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


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.

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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.

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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



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.

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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)

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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).

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