williams L, Imakaev M, Ragoczy T, Telling A, et al. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science. 2009;326: 289-93.
10. van Berkum NL, Lieberman-Aiden E, Williams L, Imakaev M, Gnirke A, Mirny LA, et al. Hi-c: a method to study the three-dimensional architecture of genomes. J Vis Exp. 2010;39:1869-1875.
11. Nagano T, Lubling Y, Stevens TJ, Schoenfelder S, Yaffe E, Dean W, et al. Single-cell hi-c reveals cell-to-cell variability in chromosome structure. Nature. 2013;502:59-64.
12. Fraser J, Rousseau M, Shenker S, Ferraiuolo MA, Hayashizaki Y, Blanchette M, et al. Chromatin conformation signatures of cellular differentiation. Genome Biol. 2009;10:37.
13. Duan Z, Andronescu M, Schutz K, McIlwain S, Kim YJ, Lee C, et al. A three-dimensional model of the yeast genome. Nature. 2010;465:363-7.
14. Zhang ZZ, Li G, Toh KC, Sung WK. Inference of spatial organizations of chromosomes using semi-definite embedding approach and hi-c data In: Deng M, et al, editors. Research in Computational Molecular Biology. Berlin: Springer; 2013. p. 317-32.
15. Rippe K. Making contacts on a nucleic acid polymer. Trends Biochem Sci. 2001;26:733-40.
16. Tanizawa H, Iwasaki O, Tanaka A, Capizzi JR, Wickramasinghe P, Lee M, et al. Mapping of long-range associations throughout the fission yeast genome reveals global genome organization linked to transcriptional regulation. Nucleic Acids Res. 2010;38:8164-177.
17. Kalhor R, Tjong H, Jayathilaka N, Alber F, Chen L. Genome architectures revealed by tethered chromosome conformation capture and population-based modeling. Nature Biotechnol. 2012;30:90-100.
18. Baù D, Sanyal A, Lajoie BR, Capriotti E, Byron M, Lawrence JB, et al. The three-dimensional folding of the alpha-globin gene domain reveals formation of chromatin globules. Nat Struct Mol Biol. 2011;18:107-14.
19. Baù D, Marti-Renom MA. Structure determination of genomic domains by satisfaction of spatial restraints. Chromosome Res. 2011;19:25-35.
20. Langowski J, Heermann DW. Computational modeling of the chromatin fiber. Semin Cell Dev Biol. 2007;18:659-67.
21. Tark-Dame M, van Driel R, Heermann DW. Chromatin folding-from biology to polymer models and back. J Cell Sci. 2011;124:839-45.
22. Tokuda N, Terada TP, Sasai M. Dynamical modeling of three-dimensional genome organization in interphase budding yeast. Biophys J. 2012; 102:296-304.
23. Iyer BVS, Kenward M, Arya G. Hierarchies in eukaryotic genome organization: insights from polymer theory and simulations. BMC Biophys. 2011;4:8.
24. Marti-Renom M, Mirny LA. Bridging the resolution gap in structural modeling of 3d genome organization. PLOS Comput Biol. 2011;7:1002125.
25. Gehlen LR, Gruenert G, Jones MB, Rodley CD, Langowski J, O'Sullivan JM. Chromosome positioning and the clustering of functionally related loci in yeast is driven by chromosomal interactions. Nucleus. 2012;3:370-83.
26. Meluzzi D, Arya G. Recovering ensembles of chromatin conformations from contact probabilities. Nucleic Acid Res. 2013;41:63-75.
27. Giorgetti L, Galupa R, Nora EP, Piolot T, Lam F, Dekker J, et al. Predictive polymer modeling reveals coupled fluctuations in chromosome conformation and transcription. Cell. 2014;157:950-63.
28. Rousseau M, Fraser J, Ferraiuolo MA, Dostie J, Blanchette M. Three-dimensional modeling of chromatin structure from interaction frequency data using markov chain monte carlo sampling. BMC Bioinf. 2011;12:414-29.
29. Yaffe E, Tanay A. Probabilistic modeling of hi-c contact maps eliminates systematic biases to characterize global chromosomal architecture. Nat Genet. 2011;43:1059-1067.
30. Hu M, Deng K, Qin Z, Dixon J, Selvaraj S, Fang J, et al. Bayesian inference of spatial organizations of chromosomes. PLOS Comp Biol. 2013; 9:1002893.
31. Varoquaux N, Ferhat A, Stafford Noble W, Vert JP. A statistical approach for inferring the 3d structure of the genome. Bioinformatics. 2014; 30:26-33.
32. Caudai C. Ricostruzione tridimensionale della struttura della cromatina da dati tipo chromosome conformation capture. Technical Report 2014-PR-003, National Research Council of Italy - ISTI, Pisa, Italy (January 2014).
33. Duggal G, Patro R, Sefer E, Wang H, Filippova D, Khuller S, et al. Resolving spatial inconsistencies in chromosome conformation measurements. Algorithms Mol Biol. 2013;8:8.
34. Hu M, Deng K, Qin Z, Liu JS. Understanding spatial organizations of chromosomes via statistical analysis of hi-c data. Quant Biol. 2013; 1:156-74.
35. Dixon JR, Selvaraj S, Yue F, Kim A, Li Y, Shen Y, et al. Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature. 2012;485:376-80.
36. Vince JA. Geometric Algebra for Computer Graphics. Berlin: Springer; 2008.
37. Olins AL, Olins DE. Spheroid chromatin units (v bodies). Science. 1974;183:330-2.
38. Imakaev M, Fudenberg G, Patton McCord R, Naumova N, Goloborodko A, Lajoie BR, et al. Iterative correction of hi-c data reveals hallmarks of chromosome organization. Nat Methods. 2012;9:999-1003.
39. Kirkpatrick S, Gellatt CDJ, Vecchi MP. Optimization by simulated annealing. Science. 1983;229:671-80.
40. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller E. Equations of state calculations by fast computing machines. J Chem Phys. 1953; 21:1087-1091.
41. Grassia FS. Practical parameterization of rotations using the exponential map. J Graph Tools. 1998;3:29-48.
42. Karney CF. Quaternions in molecular modeling. J Mol Graph Model. 2007;25:595-604.
43. Hanson AJ, Thakur S. Quaternion maps of global protein structure. J Mol Graph Model. 2012;38:256-78.
44. Magarshak Y. Quaternion representation of rna sequences and tertiary structures. Biosystems. 1993;30:21-9.
45. Consortium TEP. A user's guide to the encyclopedia of dna elements (encode). PLoS Biol. 2011;9(4):1001046-1013711001046.
46. Kent WJ, Sugnet CW, Furey TS, Roskin KM, Pringle TH, Zahler AM, et al. The human genome browser at ucsc. Genome Res. 2002;12:996-1006.
47. Versteeg R, van Schaik BDC, van Batenburg MF, Roos M, Monajemi R, Caron H, et al. The human transcriptome map reveals extremes in gene density, intron length, gc content, and repeat pattern for domains of highly and weakly expressed genes. Genome Res. 2003;13:1998-2004.
48. Mateos-Langerak J, Bohn M, de Leeuw W, Giromus O, Manders EMM, Verschure PJ, et al. Spatially confined folding of chromatin in the interphase nucleus. PNAS. 2009;106:3812-817.
Quenét, D, MCNally, JG, Dalal, Y. Through thick and thin: the conundrum of chromatin fibre folding in vivo. EMBO reports. 2012; 13 (11): 943-4
Lamond, AI, Earnshaw, WC. Structure and function in the nucleus. Science. 1998; 280: 547-53
Langer-Safer, PR, Levine, M, Ward, DC. Immunological method for mapping genes on drosophila polytene chromosomes. Proc Natl Acad Sci USA. 1982; 79: 4381-385
Amann, R, Fuchs, BM. Single-cell identification in microbial communities by improved fluorescence in situ hybridization techniques. Nat Rev Microbiol. 2008; 6: 339-48
Dekker, J, Rippe, K, Dekker, M, Kleckner, N. Capturing chromosome conformation. Science. 2002; 295: 1306-1311
Zhao, Z. Circular chromosome conformation capture (4c) uncovers extensive networks of epigenetically regulated intra- and interchromosomal interactions. Nat Genet. 2006; 38: 1341-1347
Dostie, J, Dekker, J. Mapping networks of physical interactions between genomic elements using 5c technology. Nat Protoc. 2007; 2: 988-1002
Lieberman-Aiden, E, van Berkum, NL, Williams, L, Imakaev, M, Ragoczy, T, Telling, A. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science. 2009; 326: 289-93
van Berkum, NL, Lieberman-Aiden, E, Williams, L, Imakaev, M, Gnirke, A, Mirny, LA. Hi-c: a method to study the three-dimensional architecture of genomes. J Vis Exp. 2010; 39: 1869-1875
Nagano, T, Lubling, Y, Stevens, TJ, Schoenfelder, S, Yaffe, E, Dean, W. Single-cell hi-c reveals cell-to-cell variability in chromosome structure. Nature. 2013; 502: 59-64
Fraser, J, Rousseau, M, Shenker, S, Ferraiuolo, MA, Hayashizaki, Y, Blanchette, M. Chromatin conformation signatures of cellular differentiation. Genome Biol. 2009; 10: 37
Duan, Z, Andronescu, M, Schutz, K, McIlwain, S, Kim, YJ, Lee, C. A three-dimensional model of the yeast genome. Nature. 2010; 465: 363-7
Zhang, ZZ, Li, G, Toh, KC, Sung, WK, Deng, M. Inference of spatial organizations of chromosomes using semi-definite embedding approach and hi-c data. Research in Computational Molecular Biology. 2013
Rippe, K. Making contacts on a nucleic acid polymer. Trends Biochem Sci. 2001; 26: 733-40
Tanizawa, H, Iwasaki, O, Tanaka, A, Capizzi, JR, Wickramasinghe, P, Lee, M. Mapping of long-range associations throughout the fission yeast genome reveals global genome organization linked to transcriptional regulation. Nucleic Acids Res. 2010; 38: 8164-177
Kalhor, R, Tjong, H, Jayathilaka, N, Alber, F, Chen, L. Genome architectures revealed by tethered chromosome conformation capture and population-based modeling. Nature Biotechnol. 2012; 30: 90-100
Baù, D, Sanyal, A, Lajoie, BR, Capriotti, E, Byron, M, Lawrence, JB. The three-dimensional folding of the alpha-globin gene domain reveals formation of chromatin globules. Nat Struct Mol Biol. 2011; 18: 107-14
Baù, D, Marti-Renom, MA. Structure determination of genomic domains by satisfaction of spatial restraints. Chromosome Res. 2011; 19: 25-35
Langowski, J, Heermann, DW. Computational modeling of the chromatin fiber. Semin Cell Dev Biol. 2007; 18: 659-67
Tark-Dame, M, van Driel, R, Heermann, DW. Chromatin folding–from biology to polymer models and back. J Cell Sci. 2011; 124: 839-45
Tokuda, N, Terada, TP, Sasai, M. Dynamical modeling of three-dimensional genome organization in interphase budding yeast. Biophys J. 2012; 102: 296-304
Iyer, BVS, Kenward, M, Arya, G. Hierarchies in eukaryotic genome organization: insights from polymer theory and simulations. BMC Biophys. 2011; 4: 8
Marti-Renom, M, Mirny, LA. Bridging the resolution gap in structural modeling of 3d genome organization. PLOS Comput Biol. 2011; 7: 1002125
Gehlen, LR, Gruenert, G, Jones, MB, Rodley, CD, Langowski, J, O’Sullivan, JM. Chromosome positioning and the clustering of functionally related loci in yeast is driven by chromosomal interactions. Nucleus. 2012; 3: 370-83
Meluzzi, D, Arya, G. Recovering ensembles of chromatin conformations from contact probabilities. Nucleic Acid Res. 2013; 41: 63-75
Giorgetti, L, Galupa, R, Nora, EP, Piolot, T, Lam, F, Dekker, J. Predictive polymer modeling reveals coupled fluctuations in chromosome conformation and transcription. Cell. 2014; 157: 950-63
Rousseau, M, Fraser, J, Ferraiuolo, MA, Dostie, J, Blanchette, M. Three-dimensional modeling of chromatin structure from interaction frequency data using markov chain monte carlo sampling. BMC Bioinf. 2011; 12: 414-29
Yaffe, E, Tanay, A. Probabilistic modeling of hi-c contact maps eliminates systematic biases to characterize global chromosomal architecture. Nat Genet. 2011; 43: 1059-1067
Hu, M, Deng, K, Qin, Z, Dixon, J, Selvaraj, S, Fang, J. Bayesian inference of spatial organizations of chromosomes. PLOS Comp Biol. 2013; 9: 1002893
Varoquaux, N, Ferhat, A, Stafford Noble, W, Vert, JP. A statistical approach for inferring the 3d structure of the genome. Bioinformatics. 2014; 30: 26-33
32 Caudai C. Ricostruzione tridimensionale della struttura della cromatina da dati tipo chromosome conformation capture. Technical Report 2014-PR-003, National Research Council of Italy - ISTI, Pisa, Italy (January 2014).
Duggal, G, Patro, R, Sefer, E, Wang, H, Filippova, D, Khuller, S. Resolving spatial inconsistencies in chromosome conformation measurements. Algorithms Mol Biol. 2013; 8: 8
Hu, M, Deng, K, Qin, Z, Liu, JS. Understanding spatial organizations of chromosomes via statistical analysis of hi-c data. Quant Biol. 2013; 1: 156-74
Dixon, JR, Selvaraj, S, Yue, F, Kim, A, Li, Y, Shen, Y. Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature. 2012; 485: 376-80
Vince, JA. Geometric Algebra for Computer Graphics. 2008
Olins, AL, Olins, DE. Spheroid chromatin units (v bodies). Science. 1974; 183: 330-2
Imakaev, M, Fudenberg, G, Patton McCord, R, Naumova, N, Goloborodko, A, Lajoie, BR. Iterative correction of hi-c data reveals hallmarks of chromosome organization. Nat Methods. 2012; 9: 999-1003
Kirkpatrick, S, Gellatt, CDJ, Vecchi, MP. Optimization by simulated annealing. Science. 1983; 229: 671-80
Metropolis, N, Rosenbluth, AW, Rosenbluth, MN, Teller, E. Equations of state calculations by fast computing machines. J Chem Phys. 1953; 21: 1087-1091
Grassia, FS. Practical parameterization of rotations using the exponential map. J Graph Tools. 1998; 3: 29-48
Karney, CF. Quaternions in molecular modeling. J Mol Graph Model. 2007; 25: 595-604
Hanson, AJ, Thakur, S. Quaternion maps of global protein structure. J Mol Graph Model. 2012; 38: 256-78
Magarshak, Y. Quaternion representation of rna sequences and tertiary structures. Biosystems. 1993; 30: 21-9
Consortium, TEP. A user’s guide to the encyclopedia of dna elements (encode). PLoS Biol. 2011; 9 (4): 1001046-1013711001046
Kent, WJ, Sugnet, CW, Furey, TS, Roskin, KM, Pringle, TH, Zahler, AM. The human genome browser at ucsc. Genome Res. 2002; 12: 996-1006
Versteeg, R, van Schaik, BDC, van Batenburg, MF, Roos, M, Monajemi, R, Caron, H. The human transcriptome map reveals extremes in gene density, intron length, gc content, and repeat pattern for domains of highly and weakly expressed genes. Genome Res. 2003; 13: 1998-2004
Mateos-Langerak, J, Bohn, M, de Leeuw, W, Giromus, O, Manders, EMM, Verschure, PJ. Spatially confined folding of chromatin in the interphase nucleus. PNAS. 2009; 106: 3812-817
1. Fussner E, Strauss N, Djuric U, Li R, Ahmed K, Hart M, et al. Open and closed domains in the mouse genome are configured as 10 nm chromatin fibres. EMBO reports. 2012;13(11):992-6.
2. Quenét D, MCNally JG, Dalal Y. Through thick and thin: the conundrum of chromatin fibre folding in vivo. EMBO reports. 2012;13(11):943-4.
3. Lamond AI, Earnshaw WC. Structure and function in the nucleus. Science. 1998;280:547-53.
4. Langer-Safer PR, Levine M, Ward DC. Immunological method for mapping genes on drosophila polytene chromosomes. Proc Natl Acad Sci USA. 1982;79:4381-385.
5. Amann R, Fuchs BM. Single-cell identification in microbial communities by improved fluorescence in situ hybridization techniques. Nat Rev Microbiol. 2008;6:339-48.
6. Dekker J, Rippe K, Dekker M, Kleckner N. Capturing chromosome conformation. Science. 2002;295:1306-1311.
7. Zhao Z. Circular chromosome conformation capture (4c) uncovers extensive networks of epigenetically regulated intra- and interchromosomal interactions. Nat Genet. 2006;38:1341-1347.
8. Dostie J, Dekker J. Mapping networks of physical interactions between genomic elements using 5c technology. Nat Protoc. 2007;2:988-1002.
9. Lieberman-Aiden E, van Berkum NL, Williams L, Imakaev M, Ragoczy T, Telling A, et al. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science. 2009;326: 289-93.
10. van Berkum NL, Lieberman-Aiden E, Williams L, Imakaev M, Gnirke A, Mirny LA, et al. Hi-c: a method to study the three-dimensional architecture of genomes. J Vis Exp. 2010;39:1869-1875.
11. Nagano T, Lubling Y, Stevens TJ, Schoenfelder S, Yaffe E, Dean W, et al. Single-cell hi-c reveals cell-to-cell variability in chromosome structure. Nature. 2013;502:59-64.
12. Fraser J, Rousseau M, Shenker S, Ferraiuolo MA, Hayashizaki Y, Blanchette M, et al. Chromatin conformation signatures of cellular differentiation. Genome Biol. 2009;10:37.
13. Duan Z, Andronescu M, Schutz K, McIlwain S, Kim YJ, Lee C, et al. A three-dimensional model of the yeast genome. Nature. 2010;465:363-7.
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BibTeX entry
@article{oai:it.cnr:prodotti:332990,
title = {Inferring 3D chromatin structure using a multiscale approach based on quaternions},
author = {Caudai C. and Salerno E. and Zoppè M. and Tonazzini A.},
publisher = {BioMed Central,, [London] , Regno Unito},
doi = {10.1186/s12859-015-0667-0},
journal = {BMC bioinformatics},
volume = {16},
year = {2015}
}
0000-0002-1590-7890CNR ExploRA
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ISTI Repository
DOIAlso available from
