A Mathematical Model for Inheritance of DNA Methylation Patterns in Somatic Cells

Abstract

DNA methylation is an essential epigenetic mechanism used by cells to regulate gene expression. Interestingly, DNA replication, a function necessary for cell division, disrupts the methylation pattern. Since perturbed methylation patterns are associated with aberrant gene expression and many diseases, including cancer, restoration of the correct pattern following DNA replication is crucial. However, the exact mechanisms of this restoration remain under investigation. DNA methyltransferases (Dnmts) perform methylation by adding a methyl group to cytosines at CpG sites in the DNA. These CpG sites are found in regions of high density, termed CpG islands (CGIs), and regions of low density in the genome. Nearly, every CpG site in a CGI has the same state, either methylated or unmethylated, and almost all CpG sites in regions of low CpG density are methylated. We propose a stochastic model for the dynamics of the post-replicative restoration of methylation patterns. The model considers the recruitment of Dnmts and demethylating enzymes to regions of hyper- and hypomethylation, respectively. The model also includes the interaction between Dnmt1 and PCNA, an enzyme that localizes Dnmt1 to the replication complex. Using our model, we predict that the methylation of regions of DNA can be bistable. Further, we predict that recruitment mechanisms maintain methylation in CGIs, whereas the Dnmt1–PCNA interaction maintains methylation in low-density regions.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  1. Araujo FD, Knox JD, Szyf M, Price GB, Zannis-Hadjopoulos M (1998) Concurrent replication and methylation at mammalian origins of replication. Mol Cell Biol 18(6):3475–3482

    Article  Google Scholar 

  2. Bachman KE, Rountree MR, Baylin SB (2001) Dnmt3a and Dnmt3b are transcriptional repressors that exhibit unique localization properties to heterochromatin. J Biol Chem 276(34):32282–32287. https://doi.org/10.1074/jbc.M104661200

    Article  Google Scholar 

  3. Bhutani N, Burns DM, Blau HM (2011) DNA demethylation dynamics. Cell 146(6):866–872. https://doi.org/10.1016/j.cell.2011.08.042

    Article  Google Scholar 

  4. Bird AP (1980) DNA methylation and the frequency of CpG in animal DNA. Nucleic Acids Res 8(7):1499–1504

    Article  Google Scholar 

  5. Bird A (2002) DNA methylation patterns and epigenetic memory. Genes Dev 16(1):6–21. https://doi.org/10.1101/gad.947102

    Article  Google Scholar 

  6. Bogdanović O, Veenstra GJC (2009) DNA methylation and methyl-CpG binding proteins: developmental requirements and function. Chromosoma 118:549–565

    Article  Google Scholar 

  7. Burden AF, Manley NC, Clark AD, Gartler SM, Laird CD, Hansen RS (2005) Hemimethylation and non-CpG methylation levels in a promoter region of human LINE-1 (L1) repeated elements. J Biol Chem 280(15):14413–14419. https://doi.org/10.1074/jbc.M413836200

    Article  Google Scholar 

  8. Chen T, Ueda Y, Dodge JE, Wang Z, Li E (2003) Establishment and maintenance of genomic methylation patterns in mouse embryonic stem cells by Dnmt3a and Dnmt3b. Mol Cell Biol 23(16):5594–5605. https://doi.org/10.1128/MCB.23.16.5594

    Article  Google Scholar 

  9. Deaton AM, Bird A (2011) CpG islands and the regulation of transcription. Genes Dev 25(10):1010–1022. https://doi.org/10.1101/gad.2037511

    Article  Google Scholar 

  10. Frank D, Keshet I, Shani M, Levine A, Razin A, Cedar H (1991) Demethylation of CpG islands in embryonic cells. Nature 351(6323):239–241. https://doi.org/10.1038/351239a0

    Article  Google Scholar 

  11. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361. https://doi.org/10.1021/j100540a008

    Article  Google Scholar 

  12. Gowher H, Jeltsch A (2001) Enzymatic properties of recombinant Dnmt3a DNA methyltransferase from mouse: the enzyme modifies DNA in a non-processive manner and also methylates non-CpA sites. J Mol Biol 309(5):1201–1208. https://doi.org/10.1006/jmbi.2001.4710

    Article  Google Scholar 

  13. Goyal R, Reinhardt R, Jeltsch A (2006) Accuracy of DNA methylation pattern preservation by the Dnmt1 methyltransferase. Nucleic Acids Res 34(4):1182–1188. https://doi.org/10.1093/nar/gkl002

    Article  Google Scholar 

  14. Haerter JO, Lövkvist C, Dodd IB, Sneppen K (2014) Collaboration between CpG sites is needed for stable somatic inheritance of DNA methylation states. Nucleic Acids Res 42(4):2235–2244. https://doi.org/10.1093/nar/gkt1235

    Article  Google Scholar 

  15. Hashimoto H, Vertino PM, Cheng X (2010) Molecular coupling of DNA methylation and histone methylation. Epigenomics 2(5):657–669. https://doi.org/10.2217/epi.10.44

    Article  Google Scholar 

  16. Hermann A, Goyal R, Jeltsch A (2004) The Dnmt1 DNA-(cytosine-C5)-methyltransferase methylates DNA processively with high preference for hemimethylated target sites. J Biol Chem 279(46):48350–48359. https://doi.org/10.1074/jbc.M403427200

    Article  Google Scholar 

  17. Hervouet E, Nadaradjane A, Gueguen M, Vallette FM, Cartron P-F (2012) Kinetics of DNA methylation inheritance by the Dnmt1-including complexes during the cell cycle. Cell Div 7(1):5. https://doi.org/10.1186/1747-1028-7-5

    Article  Google Scholar 

  18. Issa J-P (2014) Aging and epigenetic drift: a vicious cycle. J Clin Investig 124(1):24–29. https://doi.org/10.1172/JCI69735

    Article  Google Scholar 

  19. Jackson DA, Pombo A (1998) Replicon clusters are stable units of chromosome structure: evidence that nuclear organization contributes to the efficient activation and propagation of S phase in human cells. J Cell Biol 140(6):1285–1295. https://doi.org/10.1083/jcb.140.6.1285

    Article  Google Scholar 

  20. Jeong S, Liang G, Sharma S, Joy C, Choi SH, Han H, Yoo CB, Egger G, Yang AS, Jones PA, Lin JC, Choi SH, Han H, Yoo CB, Egger G, Yang AS, Jones PA (2009) Selective anchoring of DNA methyltransferases 3A and 3B to nucleosomes containing methylated DNA. Mol Cell Biol 29(19):5366–5376. https://doi.org/10.1128/MCB.00484-09

    Article  Google Scholar 

  21. Kafri T, Ariel M, Brandeis M, Shemer R, Urven L, McCarrey J, Cedar H, Razin A (1992) Developmental pattern of gene-specific DNA methylation in the mouse embryo and germ line. Genes Dev 6(5):705–714. https://doi.org/10.1101/gad.6.5.705

    Article  Google Scholar 

  22. Klutstein M, Nejman D, Greenfield R, Cedar H (2016) DNA methylation in cancer and aging. Cancer Res 76(12):3446–3450. https://doi.org/10.1158/0008-5472.CAN-15-3278

    Article  Google Scholar 

  23. Kulis M, Merkel A, Heath S, Queirós AC, Schuyler RP, Castellano G, Beekman R, Raineri E, Esteve A, Clot G, Verdaguer-Dot N, Duran-Ferrer M, Russiñol N, Vilarrasa-Blasi R, Ecker S, Pancaldi V, Rico D, Agueda L, Blanc J, Richardson D, Clarke L, Datta A, Pascual M, Agirre X, Prosper F, Alignani D, Paiva B, Caron G, Fest T, Muench MO, Fomin ME, Lee ST, Wiemels JL, Valencia A, Gut M, Flicek P, Stunnenberg HG, Siebert R, Küppers R, Gut IG, Campo E, Martín-Subero JI (2015) Whole-genome fingerprint of the DNA methylome during human B cell differentiation. Nat Genet 47(7):746–756. https://doi.org/10.1038/ng.3291

    Article  Google Scholar 

  24. Laird CD, Pleasant ND, Clark AD, Sneeden JL, Hassan KMA, Manley NC, Vary JC, Morgan T, Hansen RS, Stöger R (2004) Hairpin-bisulfite PCR: assessing epigenetic methylation patterns on complementary strands of individual DNA molecules. Proc Natl Acad Sci USA 101(1):204–209. https://doi.org/10.1073/pnas.2536758100

    Article  Google Scholar 

  25. Leonhardt H, Page AW, Weier HU, Bestor TH (1992) A targeting sequence directs DNA methyltransferase to sites of DNA replication in mammalian nuclei. Cell 71(5):865–873. https://doi.org/10.1016/0092-8674(92)90561-P

    Article  Google Scholar 

  26. Liang G, Chan MF, Tomigahara Y, Tsai YC, Gonzales FA, Li E, Laird PW, Jones PA (2002) Cooperativity between DNA methyltransferases in the maintenance methylation of repetitive elements. Mol Cell Biol 22(2):480–491. https://doi.org/10.1128/MCB.22.2.480

    Article  Google Scholar 

  27. Lister R, Pelizzola M, Dowen RH, David Hawkins R, Hon G, Tonti-Filippini J, Nery JR, Lee L, Ye Z, Ngo Q-M, Edsall L, Antosiewicz-Bourget J, Stewart R, Victor Ruotti A, Millar H, Thomson JA, Ren B, Ecker JR (2009) Human DNA methylomes at base resolution show widespread epigenomic differences. Nature 462(7271):315–322. https://doi.org/10.1038/nature08514

    Article  Google Scholar 

  28. Liu Y, Oakeley EJ, Sun L, Jost JP (1998) Multiple domains are involved in the targeting of the mouse DNA methyltransferase to the DNA replication foci. Nucleic Acids Res 26(4):1038–1045. https://doi.org/10.1093/nar/26.4.1038

    Article  Google Scholar 

  29. Liu X, Gao Q, Li P, Zhao Q, Zhang J, Li J, Koseki H, Wong J (2013) UHRF1 targets DNMT1 for DNA methylation through cooperative binding of hemi-methylated DNA and methylated H3K9. Nat Commun 4:1563. https://doi.org/10.1038/ncomms2562

    Article  Google Scholar 

  30. Maegawa S, Hinkal G, Kim HS, Shen L, Zhang L, Zhang J, Zhang N, Liang S, Donehower LA, Issa JPJ (2010) Widespread and tissue specific age-related DNA methylation changes in mice. Genome Res 20(3):332–340. https://doi.org/10.1101/gr.096826.109

    Article  Google Scholar 

  31. McGovern AP, Powell BE, Chevassut TJT (2012) A dynamic multi-compartmental model of DNA methylation with demonstrable predictive value in hematological malignancies. J Theor Biol 310:14–20. https://doi.org/10.1016/j.jtbi.2012.06.018

    MathSciNet  Article  MATH  Google Scholar 

  32. Meissner A, Mikkelsen TS, Hongcang G, Wernig M, Hanna J, Sivachenko A, Zhang X, Bernstein BE, Nusbaum C, Jaffe DB, Gnirke A, Jaenisch R, Lander ES (2008) Genome-scale DNA methylation maps of pluripotent and differentiated cells. Nature 454(7205):766–770. https://doi.org/10.1038/nature07107

    Article  Google Scholar 

  33. Monk M, Boubelik M, Lehnert S (1987) Temporal and regional changes in DNA methylation in the embryonic, extraembryonic and germ cell lineages during mouse embryo development. Development 99(3):371–382

    Google Scholar 

  34. Okano M, Xie S, Li E (1998) Cloning and characterization of a family of novel mammalian DNA (cytosine-5) methyltransferases. Nat Genet 19(3):219–220. https://doi.org/10.1038/890

    Article  Google Scholar 

  35. Okano M, Bell DW, Haber DA, Li E (1999) DNA methyltransferases Dnmt3a and Dnmt3b are essential for de novo methylation and mammalian development. Cell 99(3):247–257. https://doi.org/10.1016/S0092-8674(00)81656-6

    Article  Google Scholar 

  36. Ooi SKT, Chen Q, Emily B, Keqin L, Da J, Zhe Y, Hediye E-B, Paul T, Ping LS, David AC, Xiaodong C, Bestor Timothy H (2007) DNMT3L connects unmethylated lysine 4 of histone H3 to de novo methylation of DNA. Nature 448(7154):714–717. https://doi.org/10.1038/nature05987

    Article  Google Scholar 

  37. Pfeifer GP, Steigerwald SD, Hansen RS, Gartler SM, Riggs AD (1990) Polymerase chain reaction-aided genomic sequencing of an X chromosome-linked CpG island: methylation patterns suggest clonal inheritance, CpG site autonomy, and an explanation of activity state stability. Proc Natl Acad Sci USA 87(21):8252–8256. https://doi.org/10.1073/pnas.87.21.8252

    Article  Google Scholar 

  38. Pradhan S, Bacolla A, Wells RD, Roberts RJ (1999) Recombinant human DNA (cytosine-5) methyltransferase. I. Expression, purification, and comparison of novo and maintenance methylation. J Biol Chem 274(46):33002–33010. https://doi.org/10.1074/jbc.274.46.33002

    Article  Google Scholar 

  39. Rakyan VK, Hildmann T, Novik KL, Lewin J, Tost J, Cox AV, Dan Andrews T, Howe KL, Otto T, Olek A, Fischer J, Gut IG, Berlin K, Beck S (2004) DNA methylation profiling of the human major histocompatibility complex: a pilot study for the Human Epigenome Project. PLoS Biol 2(12):e405. https://doi.org/10.1371/journal.pbio.0020405

    Article  Google Scholar 

  40. Rhee I, Jair K-W, Yen R-WC, Lengauer C, Herman JG, Kinzler KW, Vogelstein B, Baylin SB, Schuebel K (2000) CpG methylation is maintained in human cancer cells lacking DNMT1. Nature 404(1998):1003–1007. https://doi.org/10.1038/35010000

    Article  Google Scholar 

  41. Riggs AD, Xiong Z (2004) Methylation and epigenetic fidelity. Proc Natl Acad Sci 101(1):4–5. https://doi.org/10.1073/pnas.03077811000307781100[pii]

    Article  Google Scholar 

  42. Schermelleh L, Haemmer A, Spada F, Rösing N, Meilinger D, Rothbauer U, Cardoso CM, Leonhardt H (2007) Dynamics of Dnmt1 interaction with the replication machinery and its role in postreplicative maintenance of DNA methylation. Nucleic Acids Res 35(13):4301–4312. https://doi.org/10.1093/nar/gkm432

    Article  Google Scholar 

  43. Schneider K, Fuchs C, Dobay A, Rottach A, Qin W, Wolf P, Álvarez-Castro JM, Nalaskowski MM, Kremmer E, Schmid V, Leonhardt H, Schermelleh L (2013) Dissection of cell cycle-dependent dynamics of Dnmt1 by FRAP and diffusion-coupled modeling. Nucleic Acids Res 41(9):4860–4876. https://doi.org/10.1093/nar/gkt191

    Article  Google Scholar 

  44. Sharma S, de Carvalho DD, Jeong S, Jones PA, Liang G (2011) Nucleosomes containing methylated DNA stabilize DNA methyltransferases 3A/3B and ensure faithful epigenetic inheritance. PLoS Genet 7(2):e1001286. https://doi.org/10.1371/journal.pgen.1001286

    Article  Google Scholar 

  45. Suzuki K, Suzuki I, Leodolter A, Alonso S, Horiuchi S, Yamashita K, Perucho M (2006) Global DNA demethylation in gastrointestinal cancer is age dependent and precedes genomic damage. Cancer Cell 9(3):199–207. https://doi.org/10.1016/j.ccr.2006.02.016

    Article  Google Scholar 

  46. Toyota M, Issa JPJ (1999) CpG island methylator phenotgpes in aging and cancer. Semin Cancer Biol 9(5):349–357. https://doi.org/10.1006/scbi.1999.0135

    Article  Google Scholar 

  47. Vandiver AR, Idrizi A, Rizzardi L, Feinberg AP, Hansen KD (2015) DNA methylation is stable during replication and cell cycle arrest. Sci Rep 5(1):17911. https://doi.org/10.1038/srep17911

    Article  Google Scholar 

  48. Vertino PM, Sekowski JA, Coll JM, Applegren N, Han S, Hickey RJ, Malkas LH (2002) DNMT1 is a component of a multiprotein DNA replication complex. Cell Cycle 1(6):416–423. https://doi.org/10.4161/cc.1.6.270

    Article  Google Scholar 

  49. von Meyenn F, Iurlaro M, Habibi E, Liu NQ, Salehzadeh-Yazdi A, Santos F, Petrini E, Milagre I, Miao Y, Xie Z, Kroeze LI, Nesterova TB, Jansen JH, Xie H, He C, Reik W, Stunnenberg HG (2016) Impairment of DNA methylation maintenance is the main cause of global demethylation in naive embryonic stem cells. Mol Cell 62(6):848–861. https://doi.org/10.1016/j.molcel.2016.04.025

    Article  Google Scholar 

  50. Walton EL, Francastel C, Velasco G (2011) Maintenance of DNA methylation: Dnmt3b joins the dance. Epigenetics 6(11):1373–1377. https://doi.org/10.4161/epi.6.11.17978

    Article  Google Scholar 

  51. Weber M, Davies JJ, Wittig D, Oakeley EJ, Haase M, Lam WL, Schübeler D (2005) Chromosome-wide and promoter-specific analyses identify sites of differential DNA methylation in normal and transformed human cells. Nat Genet 37(8):853–862. https://doi.org/10.1038/ng1598

    Article  Google Scholar 

  52. Williams K, Christensen J, Helin K (2011) DNA methylation: TET proteins—guardians of CpG islands? EMBO Rep 13(1):28–35. https://doi.org/10.1038/embor.2011.233

    Article  Google Scholar 

  53. Williams K, Christensen J, Pedersen MT, Johansen JV, Cloos PAC, Rappsilber J, Helin K (2011b) TET1 and hydroxymethylcytosine in transcription and DNA methylation fidelity. Nature 473(7347):343–348. https://doi.org/10.1038/nature10066

    Article  Google Scholar 

  54. Zagkos L, Auley MM, Roberts J, Kavallaris NI (2019) Mathematical models of DNA methylation dynamics: implications for health and ageing. J Theor Biol 462:184–193. https://doi.org/10.1016/j.jtbi.2018.11.006

    MathSciNet  Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by grants NSF-RTG 1148230 and NSF-DMS 1515130.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Kiersten Utsey.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Utsey, K., Keener, J.P. A Mathematical Model for Inheritance of DNA Methylation Patterns in Somatic Cells. Bull Math Biol 82, 84 (2020). https://doi.org/10.1007/s11538-020-00765-4

Download citation

Keywords

  • CpG island
  • DNA methyltransferase
  • Stochastic chemical reactions
  • Mean field approximation
  • Bistability