In hugheylab/limorhyde: Differential Analysis of Rhythmic Transcriptome Data

knitr::opts_chunk$set(collapse = TRUE, comment = '#>', fig.retina = 2, message = FALSE)

LimoRhyde is a framework for differential analysis of rhythmic transcriptome data. This vignette goes through the typical steps of an analysis: identifying rhythmic genes, identifying differentially rhythmic genes, and identifying differentially expressed genes.

The dataset is based on total RNA from livers of wild-type and Rev-erb$\alpha/\beta$ knockout mice, with gene expression measured by microarray (GSE34018).

Load packages and set parameters

library('annotate')
library('data.table')
library('foreach')
library('ggplot2')
library('limma')
library('limorhyde')
library('org.Mm.eg.db')
library('qs')

Here we specify the zeitgeber period and the q-value cutoffs for rhythmic and differentially rhythmic genes.

period = 24
qvalRhyCutoff = 0.15
qvalDrCutoff = 0.1

Load the data

The expression data are in a matrix with one row per gene and one column per sample. The metadata are in a table with one row per sample.

y = qread(system.file('extdata', 'GSE34018_expression_data.qs', package = 'limorhyde'))
y[1:5, 1:5]

metadata = qread(system.file('extdata', 'GSE34018_metadata.qs', package = 'limorhyde'))
metadata

We use limorhyde to calculate time_cos and time_sin, which are based on the first harmonic of a Fourier decomposition of the time column, and append them to the metadata data.table.

metadata = cbind(metadata, limorhyde(metadata$time, 'time_'))

Identify rhythmic genes

The next three steps use limma. We calculate the q-value of rhythmicity for each gene using that gene's p-value for each condition and adjusting for multiple testing.

rhyLimma = foreach(condNow = unique(metadata$cond), .combine = rbind) %do% {
  design = model.matrix(~ time_cos + time_sin, data = metadata[cond == condNow])
  fit = lmFit(y[, metadata$cond == condNow], design)
  fit = eBayes(fit, trend = TRUE)
  rhyNow = data.table(topTable(fit, coef = 2:3, number = Inf), keep.rownames = TRUE)
  setnames(rhyNow, 'rn', 'gene_id')
  rhyNow[, cond := condNow]}

rhyLimmaSummary = rhyLimma[, .(P.Value = min(P.Value)), by = gene_id]
rhyLimmaSummary[, adj.P.Val := p.adjust(P.Value, method = 'BH')]
setorderv(rhyLimmaSummary, 'adj.P.Val')

rhyLimmaSummary[1:5, ]

Identify differentially rhythmic genes

Differential rhythmicity is based on statistical interactions between cond and the time components. We pass all genes to limma (whose Empirical Bayes does best with many genes), but keep results only for rhythmic genes, and adjust for multiple testing accordingly.

design = model.matrix(~ cond * (time_cos + time_sin), data = metadata)

fit = lmFit(y, design)
fit = eBayes(fit, trend = TRUE)
drLimma = data.table(topTable(fit, coef = 5:6, number = Inf), keep.rownames = TRUE)
setnames(drLimma, 'rn', 'gene_id')

drLimma = drLimma[gene_id %in% rhyLimmaSummary[adj.P.Val <= qvalRhyCutoff]$gene_id]
drLimma[, adj.P.Val := p.adjust(P.Value, method = 'BH')]
setorderv(drLimma, 'adj.P.Val')

drLimma[1:5, ]

Identify differentially expressed genes

Differential expression is based on the coefficient for cond in a linear model with no interaction terms. We pass all genes to limma, but keep results only for non-differentially rhythmic genes, and adjust for multiple testing accordingly.

design = model.matrix(~ cond + time_cos + time_sin, data = metadata)

fit = lmFit(y, design)
fit = eBayes(fit, trend = TRUE)
deLimma = data.table(topTable(fit, coef = 2, number = Inf), keep.rownames = TRUE)
setnames(deLimma, 'rn', 'gene_id')

deLimma = deLimma[!(gene_id %in% drLimma[adj.P.Val <= qvalDrCutoff]$gene_id)]
deLimma[, adj.P.Val := p.adjust(P.Value, method = 'BH')]
setorderv(deLimma, 'adj.P.Val')

deLimma[1:5, ]

Plot the results

Numerous plots are possible. One is a volcano plot of differentially expressed genes.

ggplot(deLimma) +
  geom_point(aes(x = logFC, y = -log10(adj.P.Val)), size = 0.2, alpha = 0.5) +
  labs(x = expression(log[2] * ' fold-change'), y = expression(-log[10] * ' ' * q[DE]))

Another is a plot of expression as a function of time and genotype for individual genes. Here we show, from top to bottom, the top rhythmic gene, top differentially rhythmic gene, and top differentially expressed gene by q-value.

geneIdsNow = c(rhyLimmaSummary$gene_id[1L], drLimma$gene_id[1L], deLimma$gene_id[1L])
geneSymbolsNow = unname(getSYMBOL(geneIdsNow, 'org.Mm.eg.db'))

df = data.table(t(y[geneIdsNow, ]))
setnames(df, geneSymbolsNow)
df[, sample_id := colnames(y[geneIdsNow, ])]

df = merge(df, metadata[, .(sample_id, cond, time)], by = 'sample_id')
df = melt(df, measure.vars = geneSymbolsNow, variable.name = 'symbol',
          value.name = 'expr')
df[, symbol := factor(symbol, geneSymbolsNow)]

ggplot(df) +
  facet_grid(symbol ~ cond, scales = 'free_y') +
  geom_point(aes(x = time, y = expr, shape = cond, color = symbol), size = 2) +
  labs(x = 'Zeitgeber time (h)', y = 'Expression (norm.)') +
  scale_shape(solid = FALSE, guide = 'none') +
  scale_color_brewer(type = 'qual', palette = 'Dark2', guide = 'none') +
  scale_x_continuous(limits = c(0, 24), breaks = seq(0, 24, 4))