An Information-Theoretic Approach to Methylation Data Analysis

Transcription

1 An Information-Theoretic Approach to Methylation Data Analysis John Goutsias Whitaker Biomedical Engineering Institute The Johns Hopkins University Baltimore, MD 21218

2 Objective Present an information-theoretic approach to methylation data analysis. This leads to: Employing the Shannon entropy to quantify epigenetic stochasticity. Predicting large-scale chromatin organization (compartments A/B). Predicting smaller-scale chromatin organization (TADs). Using an information-theoretic distance to quantify epigenetic discordance. Developing a sensitivity analysis approach to quantify environmental influences on epigenetic stochasticity.

3 µ : demethylationprobability ν : methylation probability Methylation Maintenance DNA methylation 1 µ ν ν µ 0 0 methylation channel DNA methylation Po ut ( 0) = (1 ν ) Pin (0) +µ Pin (1) P (1) =ν P (0) + (1 µ ) P (1) out in in

4 Methylation Maintenance DNA methylation µ : demethylationprobability ν : methylation probability 1 µ ν ν µ 0 0 methylation channel Po ut ( 0) = (1 ν ) Pin (0) +µ Pin (1) P (1) =ν P (0) + (1 µ ) P (1) out in in DNA methylation Use methylation channels at each CpG site (noisy binary communication channels). Must estimate probabilities µ and ν from data Not possible! At steady-state, P out = P in and ν Pin(1) λ= = µ 1 P (1) in

5 Information Capacity of a Methylation Channel Maximum average information that can be conveyed during a maintenance step: { I X X } C = ma x, ) P(1) ( out in mutual information Mutual information: a measure of mutual dependence between input and output methylation. Available formula for capacity, but depends on probabilities µ and ν. Approximate formula can be derived that depends only on λ=ν / µ.

6 Probability of Transmission Error π = Pr[output methylation input methylation] Quantifies fidelity of methylation transmission through a methylation channel. Depends on probabilities µ and ν. An approximate formula can be derived that depend only on λ=ν / µ.

7 Energy Dissipation Correct transmission of the methylation state requires work. This consumes free energy that is dissipated to the surroundings in the form of heat. The minimum dissipated energy is related (for some systems) to the probability of error Relative dissipated energy: E~ kt B ln π E ε = log 2 π E max

8 Methylation Stochasticity We can characterize methylation stochasticity at a CpG site using the Shannon entropy: S = P(0) log P(0) P(1) log P(1) 2 2

9 Capacity, Relative Dissipated Energy, Entropy 1 ENTR RDE CAP log λ 2 Reliable transmission of methylation information within critical regions of the genome is facilitated by high capacity methylation channels that result in low methylation stochasticity at the cost of high energy consumption. Unreliable methylation transmission within other regions of the genome due to low capacity methylation channels that consume less energy but produce higher levels of methylation stochasticity.

10 Capacity, Relative Dissipated Energy, Entropy Scale chr1: 2 Mb hg19 34,000,000 34,500,000 35,000,000 35,500,000 36,000,000 36,500,000 37,000,000 37,500,000 38,000,000 38,500,000 39,000,000 1 _ CAP-livernormal 0 _ 10 _ RDE-livernormal 0 _ 1 _ ENTR-livernormal 0 _

11 Capacity, Relative Dissipated Energy, Entropy Scale chr1: 1 _ 1 kb hg19 150,601, ,602, ,602, ,603, ,603,500 CAP-livernormal 0 _ 15 _ RDE-livernormal 0 _ 1 _ ENTR-livernormal 0 _ CGI UCSC Genes (RefSeq, GenBank, CCDS, Rfam, trnas & Comparative Genomics) ENSA polycomb target gene proposed as candidate for type 2 diabetes

12 Capacity, Relative Dissipated Energy, Entropy NORMAL/CANCER YOUNG/OLD density lungnor mal-3 lungcancer-3 density CD4-Y3 CD4-O CAP CAP density density density RDE density RDE ENTR ENTR

13 Capacity, Relative Dissipated Energy, Entropy Scale chr1: 0.2 _ 2 Mb hg19 34,000,000 34,500,000 35,000,000 35,500,000 36,000,000 36,500,000 37,000,000 37,500,000 38,000,000 38,500,000 39,000,000 dcap-livercancer-vs-livernormal _ 8 _ drde-livercancer-vs-livernormal _ 1 _ dentr-livercancer-vs-livernormal _

14 Capacity, Relative Dissipated Energy, Entropy Scale chr1: 1 kb hg19 150,601, ,602, ,602, ,603, ,603, _ dcap-livercancer-vs-livernormal _ 8 _ drde-livercancer-vs-livernormal _ 0.6 _ dentr-livercancer-vs-livernormal _ CGI UCSC Genes (RefSeq, GenBank, CCDS, Rfam, trnas & Comparative Genomics) ENSA polycomb target gene proposed as candidate for type 2 diabetes

15 Information-Theoretic Prediction of Chromatin Organization Chromatin is organized in cell-type specific compartments A and B. Scale 20Mb EBV hg19 chr1 190,000, ,000,000 Hi-C A B Genes 2015, 6(3), Compartment A: associated with gene-rich transcriptionally active open chromatin. Compartment B: associated with gene-poor transcriptionally inactive chromatin.

16 Information-Theoretic Prediction of Chromatin Organization Scale 20Mb EBV hg EBV 12 chr1 190,000, ,000,000 Hi-C A B information capacity relative dissipated energy methylation entropy ENTR CAP RDE A B A B 0.00 Enrichment of low information capacity, low relative dissipated energy, and high entropy within compartment B! Opposite true for compartment A!

17 Information-Theoretic Prediction of Chromatin Organization Random forest regression, using information-theoretic quantities as features, learns the informational structure of compartments A/B from available groundtruth data. Achieves reliable prediction: 0.82 cross-validated average correlation and 91% average agreement between predicted and true A/B signals. A small number of local information-theoretic properties of methylation maintenance can be highly predictive of large-scale chromatin organization!

18 Information-Theoretic Prediction of Chromatin Organization 0.5 stem Clustered 34 samples using the net percentage of A/B switching as a dissimilarity measure. 31/34 samples grouped in a biologically meaningful manner! height fibro-p4 fibro-p7 fibro-p10 fibro-p31 fibro-p33 livercancer-1 livercancer-2 livercancer-3 livernormal-1 livernormal-2 livernormal-3 livernormal-5 livernormal-4 lungnormal-1 lungnormal-2 lungnormal-3 lungcancer-3 lungcancer-1 colonnormal lungcancer-2 * * CD4-Y1 coloncancer CD4-O1 CD4-O3 CD4-O2 CD4-Y3 CD4-Y2 brain-1 brain-2 * ker-y2 ker-y1 ker-o1 ker-o2

19 Quantifying Epigenetic Stochasticity Source of epigenetic stochasticity: Transmission of epigenetic information during maintenance through low capacity methylation channels that consume low levels of free energy. Quantify epigenetic stochasticity using the concept of Shannon entropy. To account for methylation dependence within a genomic region, must consider the joint Shannon entropy Note that H ( X, X,..., X ) = px (, x,..., x )log p( x, x,..., x ) 1 2 N 1 2 N N x, x,..., x N 1 2 N 1, n-th CpG site is methylated = 0, n-th CpG site is unmethylated H( X, X,..., X ) H( X ) + H( X ) + + H( X ) X n N

20 Methylation Level Partition the genome into non-overlapping genomic units of 150 bp each (determines resolution of analysis). Instead of focusing on methylation patterns within a genomic unit, we quantify methylation using the methylation level L 1 N Xn N n = 1 = X n 1, n-th CpG site is methylated = 0, n-th CpG site is unmethylated Compute the probability distribution Ising model. Pl () of the methylation level from the

21 Mean Methylation Level The mean methylation level (MML) is the average of the methylation means at the CpG sites within a genomic unit N 1 E[ L] = E[ Xn] N n 1

22 Normalized Methylation Entropy Quantify epigenetic stochasticity within each genomic unit using the normalized methylation entropy (NME) Ranges between 0 and 1 0: fully ordered state 1: fully disordered state h 1 = ()log 2 () log ( N + 1) Pl Pl l 2

23 entropy = mean log 2 (mean) (1 mean)log (1 mean) 2 Normalized Methylation Entropy MML not predictive of NME!

24 Genome-wide MML and NME Distributions stem colonnormal coloncancer livernormal-1 livercancer-1 livernormal-2 livercancer-2 livernormal-3 livercancer-3 lungnormal-1 lungcancer-1 lungnormal-2 lungcancer-2 lungnormal-3 lungcancer-3 brain-1 brain-2 fibro-p4 fibro-p7 fibro-p10 fibro-p31 fibro-p33 CD4 Y1 CD4 Y2 CD4 Y3 CD4 O1 CD4 O2 CD4 O3 ker-y1 ker-y2 ker-o1 ker-o2 livernormal-4 livernormal MML NME

25 Topologically Associating Domains Genes 2015, 6(3), Topologically associating domains (TADs): highly conserved structural features of the genome across tissue types and species. Loci within TADs tend to interact frequently with each other. Less frequent interactions take place between loci within adjacent TADs.

26 Entropy Blocks Large genomic regions of consistently low or high NME values. ordered entropy block disordered entropy block H1-TAD boundaries Scale chr1: 5 Mb hg19 30,000,000 35,000,000 40,000,000 colonnormal coloncancer livernormal-1 livercancer-1 livernormal-2 livercancer-2 livernormal-3 livercancer-3 lungnormal-1 lungcancer-1 lungnormal-2 lungcancer-2 lungnormal-3 lungcancer-3

27 Entropy Blocks Large genomic regions of consistently low or high NME values. ordered entropy block disordered entropy block H1-TAD boundaries Scale chr1: colonnormal coloncancer livernormal-1 livercancer-1 livernormal-2 livercancer-2 livernormal-3 livercancer-3 lungnormal-1 lungcancer-1 lungnormal-2 lungcancer-2 lungnormal-3 lungcancer-3 5 Mb hg19 30,000,000 35,000,000 40,000,000 Known TAD boundary annotations are visually proximal to boundaries of entropy blocks!

28 Identification of TAD boundaries phenotype 1 TAD TAD TAD TAD TAD TAD TAD TAD TAD disordered disordered ordered ordered TADs are associated with consistently low or high NME values, and can be accurately identified from entropy blocks. phenotype 3 phenotype 2 TAD TAD TAD TAD TAD TAD TAD TAD TAD disordered disordered disordered ordered ordered TAD TAD TAD TAD TAD TAD TAD TAD TAD disordered disordered ordered ordered

29 Quantifying Epigenetic Discordance Evaluate differences in probability distributions of methylation levels within genomic units using a distance metric. GENOMIC UNIT NORMAL CANCER probability probability P () c l 0 1/7 2/7 3/7 4/7 5/7 6/7 1 methylation level P () n l 0 1/7 2/7 3/7 4/7 5/7 6/7 1 methylation level DISTANCE?

30 Jensen-Shannon Distance GENOMIC UNIT NORMAL CANCER probability probability P () c l 0 1/7 2/7 3/7 4/7 5/7 6/7 1 methylation level P () n l 0 1/7 2/7 3/7 4/7 5/7 6/7 1 methylation level D 1 Pn() l + Pc() l Pn() l + Pc() l = D ( P ( l), ) DKL( P( l), ) JS KL n c D ( PQ, ) Pl ( )log KL 0 D 1 JS Pl () = 2 l Ql ()

31 Jensen-Shannon Distance 1 CANCER probability /7 2/7 3/7 4/7 5/7 6/7 1 methylation level 0 1/7 2/7 3/7 4/7 5/7 6/7 1 methylation level 0 1/7 2/7 3/7 4/7 5/7 6/7 1 methylation level 1 NORMAL probability /7 2/7 3/7 4/7 5/7 6/7 1 methylation level 0 1/7 2/7 3/7 4/7 5/7 6/7 1 methylation level 0 1/7 2/7 3/7 4/7 5/7 6/7 1 methylation level JSD = 1.0 dmml = 0.7 dnme = 0.0 JSD mainly driven by difference in MML JSD = 0.9 dmml = 0.0 dnme = 0.6 JSD mainly driven by difference in NME JSD = 1.0 dmml = 0.0 dnme = 0.0 JSD driven by factors other than MML or NME

32 Jensen-Shannon Distance 1 _ JSD-lungcancer-VS-lungnormal SALL3 0 _ 1 _ dmml-lungcancer-vs-lungnormal _ 1 _ dnme-lungcancer-vs-lungnormal _

33 Jensen-Shannon Distance 1 _ 0 _ 1 _ JSD-lungcancer-VS-lungnormal dmml-lungcancer-vs-lungnormal SALL3 SAL3 has been implicated in lung cancer _ 1 _ dnme-lungcancer-vs-lungnormal _ 1 _ JSD-lungcancer-VS-lungnormal 0 _ CGI 1 _ UCSC Genes (RefSeq, GenBank, CCDS, Rfam, trnas & Comparative Genomics) SALL3 dmml-lungcancer-vs-lungnormal _ 1 _ dnme-lungcancer-vs-lungnormal _

34 Jensen-Shannon Distance colonnormal-vs-stem lungcancer-1-vs-lungnormal Jensen-Shannon distance Jensen-Shannon distance No consistent containment of epigenetic dissimilarity within a particular genomic feature genome-wide promoters exons introns 5UTRs 3UTRs intergenic CGIs shores shelves open sea uc-enhancers uo-enhancers p-enhancers r-enhancers genome-wide promoters exons introns 5UTRs 3UTRs intergenic CGIs shores shelves open sea uc-enhancers uo-enhancers p-enhancers r-enhancers CD4-Y2-VS-stem 0.8 CD4-Y2-1-VS-lungnormal-3 Jensen-Shannon distance Jensen-Shannon distance brain-1-vs-stem brain-1-vs-lungnormal Jensen-Shannon distance Jensen-Shannon distance

35 1.00 Jensen-Shannon Distance Jensen-Shannon distance A B 0.00 coloncancer vs colonnormal livercancer1 vs livernormal-1 livercancer-2 vs livernormal-2 livercancer-3 vs livernormal-3 lungcancer-1 vs lungnormal-1 lungcancer-2 vs lungnormal-2 lungcancer-3 vs lungnormal-3 Larger epigenetic discordance is observed in compartment B than in A.

36 Quantified epigenetic discordance between two samples by calculating the average of all JSD values computed genome-wide. Computed this measure of epigenetic discordance between 17 representative samples. Formed the corresponding dissimilarity matrix. Used multidimensional scaling to find a 2D configuration of points whose interpoint distances approximately correspond to the epigenetic dissimilarities among the samples. Jensen-Shannon Distance

37 Jensen-Shannon Distance Quantified epigenetic discordance between two samples by calculating the average of all JSD values computed genome-wide. Computed this measure of epigenetic discordance between 17 representative samples. Formed the corresponding dissimilarity matrix. Used multidimensional scaling to find a 2D configuration of points whose interpoint distances approximately correspond to the epigenetic dissimilarities among the samples. MESODERM ECTODERM differentiation ENDODERM lungcancer-3 lungnor mal-3 lungcancer-1 lungnor mal-1 CD4-O2CD4-O1 CD4-Y3 liver normal-1 CD4-Y2 colonnor mal coloncancer brain-1 stem liver nor mal-2 brain-2 carcinogenesis // grouping of samples into categories based on lineage // livercancer-2 livercancer-1

38 Sensitivity Analysis Epigenetic changes integrate environmental signals with genetic variation to modulate phenotype. Quantify influence of environmental exposure on methylation stochasticity. View environmental variability as a process that directly influences the parameters of the methylation potential energy landscape (Ising parameters).

39 Entropic Sensitivity Index Consider the case for which the Ising parameters θ fluctuate around their true values by a random amount G θ, where G is a zero-mean normal distribution with standard deviation σ. Can show that η σ σh variation in entropy (NME) hg ( ) η= g g = 0 environmental variation Entropic sensitivity index (ESI)

40 Sensitivity Analysis entropic sensitivity index stem colonnormal coloncancer livernormal-1 livercancer-1 livernormal-2 livercancer-2 livernormal-3 livercancer-3 livernormal-4 livernormal-5 lungnormal-1 lungcancer-1 lungnormal-2 lungcancer-2 lungnormal-3 lungcancer-3 brain-1 brain-2 fibro-p4 fibro-p7 fibro-p10 fibro-p31 fibro-p33 CD4 Y1 CD4 Y2 CD4 Y3 CD4 O1 CD4 O2 CD4 O3 ker-y1 ker-y2 ker-o1 ker-o2 Globally observed differences in entropic sensitivity among tissues.

41 Sensitivity Analysis entropic sensitivity index compartment A compartment B stem colonnormal coloncancer livernormal-1 livercancer-1 livernormal-2 livercancer- 2 livernormal-3 livercancer-3 livernormal-4 livernormal-5 lungnormal-1 lungcancer-1 lungnormal-2 lungcancer2 lungnormal-3 lungcancer-3 brain-1 brain-2 fibro-p4 fibro- P7 fibro-p10 fibro-p31 fibro-p33 CD4 Y1 CD4 Y2 CD4 Y3 CD4 O1 CD4 O2 CD4 O3 ker-y1 ker-y2 ker-o1 ker-o2 Entropic sensitivity within compartment A is higher than in compartment B.

42 Sensitivity Analysis entropic sensitivity index compartment A compartment B colonnormal coloncancer livernormal-1 livercancer-1 livernormal-2 livercancer-2 livernormal-3 Observed differences between normal and cancer are largely confined to compartment B. livercancer-3 livernormal-4 livernormal-5 lungnormal-1 lungcancer-1 lungnormal-2 lungcancer2 lungnormal-3 lungcancer-3

43 Sensitivity Analysis (Normal-Cancer) Scale 20 Mb hg19 chr1: 25,000,000 30,000,000 35,000,000 40,000,000 45,000,000 50,000,000 55,000,000 60,000,000 65,000, _ ESI-colonnormal 0 _ 1.5 _ ESI-coloncancer 0 _ 0.5 _ desi-coloncancer-vs-colonnormal _ 1.5 _ ESI-lungnormal-1 0 _ 1.5 _ ESI-lungcancer-1 0 _ 0.5 _ desi-lungcancer-1-vs-lungnormal _

44 Sensitivity Analysis (Normal-Cancer) Scale 5 kb hg19 chr1: 150,595, ,597, ,599, ,601, ,603, ,605,000 1 _ NME-livernormal-1 0 _ 1 _ NME-livercancer-1 0 _ 3 _ ESI-livernormal-1 0 _ 3 _ ESI-livercancer-1 0 _ 3 _ desi-livercancer-1-vs-livernormal _ CGI ENSA ENSA ENSA ENSA ENSA ENSA ENSA ENSA UCSC Genes (RefSeq, GenBank, CCDS, Rfam, trnas & Comparative Genomics) ENSA ENSA polycomb target gene proposed as a candidate gene for type 2 diabetes

45 Sensitivity Analysis (Young-Old) Scale 100 Mb hg19 chr1: 50,000, ,000, ,000, ,000, _ desi-cd4-y2-vs-cd4-y _ 0.5 _ desi-cd4-y3-vs-cd4-y _ 0.5 _ desi-cd4-y3-vs-cd4-y _ 0.5 _ desi-cd4-o3-vs-cd4-y _ 0.5 _ desi-cd4-o3-vs-y _ 0.5 _ desi-cd4-o3-vs-cd4-y _

46 Sensitivity Analysis (Young-Old) Scale 1 kb hg19 chr21: 27,541,000 27,541,500 27,542,000 27,542,500 27,543,000 27,543,500 27,544,000 27,544,500 2 _ ESI-CD4-Y1 0 _ 2 _ ESI-CD4-Y2 0 _ 2 _ ESI-CD4-Y3 0 _ CGI 2 _ UCSC Genes (RefSeq, GenBank, CCDS, Rfam, trnas & Comparative Genomics) desi-cd4-o3-vs-cd4-y1 APP amyloid precursor protein gene implicated in Alzheimer s _ 2 _ desi-cd4-o3-vs-cd4-y _ 2 _ desi-cd4-o3-vs-y _

47 Conclusion An information-theoretic approach to epigenomics based on the Ising model provides a formal foundation to methylation analysis. Yields fundamental insights into epigenetic behavior. Demonstrates a relationship between chromatin structure methylation channels entropic sensitivity This may maximize an organism s efficiency in storing epigenetic information and help explain developmental plasticity.

48 Conclusion Pluripotent stem cells require relatively high energy to maintain high capacity methylation channels within a portion of the genome, achieving reduced methylation stochasticity. Regions characterized by increased entropic sensitivity are associated with highly deformable potential energy landscapes, which may correspond to differentiation branch points. After differentiation, some large genomic domains, such as regions associated with pluripotency, need not maintain high channel capacities and energy consumption their sequestration providing increased energy efficiency with the cost of high epigenetic stochasticity and reduced responsiveness.