Practical 30: Genomics, systems biology and multi-omics
Calculate methylation proportions with explicit read denominators; distinguish measurement precision from biological replication; inspect a composition-driven group difference.
Can a bulk-tissue methylation difference arise with no within-cell-type regulatory change?
Two fictional cell types have constant methylation probabilities .2 and .8. Group-specific cell mixture determines the pooled probability. Reads are binomial conditional on that probability; this simplified model does not represent all assay or biological variation.
No biological download is required. Numerical inputs are hypothetical, not observed animal data. The runnable examples use base R. Count and abundance units are specified where used.
Change cell proportions without changing either cell type’s methylation.
cell_methylation <- c(typeA=.2,typeB=.8)
mixture <- rbind(control=c(.8,.2),supplement=c(.3,.7))
probability <- as.vector(mixture%*%cell_methylation)
names(probability) <- rownames(mixture)
probability control supplement
0.32 0.62 stopifnot(abs(probability[1]-.32)<1e-12,abs(probability[2]-.62)<1e-12)The expected bulk difference is .30, caused entirely by composition in this hypothetical model.
Read depth changes conditional measurement precision but not the number of animals.
set.seed(3001)
group <- rep(c("control","supplement"),each=6)
depth <- rep(c(10,20,40,80,10,20),2)
truth <- probability[group]
methylated <- rbinom(12,depth,truth)
unmethylated <- depth-methylated
observed <- methylated/depth
out <- data.frame(animal=paste0("a",1:12),group,depth,methylated,unmethylated,observed,
conditional_SE=sqrt(truth*(1-truth)/depth))
out animal group depth methylated unmethylated observed conditional_SE
1 a1 control 10 5 5 0.5000 0.14751271
2 a2 control 20 6 14 0.3000 0.10430724
3 a3 control 40 13 27 0.3250 0.07375636
4 a4 control 80 25 55 0.3125 0.05215362
5 a5 control 10 6 4 0.6000 0.14751271
6 a6 control 20 6 14 0.3000 0.10430724
7 a7 supplement 10 5 5 0.5000 0.15349267
8 a8 supplement 20 11 9 0.5500 0.10853571
9 a9 supplement 40 23 17 0.5750 0.07674634
10 a10 supplement 80 51 29 0.6375 0.05426785
11 a11 supplement 10 5 5 0.5000 0.15349267
12 a12 supplement 20 15 5 0.7500 0.10853571stopifnot(all(methylated+unmethylated==depth),all(observed>=0),all(observed<=1))Twelve animals remain twelve animals even if their read counts are large. The supplied conditional SE assumes the true mixture probability is known.
A mean of animal proportions and a pooled read fraction use different weighting.
animal_mean <- tapply(observed,group,mean)
read_weighted <- tapply(methylated,group,sum)/tapply(depth,group,sum)
data.frame(group=names(animal_mean),animal_mean=as.vector(animal_mean),
read_weighted=as.vector(read_weighted)) group animal_mean read_weighted
1 control 0.3895833 0.3388889
2 supplement 0.5854167 0.6111111boxplot(observed~group,xlab="Group",ylab="Observed methylated-read fraction",col="#86B7A3")
Pooling reads gives deeper samples more weight. It is not automatically the correct estimator of an average-animal contrast.
With zero methylated reads, the observed proportion is zero but the underlying proportion need not be exactly zero. An exact binomial interval under independent conditional read sampling remains positive above the boundary.
intervals <- t(sapply(c(10,100),function(depth) {
binom.test(0,depth)$conf.int
}))
data.frame(depth=c(10,100),lower=intervals[,1],upper=intervals[,2]) depth lower upper
1 10 0 0.30849711
2 100 0 0.03621669These intervals describe a conditional read model, not uncertainty in a treatment effect across animals. Conversion, mapping and read dependence can require additional modeling.
Read-weighted and equal-animal summaries differ when depth is unequal. Pooling all reads can let a deeply sequenced animal dominate. Use animal-level design and an assay-appropriate model for group inference.
A bulk methylation shift can reflect changed cell composition. To distinguish it from within-cell changes, consider cell-type information and matched timing. A regulatory claim also requires sequence context and evidence linking the measured region to the proposed gene or phenotype.
Does observing zero methylated reads establish a universally unmethylated site?
No. It describes the sampled evidence under an assay. Read depth, conditional uncertainty, technical limitations and biological variation across animals still matter.
Coverage, conversion efficiency, mapping, tissue/cell composition and assay specificity must be evaluated in actual studies. A group contrast in bulk methylation does not establish a within-cell regulatory mechanism or phenotypic mediation.
B07 Epigenomics, B02 Design and B15 Integration.
Continue with advanced measurement units. Return to the practical index or the unified map.