Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Potential energy landscapes identify the information-theoretic nature of the epigenome

Abstract

Epigenetics is the study of biochemical modifications carrying information independent of DNA sequence, which are heritable through cell division. In 1940, Waddington coined the term “epigenetic landscape” as a metaphor for pluripotency and differentiation, but methylation landscapes have not yet been rigorously computed. Using principles from statistical physics and information theory, we derive epigenetic energy landscapes from whole-genome bisulfite sequencing (WGBS) data that enable us to quantify methylation stochasticity genome-wide using Shannon's entropy, associating it with chromatin structure. Moreover, we consider the Jensen–Shannon distance between sample-specific energy landscapes as a measure of epigenetic dissimilarity and demonstrate its effectiveness for discerning epigenetic differences. By viewing methylation maintenance as a communications system, we introduce methylation channels and show that higher-order chromatin organization can be predicted from their informational properties. Our results provide a fundamental understanding of the information-theoretic nature of the epigenome that leads to a powerful approach for studying its role in disease and aging.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Estimation of epiallelic probabilities, epipolymorphisms, and normalized epiallelic entropies.
Figure 2: Potential energy landscapes.
Figure 3: Mean methylation level and normalized entropy.
Figure 4: Informational distances and lineages.
Figure 5: Entropy blocks and TAD boundaries.
Figure 6: Information-theoretic properties of methylation channels.
Figure 7: Information-theoretic prediction of large-scale chromatin organization.
Figure 8: Entropic sensitivity distributions in single samples and comparative studies.

Accession codes

Primary accessions

Gene Expression Omnibus

References

  1. Waddington, C.H. The Strategy of the Genes (Allen and Unwin, 1957).

  2. Feinberg, A.P. & Irizarry, R.A. Stochastic epigenetic variation as a driving force of development, evolutionary adaptation, and disease. Proc. Natl. Acad. Sci. USA 107 (Suppl. 1), 1757–1764 (2010).

    CAS  PubMed  Google Scholar 

  3. Hansen, K.D. et al. Increased methylation variation in epigenetic domains across cancer types. Nat. Genet. 43, 768–775 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  4. Pujadas, E. & Feinberg, A.P. Regulated noise in the epigenetic landscape of development and disease. Cell 148, 1123–1131 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  5. Timp, W. & Feinberg, A.P. Cancer as a dysregulated epigenome allowing cellular growth advantage at the expense of the host. Nat. Rev. Cancer 13, 497–510 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  6. Landan, G. et al. Epigenetic polymorphism and the stochastic formation of differentially methylated regions in normal and cancerous tissues. Nat. Genet. 44, 1207–1214 (2012).

    CAS  PubMed  Google Scholar 

  7. Shipony, Z. et al. Dynamic and static maintenance of epigenetic memory in pluripotent and somatic cells. Nature 513, 115–119 (2014).

    CAS  PubMed  Google Scholar 

  8. Bock, C. Analysing and interpreting DNA methylation data. Nat. Rev. Genet. 13, 705–719 (2012).

    CAS  PubMed  Google Scholar 

  9. Pressé, S., Ghosh, K., Lee, J. & Dill, K.A. Principles of maximum entropy and maximum caliber in statistical physics. Rev. Mod. Phys. 85, 1115–1141 (2013).

    Google Scholar 

  10. Cedar, H. & Bergman, Y. Programming of DNA methylation patterns. Annu. Rev. Biochem. 81, 97–117 (2012).

    CAS  PubMed  Google Scholar 

  11. Heyn, H. et al. Distinct DNA methylomes of newborns and centenarians. Proc. Natl. Acad. Sci. USA 109, 10522–10527 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  12. Ziller, M.J. et al. Charting a dynamic DNA methylation landscape of the human genome. Nature 500, 477–481 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  13. Bell, R.E. et al. Enhancer methylation dynamics contribute to cancer plasticity and patient mortality. Genome Res. 26, 601–611 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  14. Eden, E., Navon, R., Steinfeld, I., Lipson, D. & Yakhini, Z. GOrilla: a tool for discovery and visualization of enriched GO terms in ranked gene lists. BMC Bioinformatics 10, 48 (2009).

    PubMed  PubMed Central  Google Scholar 

  15. Mohn, F. et al. Lineage-specific Polycomb targets and de novo DNA methylation define restriction and potential of neuronal progenitors. Mol. Cell 30, 755–766 (2008).

    CAS  PubMed  Google Scholar 

  16. Dixon, J.R. et al. Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature 485, 376–380 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  17. Nora, E.P. et al. Spatial partitioning of the regulatory landscape of the X-inactivation centre. Nature 485, 381–385 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  18. Gibcus, J.H. & Dekker, J. The hierarchy of the 3D genome. Mol. Cell 49, 773–782 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  19. Huang, J., Marco, E., Pinello, L. & Yuan, G.C. Predicting chromatin organization using histone marks. Genome Biol. 16, 162 (2015).

    PubMed  PubMed Central  Google Scholar 

  20. Cover, T.M. & Thomas, J.A. Elements of Information Theory (John Wiley & Sons, 1991).

  21. Savarese, F. et al. Satb1 and Satb2 regulate embryonic stem cell differentiation and Nanog expression. Genes Dev. 23, 2625–2638 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  22. Karantzali, E. et al. Sall1 regulates embryonic stem cell differentiation in association with Nanog. J. Biol. Chem. 286, 1037–1045 (2011).

    CAS  PubMed  Google Scholar 

  23. Liu, K. et al. The multiple roles for Sox2 in stem cell maintenance and tumorigenesis. Cell. Signal. 25, 1264–1271 (2013).

    CAS  PubMed  Google Scholar 

  24. Ozair, M.Z., Noggle, S., Warmflash, A., Krzyspiak, J.E. & Brivanlou, A.H. SMAD7 directly converts human embryonic stem cells to telencephalic fate by a default mechanism. Stem Cells 31, 35–47 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. Gopinath, S.D., Webb, A.E., Brunet, A. & Rando, T.A. FOXO3 promotes quiescence in adult muscle stem cells during the process of self-renewal. Stem Cell Rep. 2, 414–426 (2014).

    CAS  Google Scholar 

  26. Mahaira, L.G. et al. IGF2BP1 expression in human mesenchymal stem cells significantly affects their proliferation and is under the epigenetic control of TET1/2 demethylases. Stem Cells Dev. 23, 2501–2512 (2014).

    CAS  PubMed  Google Scholar 

  27. Lee, B.K. et al. Tgif1 counterbalances the activity of core pluripotency factors in mouse embryonic stem cells. Cell Rep. 13, 52–60 (2015).

    CAS  PubMed  Google Scholar 

  28. Luo, Z. et al. Zic2 is an enhancer-binding factor required for embryonic stem cell specification. Mol. Cell 57, 685–694 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  29. Dekker, J., Marti-Renom, M.A. & Mirny, L.A. Exploring the three-dimensional organization of genomes: interpreting chromatin interaction data. Nat. Rev. Genet. 14, 390–403 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  30. Fortin, J.P. & Hansen, K.D. Reconstructing A/B compartments as revealed by Hi-C using long-range correlations in epigenetic data. Genome Biol. 16, 180 (2015).

    PubMed  PubMed Central  Google Scholar 

  31. Dixon, J.R. et al. Chromatin architecture reorganization during stem cell differentiation. Nature 518, 331–336 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  32. Timp, W. et al. Large hypomethylated blocks as a universal defining epigenetic alteration in human solid tumors. Genome Med. 6, 61 (2014).

    PubMed  PubMed Central  Google Scholar 

  33. Berman, B.P. et al. Regions of focal DNA hypermethylation and long-range hypomethylation in colorectal cancer coincide with nuclear lamina–associated domains. Nat. Genet. 44, 40–46 (2011).

    PubMed  PubMed Central  Google Scholar 

  34. Yu, H. et al. Tet3 regulates synaptic transmission and homeostatic plasticity via DNA oxidation and repair. Nat. Neurosci. 18, 836–843 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  35. Nakamura, T. et al. Fusion of the nucleoporin gene NUP98 to HOXA9 by the chromosome translocation t(7;11)(p15;p15) in human myeloid leukaemia. Nat. Genet. 12, 154–158 (1996).

    CAS  PubMed  Google Scholar 

  36. Kaneda, H. et al. FOXQ1 is overexpressed in colorectal cancer and enhances tumorigenicity and tumor growth. Cancer Res. 70, 2053–2063 (2010).

    CAS  PubMed  Google Scholar 

  37. Schlaeger, T.M. et al. A comparison of non-integrating reprogramming methods. Nat. Biotechnol. 33, 58–63 (2015).

    CAS  PubMed  Google Scholar 

  38. Vandiver, A.R. et al. Age and sun exposure–related widespread genomic blocks of hypomethylation in nonmalignant skin. Genome Biol. 16, 80 (2015).

    PubMed  PubMed Central  Google Scholar 

  39. Hansen, K.D. et al. Large-scale hypomethylated blocks associated with Epstein–Barr virus–induced B-cell immortalization. Genome Res. 24, 177–184 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  40. Wu, H., Caffo, B., Jaffee, H.A., Irizarry, R.A. & Feinberg, A.P. Redefining CpG islands using hidden Markov models. Biostatistics 11, 499–514 (2010).

    PubMed  PubMed Central  Google Scholar 

  41. Visel, A., Minovitsky, S., Dubchak, I. & Pennacchio, L.A. VISTA Enhancer Browser—a database of tissue-specific human enhancers. Nucleic Acids Res. 35, D88–D92 (2007).

    CAS  PubMed  Google Scholar 

  42. Wen, B. et al. Euchromatin islands in large heterochromatin domains are enriched for CTCF binding and differentially DNA-methylated regions. BMC Genomics 13, 566 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  43. Guelen, L. et al. Domain organization of human chromosomes revealed by mapping of nuclear lamina interactions. Nature 453, 948–951 (2008).

    CAS  PubMed  Google Scholar 

  44. Huyer, W. & Neumaier, A. Global optimization by multilevel coordinate search. J. Glob. Optim. 14, 331–355 (1999).

    Google Scholar 

  45. Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P. Numerical Recipes. The Art of Scientific Computing (Cambridge University Press, 2007).

  46. Mohammad-Djafari, A. in Maximum Entropy and Bayesian Methods (eds. Smith, C.R., Erickson, G.J. & Neudorfer, P.O.) 221–234 (Kluwer Academic Publishers, 1991).

  47. Lin, J. Divergence measures based on the Shannon entropy. IEEE Trans. Inf. Theory 37, 145–151 (1991).

    Google Scholar 

  48. Favorov, A. et al. Exploring massive, genome scale datasets with the GenometriCorr package. PLoS Comput. Biol. 8, e1002529 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  49. Rao, S.S. et al. A 3D map of the human genome at kilobase resolution reveals principles of chromatin looping. Cell 159, 1665–1680 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  50. Murtagh, F. & Legendre, P. Ward's hierarchical agglomerative clustering method: which algorithms implement Ward's criterion? J. Classif. 31, 274–295 (2014).

    Google Scholar 

Download references

Acknowledgements

We thank X. Li, A. Vandiver, and J. Walston (Johns Hopkins University) for cells and/or FASTQ files; R. Trygvadottir, B. Berndsen, A. Idrizi, and C. Callahan (Johns Hopkins University) for sequencing; J.-P. Fortin and K. Hansen for providing A and B compartment data; I. Morrison (University of Otago) and A. Gimelbrant (Dana-Farber Cancer Institute) for access to imprinted gene and MAE data sets; A. Meissner and M. Ziller (Broad Institute) for access to bisulfite sequencing data sets; and W. Timp and K. Hansen (Johns Hopkins University) for critical reading of the manuscript. This work was supported by US National Institutes of Health (NIH) grants R01CA054358 and DP1ES022579 to A.P.F., National Science Foundation grants CCF-1217213 and CCF-1656201 to J.G., and NIH grant AG021334 to J. Walston. E.P. was supported by the Medical Scientist Training Program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Author information

Authors and Affiliations

Authors

Contributions

A.P.F., E.P., G.J., and J.G. designed the study. G.J. and J.G. developed the mathematical and computational methods. G.J. wrote the computer code and implemented the methods. A.P.F. and E.P. designed and led the experiments. E.P. procured outside data and performed quality control, preprocessing, and bisulfite alignment. G.J., E.P., A.P.F., and J.G. analyzed the data. A.P.F., G.J., and J.G. wrote the manuscript with the assistance of E.P.

Corresponding authors

Correspondence to John Goutsias or Andrew P Feinberg.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–8 and Supplementary Note. (PDF 21265 kb)

Supplementary Table 1

List of WGBS data samples. (XLSX 13 kb)

Supplementary Table 2

Gene rankings based on the absolute differential methylation level (dMML), the Jensen–Shannon distance (JSD), and the relative Jensen–Shannon distance (RJSD). (XLSX 14984 kb)

Supplementary Table 3

GO annotation results using gene rankings based on the absolute differential mean methylation level (dMML), the Jensen–Shannon distance (JSD), and the relative Jensen–Shannon distance (RJSD). (XLSX 577 kb)

Supplementary Table 4

Gene ranking based on decreasing normalized methylation entropy (NME) in stem. (XLSX 450 kb)

Supplementary Table 5

Frequencies of A–B compartment switching among 34 samples. (XLSX 123 kb)

Supplementary Table 6

Odds ratio (OR)-based statistical analysis results of enrichment of hypomethylated blocks, LADs, and LOCKs within compartment B in the normal lung samples. (XLSX 11 kb)

Supplementary Table 7

Gene rankings based on decreasing values of the entropic sensitivity index (ESI) in stem and normal colon. (XLSX 1187 kb)

Supplementary Table 8

Gene ranking based on decreasing absolute differential entropic sensitivity (dESI) when comparing normal colon to colon cancer. (XLSX 661 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jenkinson, G., Pujadas, E., Goutsias, J. et al. Potential energy landscapes identify the information-theoretic nature of the epigenome. Nat Genet 49, 719–729 (2017). https://doi.org/10.1038/ng.3811

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/ng.3811

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing