Skip to main content
SpringerLink
Log in

The Physical Behavior of Interphase Chromosomes: Polymer Theory and Coarse-Grain Computer Simulations

  • Protocol
  • First Online:
Hi-C Data Analysis

Part of the book series: Methods in Molecular Biology ((MIMB,volume 2301))

  • 2111 Accesses

Abstract

Fluorescence in situ hybridization and chromosome conformation capture methods point to the same conclusion: that chromosomes appear to the external observer as compact structures with a highly nonrandom three-dimensional organization. In this work, we recapitulate the efforts made by us and other groups to rationalize this behavior in terms of the mathematical language and tools of polymer physics. After a brief introduction dedicated to some crucial experiments dissecting the structure of interphase chromosomes, we discuss at a nonspecialistic level some fundamental aspects of theoretical and numerical polymer physics. Then, we inglobe biological and polymer aspects into a polymer model for interphase chromosomes which moves from the observation that mutual topological constraints, such as those typically present between polymer chains in ordinary melts, induce slow chain dynamics and “constraint” chromosomes to resemble double-folded randomly branched polymer conformations. By explicitly turning these ideas into a multi-scale numerical algorithm which is described here in full details, we can design accurate model polymer conformations for interphase chromosomes and offer them for systematic comparison to experiments. The review is concluded by discussing the limitations of our approach and pointing to promising perspectives for future work.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Segal E, Fondufe-Mittendorf Y, Chen L, Thåström AC, Field Y, Moore IK, Wang JPZ, Widom J (2006) A genomic code for nucleosome positioning. Nature 442:772–778

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Gaffney DJ, McVicker G, Pai AA, Fondufe-Mittendorf YN, Lewellen N, Michelini K, Widom J, Gilad Y, Pritchard JK (2012) Controls of nucleosome positioning in the human genome. Plos Genet 8:e1003036

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Ozer G, Luque A, Schlick T (2015) The chromatin fiber: multiscale problems and approaches. Curr Opin Struct Biol 31:124–139

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Alberts B, Johnson A, Lewis J, Morgan D, Raff M, Roberts K, Walter P (2014) Molecular biology of the cell, 6th edn. Garland Science, New York

    Google Scholar 

  5. Rabl C (1885) Über Zelltheilung. Morph Jb 10:214–330

    Google Scholar 

  6. Boveri T (1909) Die Blastomerenkerne von Ascaris megalocephala und die Theorie der Chromosomenindividualität. Arch Zellforsch 3:181–268

    Google Scholar 

  7. Cremer T, Cremer C (2001) Chromosome territories, nuclear architecture and gene regulation in mammalian cells. Nat Rev Genet 2:292–301

    Article  CAS  PubMed  Google Scholar 

  8. Cremer T, Cremer M (2010) Chromosome territories. CSH Perspect Biol 2:1–22

    Google Scholar 

  9. Bolzer A, Kreth G, Solovei I, Koehler D, Saracoglu K, Fauth C, Muller S, Eils R, Cremer C, Speicher MR, Cremer T (2005) Three-dimensional maps of all chromosomes in human male fibroblast nuclei and prometaphase rosettes. Plos Biol 3:826–842

    Article  CAS  Google Scholar 

  10. Solovei I, Kreysing M, Lanctôt C, Kösem S, Peichl L, Cremer T, Guck J, Joffe B (2009) Nuclear architecture of rod photoreceptor cells adapts to vision in mammalian evolution. Cell 137:356–368

    Article  CAS  PubMed  Google Scholar 

  11. Hahnfeldt P, Hearst JE, Brenner DJ, Sachs RK, Hlatky LR (1993) Polymer models for interphase chromosomes. Proc Natl Acad Sci USA 90:7854–7858

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Sachs RK, van den Engh G, Trask B, Yokota H, Hearst JE (1995) A random-walk/giant-loop model for interphase chromosomes. Proc Natl Acad Sci U S A 92:2710–2714

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Münkel C, Eils R, Dietzel S, Zink D, Mehring C, Wedemann G, Cremer T, Langowski J (1999) Compartmentalization of interphase chromosomes observed in simulation and experiment. J Mol Biol 285:1053–1065

    Article  PubMed  Google Scholar 

  14. Dekker J, Rippe K, Dekker M, Kleckner N (2002) Capturing chromosome conformation. Science 295:1306–1311

    Article  CAS  PubMed  Google Scholar 

  15. Simonis M, Klous P, Splinter E, Moshkin Y, Willemsen R, de Wit E, van Steensel B, de Laat W (2006) Nuclear organization of active and inactive chromatin domains uncovered by chromosome conformation capture–on-chip (4c). Nat Genet 38:1348–1354

    Article  CAS  PubMed  Google Scholar 

  16. Dostie J, Richmond TA, Arnaout RA, Selzer RR, Lee WL, Honan TA, Rubio ED, Krumm A, Lamb J, Nusbaum C, Green RD, Dekker J (2006) Chromosome conformation capture carbon copy (5c): a massively parallel solution for mapping interactions between genomic elements. Genome Res 16:1299–1309

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Lieberman-Aiden E, van Berkum NL, Williams L, Imakaev M, Ragoczy T, Telling A, Amit I, Lajoie BR, Sabo PJ, Dorschner MO, Sandstrom R, Bernstein B, Bender MA, Groudine M, Gnirke A, Stamatoyannopoulos J, Mirny LA, Lander ES, Dekker J (2009) Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science 326:289–293

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Dixon JR, Selvaraj S, Yue F, Kim A, Li Y, Shen Y, Hu M, Liu JS, Ren B (2012) Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature 485:376–380

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Gibcus JH, Samejima K, Goloborodko A, Samejima I, Naumova N, Nuebler J, Kanemaki MT, Xie L, Paulson JR, Earnshaw WC, Mirny LA, Dekker J (2018) A pathway for mitotic chromosome formation. Science 359:eaao6135

    Google Scholar 

  20. Mirny LA (2011) The fractal globule as a model of chromatin architecture in the cell. Chromosom Res 19:37–51

    Article  CAS  Google Scholar 

  21. Grosberg AY (2012) How two meters of DNA fit into a cell nucleus: polymer models with topological constraints and experimental data. Polym Sci Ser C 54:1–10

    Article  CAS  Google Scholar 

  22. Rosa A, Zimmer C (2014) Computational models of large-scale genome architecture. Int Rev Cell Mol Biol 307:275–349

    Article  CAS  PubMed  Google Scholar 

  23. Halverson JD, Smrek J, Kremer K, Grosberg AY (2014) From a melt of rings to chromosome territories: the role of topological constraints in genome folding. Rep Prog Phys 77:022601

    Article  PubMed  CAS  Google Scholar 

  24. Jost D, Rosa A, Vaillant C, Everaers R (2017) A polymer physics view on universal and sequence-specific aspects of chromosome folding. In: Lavelle C, Victor JM (eds) Nuclear architecture and dynamics, vol 2. Academic Press, Amsterdam, pp 149–169

    Google Scholar 

  25. Haddad N, Jost D, Vaillant C (2017) Perspectives: using polymer modeling to understand the formation and function of nuclear compartments. Chromosom Res 25:35–50

    Article  CAS  Google Scholar 

  26. Bianco S, Chiariello AM, Annunziatella C, Esposito A, Nicodemi M (2017) Predicting chromatin architecture from models of polymer physics. Chromosom Res 25:25–34

    Article  CAS  Google Scholar 

  27. Chiang M, Michieletto D, Brackley CA, Rattanavirotkul N, Mohammed H, Marenduzzo D, Chandra T (2019) Polymer modeling predicts chromosome reorganization in senescence. Cell Rep 28:3212–3223

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Michieletto D, Gilbert N (2019) Role of nuclear rna in regulating chromatin structure and transcription. Curr Opin Cell Biol 58:120–125

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Merlotti A, Rosa A, Remondini D (2020) Merging 1d and 3d genomic information: challenges in modelling and validation. BBA – Gene Regul Mech 1863:194415

    Google Scholar 

  30. Staudinger H (1919) Schweiz Chem Z 3:1–5, 28–33, 60–64

    Google Scholar 

  31. Staudinger H (1920) Über polymerisation. Ber Dtsch Chem Gesell 53:1078–1085

    Google Scholar 

  32. Suter UW (2013) Why was the macromolecular hypothesis such a big deal? In: Percec V (ed) Hierarchical macromolecular structures: 60 Years after the Staudinger Nobel Prize I. Springer International Publishing, Cham, pp 61–80

    Chapter  Google Scholar 

  33. Rubinstein M, Colby RH (2003) Polymer physics. Oxford University Press, New York

    Google Scholar 

  34. Chaikin PM, Lubensky TC (2000) Principles of condensed matter physics. Cambridge University Press, Cambridge

    Google Scholar 

  35. De Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, New York

    Google Scholar 

  36. Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford University Press, New York

    Google Scholar 

  37. Des Cloizeaux J, Jannink G (1990) Polymers in solution: their modelling and structure. Clarendon Press, Oxford

    Google Scholar 

  38. Grosberg AY, Khokhlov AR (1994) Statistical physics of macromolecules. AIP Press, New York

    Google Scholar 

  39. Huang K (1987) Statistical mechanics, 2nd edn. Wiley, Hoboken

    Google Scholar 

  40. Rosa A, Everaers R (2008) Structure and dynamics of interphase chromosomes. Plos Comput Biol 4:e1000153

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  41. Rosa A, Becker NB, Everaers R (2010) Looping probabilities in model interphase chromosomes. Biophys J 98:2410–2419

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Nishino Y, Eltsov M, Joti Y, Ito K, Takata H, Takahashi Y, Hihara S, Frangakis AS, Imamoto N, Ishikawa T, Maeshima K (2012) Human mitotic chromosomes consist predominantly of irregularly folded nucleosome fibres without a 30-nm chromatin structure. EMBO J 31:1644–1653

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Maeshima K, Rogge R, Tamura S, Joti Y, Hikima T, Szerlong H, Krause C, Herman J, Seidel E, DeLuca J, Ishikawa T, Hansen JC (2016) Nucleosomal arrays self-assemble into supramolecular globular structures lacking 30-nm fibers. EMBO J 35:1115–1132

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Florescu AM, Therizols P, Rosa A (2016) Large scale chromosome folding is stable against local changes in chromatin structure. Plos Comput Biol 12:e1004987

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  45. Marko JF, Siggia ED (1995) Stretching DNA. Macromolecules 28:8759–8770

    Article  CAS  Google Scholar 

  46. Bystricky K, Heun P, Gehlen L, Langowski J, Gasser SM (2004) Long-range compaction and flexibility of interphase chromatin in budding yeast analyzed by high-resolution imaging techniques. Proc Natl Acad Sci U S A 101:16495–16500

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Redner S (1980) Distribution functions in the interior of polymer chains. J Phys A: Math Gen 13:3525–3541

    Article  CAS  Google Scholar 

  48. Everaers R, Graham IS, Zuckermann MJ (1995) End-to-end distance distributions and asymptotic behaviour of self-avoiding walks in two and three dimensions. J Phys A: Math Gen 28:1271–1288

    Article  Google Scholar 

  49. Rosa A, Everaers R (2017) Beyond Flory theory: distribution functions for interacting lattice trees. Phys Rev E 95:012117

    Article  PubMed  Google Scholar 

  50. Rosa A, Everaers R (2019) Conformational statistics of randomly branching double-folded ring polymers. Eur Phys J E 42:7

    Article  PubMed  CAS  Google Scholar 

  51. des Cloizeaux J (1980) Short range correlation between elements of a long polymer in a good solvent. J Phys France 41:223–238

    Google Scholar 

  52. Duplantier B (1989) Statistical mechanics of polymer networks of any topology. J Stat Phys 54:581–680

    Article  Google Scholar 

  53. Flory PJ (1949) The configuration of real polymer chains. J Chem Phys 17:303–310

    Article  CAS  Google Scholar 

  54. Wittmer JP, Beckrich P, Meyer H, Cavallo A, Johner A, Baschnagel J (2007) Intramolecular long-range correlations in polymer melts: the segmental size distribution and its moments. Phys Rev E 76:011803

    Article  CAS  Google Scholar 

  55. Bouchaud JP, Georges A (1989) Flory formula as an extended law of large numbers. Phys Rev B 39:2846–2849

    Article  CAS  Google Scholar 

  56. Halverson JD, Lee WB, Grest GS, Grosberg AY, Kremer K (2011) Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics. J Chem Phys 134:204904

    Article  PubMed  Google Scholar 

  57. Rosa A, Everaers R (2014) Ring polymers in the melt state: the physics of crumpling. Phys Rev Lett 112:118302

    Article  PubMed  CAS  Google Scholar 

  58. Madras N, Sokal AD (1988) The pivot algorithm: a highly efficient Monte Carlo method for the self-avoiding walk. J Stat Phys 50:109–186

    Article  Google Scholar 

  59. Grosberg AY (2014) Annealed lattice animal model and flory theory for the melt of non-concatenated rings: towards the physics of crumpling. Soft Matter 10:560–565

    Article  CAS  PubMed  Google Scholar 

  60. Schram RD, Rosa A, Everaers R (2019) Local loop opening in untangled ring polymer melts: a detailed “Feynman test” of models for the large scale structure. Soft Matter 15:2418–2429

    Article  CAS  PubMed  Google Scholar 

  61. Krauth W (2006) Statistical mechanics algorithms and computations. Oxford University Press, Oxford

    Google Scholar 

  62. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Article  CAS  Google Scholar 

  63. Newman MEJ, Barkema GT (2001) Monte Carlo methods in statistical physics. Clarendon Press, Oxford

    Google Scholar 

  64. Allen MP, Tildesley DJ (1989) Computer simulation of liquids. Oxford University Press, New York

    Google Scholar 

  65. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comp Phys 117:1–19

    Article  CAS  Google Scholar 

  66. Auhl R, Everaers R, Grest GS, Kremer K, Plimpton SJ (2003) Equilibration of long chain polymer melts in computer simulations. J Chem Phys 119:12718–12728

    Article  CAS  Google Scholar 

  67. Kremer K, Grest GS (1990) Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J Chem Phys 92:5057–5086

    Article  CAS  Google Scholar 

  68. Le Dily F, Baù D, Pohl A, Vicent GP, Serra F, Soronellas D, Castellano G, Wright RHG, Ballare C, Filion G, Marti-Renom MA, Beato M (2014) Distinct structural transitions of chromatin topological domains correlate with coordinated hormone-induced gene regulation. Genes Dev 28:2151–2162

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  69. Therizols P, Illingworth RS, Courilleau C, Boyle S, Wood AJ, Bickmore WA (2014) Chromatin decondensation is sufficient to alter nuclear organization in embryonic stem cells. Science 346:1238–1242

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  70. Finn EH, Misteli T (2019) Molecular basis and biological function of variability in spatial genome organization. Science 365:eaaw9498

    Google Scholar 

  71. Khokhlov AR, Nechaev SK (1985) Polymer chain in an array of obstacles. Phys Lett A 112:156–160

    Article  Google Scholar 

  72. Rubinstein M (1986) Dynamics of ring polymers in the presence of fixed obstacles. Phys Rev Lett 57:3023–3026

    Article  CAS  PubMed  Google Scholar 

  73. Obukhov SP, Rubinstein M, Duke T (1994) Dynamics of a ring polymer in a gel. Phys Rev Lett 73:1263–1266

    Article  CAS  PubMed  Google Scholar 

  74. Kapnistos M, Lang M, Vlassopoulos D, Pyckhout-Hintzen W, Richter D, Cho D, Chang T, Rubinstein M (2008) Unexpected power-law stress relaxation of entangled ring polymers. Nat Mater 7:997–1002

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  75. Grosberg AY, Nechaev SK (2015) From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers. J Phys A: Math Theor 48:345003

    Article  CAS  Google Scholar 

  76. Smrek J, Grosberg AY (2015) Understanding the dynamics of rings in the melt in terms of the annealed tree model. J Phys: Condens Matter 27:064117

    CAS  Google Scholar 

  77. Michieletto D, Turner MS (2016) A topologically driven glass in ring polymers. Proc Natl Acad Sci U S A 113:5195–5200

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Michieletto D (2016) On the tree-like structure of rings in dense solutions. Soft Matter 12:9485–9500

    Article  CAS  PubMed  Google Scholar 

  79. Michieletto D, Nahali N, Rosa A (2017) Glassiness and heterogeneous dynamics in dense solutions of ring polymers. Phys Rev Lett 119:197801

    Article  PubMed  Google Scholar 

  80. Vettorel T, Grosberg AY, Kremer K (2009) Territorial polymers. Phys Today 62:72

    Google Scholar 

  81. Rosa A, Everaers R (2016) Computer simulations of melts of randomly branching polymers. J Chem Phys 145:164906

    Article  PubMed  CAS  Google Scholar 

  82. Seitz WA, Klein DJ (1981) Excluded volume effects for branched polymers: Monte Carlo results. J Chem Phys 75:5190–5193

    Article  CAS  Google Scholar 

  83. Rosa A, Everaers R (2016) Computer simulations of randomly branching polymers: annealed versus quenched branching structures. J Phys A: Math Theor 49:345001

    Article  Google Scholar 

  84. Grosberg AY, Rabin Y, Havlin S, Neer A (1993) Crumpled globule model of the three-dimensional structure of DNA. EPL (Europhys Lett) 23:373–378

    Article  CAS  Google Scholar 

  85. Tavares-Cadete F, Norouzi D, Dekker B, Liu Y, Dekker J (2020) Multi-contact 3C reveals that the human genome during interphase is largely not entangled. Nat Struct Mol Biol 27:1105–1114

    Google Scholar 

  86. Valet M, Rosa A (2014) Viscoelasticity of model interphase chromosomes. J Chem Phys 141:245101

    Article  PubMed  CAS  Google Scholar 

  87. Papale A, Rosa A (2019) Microrheology of interphase chromosomes with spatial constraints: a computational study. Phys Biol 16:066002

    Article  CAS  PubMed  Google Scholar 

  88. Jost D, Carrivain P, Cavalli G, Vaillant C (2014) Modeling epigenome folding: formation and dynamics of topologically associated chromatin domains. Nucleic Acids Res 42:9553–9561

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  89. MacPherson Q, Beltran B, Spakowitz AJ (2018) Bottom–up modeling of chromatin segregation due to epigenetic modifications. Proc Natl Acad Sci U S A 115:12739–12744

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  90. Ghosh SK, Jost D (2018) How epigenome drives chromatin folding and dynamics, insights from efficient coarse-grained models of chromosomes. Plos Comput Biol 14:e1006159

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  91. Brackley CA, Johnson J, Michieletto D, Morozov AN, Nicodemi M, Cook PR, Marenduzzo D (2017) Nonequilibrium chromosome looping via molecular slip links. Phys Rev Lett 119:138101

    Article  CAS  PubMed  Google Scholar 

  92. Nuebler J, Fudenberg G, Imakaev M, Abdennur N, Mirny LA (2018) Chromatin organization by an interplay of loop extrusion and compartmental segregation. Proc Natl Acad Sci U S A 115:E6697–E6706

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  93. Brahmachari S, Marko JF (2019) Chromosome disentanglement driven via optimal compaction of loop-extruded brush structures. Proc Natl Acad Sci U S A 116:24956–24965

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  94. Mateos-Langerak J, Bohn M, de Leeuw W, Giromus O, Manders EMM, Verschure PJ, Indemans MHG, Gierman HJ, Heermann DW, van Driel R, Goetze S (2009) Spatially confined folding of chromatin in the interphase nucleus. Proc Natl Acad Sci U S A 106:3812–3817

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

The author wish to thank Ralf Everaers for many years of fruitful collaboration and discussions on the modeling of interphase chromosomes and the role of topological constraints in polymer systems.

Author information

Authors and Affiliations

  1. SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136, Trieste, Italy

    Angelo Rosa

Authors
  1. Angelo Rosa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Angelo Rosa .

Editor information

Editors and Affiliations

  1. Department of Life Sciences, University of Modena and Reggio Emilia, Modena, Italy

    Silvio Bicciato

  2. IFOM, The FIRC Institute of Molecular Oncology, Milan, Italy

    Francesco Ferrari

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Science+Business Media, LLC, part of Springer Nature

About this protocol

Check for updates. Verify currency and authenticity via CrossMark

Cite this protocol

Rosa, A. (2022). The Physical Behavior of Interphase Chromosomes: Polymer Theory and Coarse-Grain Computer Simulations. In: Bicciato, S., Ferrari, F. (eds) Hi-C Data Analysis. Methods in Molecular Biology, vol 2301. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-1390-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-1-0716-1390-0_12

  • Published:

  • Publisher Name: Humana, New York, NY

  • Print ISBN: 978-1-0716-1389-4

  • Online ISBN: 978-1-0716-1390-0

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics

Search

Navigation