Introduction to Bulk RNAseq data analysis
Differential Expression of RNA-seq data - Part 2
Last modified: 28 Nov 2021
library(DESeq2)
library(tidyverse)txi <- readRDS("RObjects/txi.rds")
sampleinfo <- read_tsv("data/samplesheet_corrected.tsv", col_types="cccc") %>%
mutate(Status = fct_relevel(Status, "Uninfected"))
simple.model <- as.formula(~ Status)
ddsObj.raw <- DESeqDataSetFromTximport(txi = txi,
colData = sampleinfo,
design = simple.model)## using counts and average transcript lengths from tximportkeep <- rowSums(counts(ddsObj.raw)) > 5
ddsObj.filt <- ddsObj.raw[keep,]
ddsObj <- DESeq(ddsObj.filt)## estimating size factors## using 'avgTxLength' from assays(dds), correcting for library size## estimating dispersions## gene-wise dispersion estimates## mean-dispersion relationship## final dispersion estimates## fitting model and testingresults.simple <- results(ddsObj, alpha=0.05)Exercise 2
So far we have fitted a simple model considering just “Status,” but in reality we want to model the effects of both “Status” and “Time Point.”
Let’s start with the model with only main effects - an additive model with no interaction. The main assumption here is that the effects of Status and the effects of Time Point are indepedent.
Recapitulate the above steps to generate a new DESeq2 object with the additive model. Then we will extract the results table as above.
Load the raw data, remembering to set the factor on the Status so that
“Uninfected” will be set as the intercept:
txi <- readRDS("RObjects/txi.rds") sampleinfo <- read_tsv("data/samplesheet_corrected.tsv", col_types="cccc") %>% mutate(Status = fct_relevel(Status, "Uninfected"))Create the model:
additive.model <- as.formula(~ TimePoint + Status)Then build the DESeq from the raw data, the sample meta data and the model:
ddsObj.raw <- DESeqDataSetFromTximport(txi = txi, colData = sampleinfo, design = additive.model)Filter the data set:
keep <- rowSums(counts(ddsObj.raw)) > 5 ddsObj.filt <- ddsObj.raw[keep,]You are now ready to run the differential gene expression analysis Run the DESeq2 analysis
Run the size factor estimation, dispersion estimation and modelling steps using the
DESeqcommand as above.Extract the default contrast using the
resultscommand into a new object calledresults.additive
- What contrast are these results for? If you have constructed the model correctly, then it should be the same as previous
results.simple- How many genes have an adjusted p-value of less than 0.05
The default contrast of results
The results function has returned the results for the contrast “Infected vs Uninfected.” Let’s have a look at the model matrix to understand why DESeq2 has given us this particular contrast.
model.matrix(additive.model, data = sampleinfo)## (Intercept) TimePointd33 StatusInfected
## 1 1 0 1
## 2 1 0 1
## 3 1 0 1
## 4 1 1 1
## 5 1 1 0
## 6 1 1 1
## 7 1 0 0
## 8 1 0 0
## 9 1 0 0
## 10 1 1 0
## 11 1 1 1
## 12 1 1 0
## attr(,"assign")
## [1] 0 1 2
## attr(,"contrasts")
## attr(,"contrasts")$TimePoint
## [1] "contr.treatment"
##
## attr(,"contrasts")$Status
## [1] "contr.treatment"By default, results has returned the contrast encoded by the final column in the model matrix. DESeq2 has the command resultsNames that allows us to view the contrasts that are available directly from the DESeq2 object.
resultsNames(ddsObj)## [1] "Intercept" "TimePoint_d33_vs_d11"
## [3] "Status_Infected_vs_Uninfected"Let’s just rename results.additive so that we know which contrast results it contains.
results.InfectedvUninfected <- results.additive
rm(results.additive)Let’s get the top 100 genes by adjusted p-value
topGenesIvU <- as.data.frame(results.InfectedvUninfected) %>%
rownames_to_column("GeneID") %>%
top_n(100, wt=-padj)
topGenesIvUExercise 3
If we want a different contrast we can just pass the
resultsfunction the name of the contrast, as given byresultsNames(ddsObj). Look at the help page for theresultscommand to see how to do this.
- Retrieve the results for the contrast of d33 versus d11.
- How many differentially expressed genes are there at FDR < 0.05?
Should we be using the interaction model?
So far we have modeled gene expression as a function of Status and Time Point with an additive model. Realistically, we expect the two factors interact such that differences in gene expression between infected and uninfected mice are not the same at different time point:
Let’s plot a PCA from vst transformed data. Can you anticipate if the interaction term will be important?
vstcounts <- vst(ddsObj.raw, blind=TRUE)## using 'avgTxLength' from assays(dds), correcting for library sizeplotPCA(vstcounts, intgroup = c("Status", "TimePoint"))
In this case we can, from both the PCA and our understanding of the biology, be fairly certain that the interaction model is the appropriate model to use. This is not always the case and so we need a way to compare two models.
Comparing two design models
Let’s take a simple example to start with.
Suppose we thought that maybe TimePoint was irrelevant and really the only differences might be between Infected and Uninfected groups. We could fit the simpler model and this would give us more degrees of freedom and therefore more power, but how would we know if it was a better model of not?
We can compare two models by using the “likelihood ratio test” (LRT).
To do so we provide the LRT with a simpler model (one with less parameters) than the one currently being used.
Currently ddsObj is using the model ~TimePoint + Status. Here we want to compare to a model without the TimePoint parameter: ~Status, this was our simple.model from earlier.
ddsObj.LRT <- DESeq(ddsObj, test = "LRT", reduced = simple.model)## using pre-existing normalization factors## estimating dispersions## found already estimated dispersions, replacing these## gene-wise dispersion estimates## mean-dispersion relationship## final dispersion estimates## fitting model and testingresults.Additive_v_Simple <- results(ddsObj.LRT)
results.Additive_v_Simple## log2 fold change (MLE): Status Infected vs Uninfected
## LRT p-value: '~ TimePoint + Status' vs '~ Status'
## DataFrame with 20091 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue
## <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSMUSG00000000001 1102.56094 -0.0110965 0.106195 0.3226536 0.5700173
## ENSMUSG00000000028 58.60055 0.3007930 0.265626 0.0560662 0.8128250
## ENSMUSG00000000037 49.23586 -0.0481414 0.429685 0.0318005 0.8584663
## ENSMUSG00000000049 7.98789 0.4110498 0.656171 0.4373766 0.5083914
## ENSMUSG00000000056 1981.00402 -0.1907691 0.119694 2.7850130 0.0951499
## padj
## <numeric>
## ENSMUSG00000000001 0.939329
## ENSMUSG00000000028 0.978399
## ENSMUSG00000000037 0.982281
## ENSMUSG00000000049 0.926027
## ENSMUSG00000000056 0.695076
## [ reached getOption("max.print") -- omitted 6 rows ]The second line of the results output shows us the test we are doing:
LRT p-value: '~ TimePoint + Status' vs '~ Status'
The null hypothesis is that there is no significant difference between the two models, i.e. the simpler model is sufficient to explain the variation in gene expression between the samples. If the the adjusted p-value for a gene passes a significance threshold (e.g. padj < 0.05) then we should consider using the more complex model for this gene.
sum(results.Additive_v_Simple$padj < 0.05, na.rm=TRUE)## [1] 66We can see that for 66 genes the more complex model does fit the data better. Although we have a result for each gene, in practice we should choose one model or the other and apply it to all genes. Curiously then, this suggests that overall the simple model is more appropriate than the additive model. Let’s look into the interaction model.
Exercise 4
When we looked at the PCA it did seem that an interaction model might be warranted. Let’s test that.
Create a new DESeq2 object using a model with an interaction between TimePoint and Status. The model formula should be
~TimePoint + Status + TimePoint:Statuswhere
TimePoint:Statusis the parameter for the interaction beteween TimePoint and Status.Note that
*can be used as shortcut to add the interaction term, e.g.~TimePoint * Status, however, writing out in long form is clearer here. > Remember to filter to remove uninformative genes.
- Run the statistical analysis using the
DESeqcommand and create a new analysis object calledddsObj.interaction.- Use the LRT to compare this to the simpler additive model (
~TimePoint + Status)- Extract a table of results using
results. For how many genes is interaction model a better fit?
Extracting specific contrasts from an interactive model
If we are settled on using the interaction model, then we need to extract our contrasts with reference to this. That is, we can no longer ask the general question “What is the difference in gene expression between Infected and Uninfected?” but must rather ask two quesions:
- “What is the difference in gene expression between Infected and Uninfected at 11 days post infection?”
- “What is the difference in gene expression between Infected and Uninfected at 33 days post infection?”
If we view the resultsNames for the interaction model, we can see the intercept is Uninfected and 11 days post infection:
resultsNames(ddsObj.interaction)## [1] "Intercept" "TimePoint_d33_vs_d11"
## [3] "Status_Infected_vs_Uninfected" "TimePointd33.StatusInfected"The main effect Status_Infected_vs_Uninfected is therefore the difference between Infected and Uninfected at 11 days post infection.
results.interaction.11 <- results(ddsObj.interaction,
name="Status_Infected_vs_Uninfected",
alpha=0.05)To get the results for Infected versus Uninfected at 33 days post infection, we would need to add the interaction term TimePointd33.StatusInfected.
In the help page for results it shows us how to do this with a contrast in example 3.
results.interaction.33 <- results(ddsObj.interaction,
contrast = list(c("Status_Infected_vs_Uninfected", "TimePointd33.StatusInfected")),
alpha=0.05)Number of genes with padj < 0.05 for Test v Control at day 11:
sum(results.interaction.11$padj < 0.05, na.rm = TRUE)## [1] 1072Number of genes with padj < 0.05 for Test v Control at day 33:
sum(results.interaction.33$padj < 0.05, na.rm = TRUE)## [1] 2782We can see that there is a strong difference in the effects of infection on gene expression between days 11 and 33.
Exercise 5
Let’s investigate the uninfected mice
- Extract the results for d33 v d11 for Uninfected mice.
How many genes have an adjusted p-value less than 0.05?
Is this remarkable?
- Extract the results for d33 v d11 for Infected mice.
How many genes have an adjusted p-value less than 0.05?Do these results suggest another approach to analysing this data set?
Save the results
Finally save the corrected sample metadata, the DESeq2 dataset, and the two DESeq2 results objects.
write_tsv(sampleinfo, "results/samplesheet_corrected.tsv")
saveRDS(ddsObj.interaction, "results/DESeqDataSet.interaction.rds")
saveRDS(results.interaction.11, "results/DESeqResults.interaction_d11.rds")
saveRDS(results.interaction.33, "results/DESeqResults.interaction_d33.rds")