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Epigenetic Analysis
BIOS 691- 803
Statistics for Systems Biology
Spring 2008
Kinds of Questions
• Where are the epigenetic modifications?
• How do they co-vary?
• How do epigenetic changes affect
expression of genes?
Covariation of Epigenetic Measures
• Motivating questions
– How are epigenetic modifications related?
– What are the major determinants of
epigenetic state?
• Statistical techniques
– Covariance calculation
– Principal component analysis
– Linear models
Location and Covariance
• Question: do epigenetic modifiers act on
specific targets or do they act on whole
regions of DNA?
• Direct experimental evidence contradictory
• Statistics may help:
– Covariation patterns may be evidence
CalcA in NCI60
• Calcitonin A gene
• Two CpG clusters
plus 3 odd CpG’s
• High correlation
within clusters
CDH1 in NCI 60
Covariation in Methylation of 7 Genes
• Individual genes have multiple CpG sites
• Most variation: overall methylation
Correlation Map of 108
CpG sites in 6 genes across
5 ECOG pilot samples
Red = 1
White = 0
Blue < 0
Epigenomic Analysis
Methylation and Expression
• Single gene (E-cadherin) results suggest
overall methylation correlated with
expression
Methylation and Expression
• HELP assay gives genome-wide sampling
of methylation sites at 15K genes
• If select genes with S/N > 2 in both
measures, then correlations with
associated genes are bi-modal
Epigenomic Analysis
What Causes Methylation?
• NCI-60 derived from various tissues
• Tissue characteristic profile + specific
history of cells
• Fit linear model to each methylation site
– 9 tissues for 60 observations
• 51 error df
• Overall 41% of variance attributable to
tissue
• What causes the remainder of methylation
differences?
PCA for Cell-specific Factors
1.0
0.5
0.0
Variances
1.5
pp
• Residual variance has one strong PC
• Remainder are ‘noise’
• 1st PC is almost constant
– Reflects overall level of methylation
– Is this an artifact or is it real?
– Significantly correlated with expression of
DNMT1 & DNMT3A
Relations Between Epigenetic
Measures - III
Stem Cells & Cancer
Issue: Cancer Stem Cells?
• Hypothesis: cancers arise from stem cells rather
than differentiated epithelial cells
• How would you tell the difference between
partially differentiated stem cells and dedifferentiated epithelial cells?
• Proposal: compare characteristic epigenetic
modifications of stem cells with cancers
• Epigenetic modifications are distinct
– PRC2 (stem cells) vs methylation (cancer)
Statistical Methodology
• Test of association 2 x 2 table
PRC2
not
Methylated 34
43
Not
97
3
• Fisher Exact p ~ 10-5
Statistical Methodology
• Test of association 2 x 2 table
PRC2
not
Methylated 34
43
Not
97
3
• Fisher Exact p ~ 10-5
• Alternatives
– T-test (predictor: PRC2)
– Linear model (predictor: methylation: T – N )
PRC2 – Methylation Association
Are CIMP’s Stem Cell Clones?
• Distinctive PRC2 sites appear
preferentially methylated in CIMP tumors
Correlations between epigenetic
and expression measures – I
Copy Number and Expression
Copy Number and Expression
• Large sections of DNA containing many
genes are often copied or deleted
• We think most control elements are copied
or deleted also
• If more (or fewer) copies of a gene then
ceteris paribus there should be more
(fewer) copies of RNA
Integrative Studies of
CGH & Gene Expression
• Expect to see strong correlation between
copy number and expression in data
• Previous studies report report weak effects
– Average correlations from (0.04 to 0.27)
• NCI 60 study average correlation 0.16
Why Not?
• H1: there really isn’t much effect – biology
– Somehow the cells are compensating
– In any case there shouldn’t be any effect on
non-expressed genes
• H2: we may not be able to measure the
effect that is there – technical error
– Probes may be insensitive/cross-hybridizing
– Signal/noise too low even when probes are
sensitive
Eliminating Uninformative Genes
• Genes which are silenced will not show
effect of copy number variation
– Mean signal a rough proxy
– Remove genes with mean signal above 6.3
• Only genes with significant copy number
variation (above measurement noise) will
show effect
– Select genes with SD of copy number > 0.5
Correlations of Selected Measures
Black: All correlations
Red: Reliably measured correlations
Estimating True Correlations
• If measurement noise of SD ~ 0.3
degrades expression measures, then true
correlations of variables will be mostly
closer to 0 than correlations of measures
• Given a correlation and measured
standard deviations, what are most likely
true standard deviations and true
correlation?
MLE of Noisy Correlations
•
•
•
•
Noise can be estimated from replicates
If N large can estimate ˆ  r 1  e12 / s 2 1  e22 / s 2 
SD of originals can be estimated by ML
Given s and e, the MLE of correlation can be
inferred
• For NCI 60 median MLE correlation ~ 0.65
Epigenomic Analysis
Correlations between epigenetic
and expression measures – II
Chromatin and Expression
Do Epigenetic Marks Regulate
Transcription?
• Several studies finding only weak
evidence by correlation analysis
• Same technical issue: S/N ratio
• Questions
– Does methylation shut down most genes?
– Which histone marks indicate active
transcription?
Methylation and Expression
• HELP assay gives genome-wide sampling
of methylation sites at 15K genes
• Select genes with S/N > 2 in both
measures
• Correlations with gene expression values
are bi-modal
Epigenomic Analysis
Interpretation of Meth-Expr Corrs
• MLE of negative mode ~ -0.8
• ~ 2/3 of genes under that hump
• Unclear whether positive hump is real or
an artifact of small sample size
• Possible explanations:
– True induction by methylation
• Methylation of insulator
– Irrelevant CpG site
Acetylation and Expression
• Histones often acetylated during
expression
• Histone 3 lysine 9 (H3K9) acetylation
measured
• Measures corrupted by noise
– Blue: S/N > 2.5
– Red: S/N > 2
– Black: S/N > 1.5
Biological Prediction
• H3K9 acetylation
• Is this real?
gene expression
– Experimental test: find genes with high
acetylation variance, and little expression
variance by microarray
• Results (7 genes)
• Confirm hypothesis
• Implies:
– Expression arrays are not sensitive
Epigenomic Analysis