Objectives

  • ‘Unblind’ our sample IDs
  • Understand possible confounding factors
  • Understand the impact of batches or additional covariates
  • Filter count table

Differential Expression Workflow

Here we will proceed setting up the inputs needed to initialize DESeq2 before testing for differential expression.


DESeq2 objects

Bioconductor software packages often define and use custom classes within R to store data in a way that better fits expectations around biological data, such as illustrated below from Huber et al. 2015.

A breakdown of the SummarizedExperiment class.

These custom data structures have pre-specified data slots, which hold specific types/classes of data and therefore can be more easily accessed by functions from the same package.

To create the DESeqDataSet we need two tables:

  1. A count matrix (which we already loaded and saved as the object count_table) and
  2. A table that assigns the condition labels for each sample (which we will generate below).

Sample Information

As introduced at the beginning of the workshop, we have downloaded and prepared data from an existing publication (Zhang et al., 2019), wherein one goal is to understand the gene expression differences in wild-type mice that are “iron replete” (we label these “plus”) and “iron deficient” (we label these “minus”).

Read Sample Table

Our next step will be to describe the samples within our R session, so that we make the proper comparisons with DESeq2. Let’s check the sample names from the count table.

colnames(counts_rounded)
[1] "sample_A" "sample_B" "sample_C" "sample_D" "sample_E" "sample_F"

Based on the sample names that are the columns of counts_rounded, our samples are blinded, e.g. the sample names don’t clearly correspond to treatment groups. We will need to specify which sample IDs connect to which experimental conditions.

Typically sample phenotype data, including experimental conditions, are stored as Excel or CSV files that we can read into R, and then use when creating a DESeq2 object. If you are unfamilar with CSV files or how to generate them, there are tutorials available to guide you through the process.

Tip: Sample naming conventions

Use only alpha-numeric characters (A-Z, a-z, 0-9), and separate parts of the name with underscores (_) or dots (.). Do not begin sample names with numbers.

We’ll load our ‘pre-made’ sample information sheet, samplesheet.csv, to unblind our samples.

samplesheet = read.table("data/samplesheet.csv",
                       sep = ",",
                       header = TRUE,
                       row.names = 1)

We can look at the object by typing its name and hitting Enter. Note, for larger experiments, you may want to use head().

samplesheet
         genotype condition
sample_A       wt      plus
sample_B       wt      plus
sample_C       wt      plus
sample_D       wt     minus
sample_E       wt     minus
sample_F       wt     minus

Checkpoint: If you have loaded samplesheet, please indicate with the green ‘check’ button. Otherwise, please use the red ‘x’ button to have the command repeated

In this example data, all mice are wild-type and the iron replete mice are labeled as “plus” and the iron deficient mice are labeled as “minus”. Again, for larger experiments, you may want to examine the coding of the samples by looking at the unique() values of the relevant columns.

unique(samplesheet$condition)
[1] "plus"  "minus"

Replicates in RNA-seq experiments

A frequent question for RNA-seq projects is “How many replicates do I need?”.

The general goal of our analyses is to separate the “interesting” biological contributions from the “uninteresting” technical or other contributions that either cannot be or were not controlled in the experimental design. The more sources of variation, such as samples coming from heterogenous tissues or experiments with incomplete knockdowns, the more replicates (>3) are recommended.

Image of technical, biological, and experimental contributors to gene expression, from HBC training materials

For a more in depth discussion of experimental design considerations, particularly for the number of replicates, please read A Beginner’s Guide to Analysis of RNA Sequencing Data and papers like this one by Hart et al that focus on estimating statistical power for RNA-seq experiments.

Sequencing depth recommendations

A related experimental design consideration we often discuss with researchers is how much sequencing depth should be generated per sample. This figure shared by Illumina in their technical talks is helpful to understand the relative importance of replicates versus sequencing depth.

Illumina’s differential expression recovery across replicate number and sequencing depth

Generally, for human and mouse experiments the recommendation is 30-40 million reads per sample to capture both highly expressed (abundant) and lowly expressed (rarer) transcripts, assuming that ~25,000 protein-coding genes would be measured for a polyA library prep. However, as the image above shows, sequencing depth has less of an impact than number of replicates in detecting differentially expressed genes (DEGs).

Sample table formatting

Next, we’ll format our table so that we have the appropriate data type (an ordered factor) for DESeq2 to recognize our treatment groups and appropriately compare samples.

# tidy version
samplesheet_ready <- samplesheet %>% mutate(condition = factor(condition, 
                                          levels = c('plus', 'minus')))

# base version
samplesheet_ready <- samplesheet
samplesheet_ready$condition = factor(samplesheet_ready$condition,
                            levels = c('plus', 'minus'))

unique(samplesheet_ready$condition)
[1] plus  minus
Levels: plus minus

Notice that we set the levels in a particular order. This is important for setting the “Control” (or “Reference”) group as the denominator in the default comparisons when we setup our DESeq2 model.

Before we proceed, we need to make sure that the sample labels (column names) in the count table match the sample information table (row names), including the order. If the sample labels don’t match, then we will see an error and need to correct the labels prior to proceeding. Checking the sample information table is extremely important to ensure that the correct samples are grouped together for comparisons.

all(colnames(count_table) == rownames(samplesheet_ready))
[1] TRUE

This line of code checks if both the identity and order match between our count_table and our samplesheet. If, in the course of using your own data, this returns FALSE, try using the match() function to rearrange the columns of count_table (or the rows of samplesheet) to get them to match.

Checkpoint: If you your sample info check returns TRUE, please indicate with the green ‘yes’ button. Otherwise, please use the red ‘x’ button to have the command repeated

Creating DESeq2 object

To create the DESeqDataSet we will need the count_table and the samplesheet. We will also need a design formula to specify our model.

Making model choices

The design formula specified informs many of the DESeq2 functions how to treat the samples in the analysis, specifically which column(s) in the sample metadata table are relevant to the experimental design.

In this case, we aren’t aware of any covariates that should be considered in our comparisons. However, if there are additional attributes of the samples that may impact the DE comparisons, like date of collection, sex, or patient of origin, these should be added as additional columns in the sample information table and added to a design formula.

More complex questions, including adding “interaction terms” between multiple group labels are helpfully described in this support thread as well as in the DESeq2 vignette, which is an excellent document.

The design formula specifies the column(s) in the metadata table and how they should be used in the analysis. For our dataset we only have one column we are interested in, that is condition. This column has two factor levels, which tells DESeq2 that for each gene we want to evaluate gene expression change with respect to these different levels.

## Create DESeq object, line by line
dds = DESeqDataSetFromMatrix(countData = counts_rounded,
                              colData = samplesheet_ready,
                              design = ~ condition)
converting counts to integer mode
dds
class: DESeqDataSet 
dim: 55492 6 
metadata(1): version
assays(1): counts
rownames(55492): ENSMUSG00000000001 ENSMUSG00000000003 ... mcherry tdtomato
rowData names(0):
colnames(6): sample_A sample_B ... sample_E sample_F
colData names(2): genotype condition

Notice that printing the dds object helpfully shows us some helpful information:

  • The dimension (number of genes by number of samples),
  • The gene identifiers,
  • The sample identifiers,
  • The additional column names giving information about the samples

Checkpoint: If you see dds in your environment panel, please indicate with the green ‘check’ button. Otherwise, please use use the red ‘x’ button in your zoom reaction panel to have this step repeated. You can use the red ‘x’ to be put in a breakout room for help


Pre-filtering

While not necessary, pre-filtering the count table helps to not only reduce the size of the DESeq2 object, but also gives you a sense of how many genes were reasonably measured at the sequencing depth generated for your samples.

Here we will filter out any genes that have less than 10 counts across any of the samples. This is a fairly standard level of filtering, but can filter data less/more depending on quality control metrics from alignments and sequencing depth or total number of samples.

keep = rowSums(counts(dds)) >= 10
dds_filtered = dds[keep,]
dds_filtered
class: DESeqDataSet 
dim: 16249 6 
metadata(1): version
assays(1): counts
rownames(16249): ENSMUSG00000000001 ENSMUSG00000000028 ... ENSMUSG00000118651
  ENSMUSG00000118653
rowData names(0):
colnames(6): sample_A sample_B ... sample_E sample_F
colData names(2): genotype condition

Notice the dds_filtered object has less elements than the unfiltered dds object, indicating that a number of genes were not measured in our experiment.

Checkpoint: Questions?

Optional content

Click for how to model batch effects with DESeq2

Differences between samples can also be due to technical reasons, such as collection on different days or different sequencing runs. Differences between samples that are not due to biological factors as called batch effects. We can include batch effects in our design model in the same way as covariates, as long as the technical groups do not overlap, or confound, the biological treatment groups.

Let’s try add some additional meta-data information where we have counfounding batch effects and create another DESeq2 object.

samplesheet_batch = samplesheet_ready
samplesheet_batch$batch = factor(c(rep(c("Day1"), 2),
                       rep(c("Day2"), 2),
                       rep(c("Day3"), 2)),
                     levels = c("Day1", "Day2", "Day3"))

dds_batch = DESeqDataSetFromMatrix(countData = counts_rounded,
                      colData = samplesheet_batch,
                      design = ~ batch + condition)
converting counts to integer mode


Summary

In this section, we:

  • Loaded the necessary input files into our R session
  • Discussed model design for DESeq2
  • Initialized a DESeq2 data set
  • Filtered our count data

Now that we’ve created our DESeq2 objects, including specifying what model is appropriate for our data, and filtered our data, we can proceed with assessing the impact of the experimental conditions on gene expression for our samples.


Sources

Training resources used to develop materials:


These materials have been adapted and extended from materials listed above. These are open access materials distributed under the terms of the Creative Commons Attribution license (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

---
title: "Module 07: DE Initialization"
author: "UM Bioinformatics Core"
date: "`r Sys.Date()`"
output:
        html_document:
            includes:
                in_header: header.html
            theme: paper
            toc: true
            toc_depth: 4
            toc_float: true
            number_sections: false
            fig_caption: true
            markdown: GFM
            code_download: true
---

<style type="text/css">
body, td {
   font-size: 18px;
}
code.r{
  font-size: 12px;
}
pre {
  font-size: 12px
}
</style>

```{r, include = FALSE}
source("../bin/chunk-options.R")
knitr_fig_path("07-")
```

```{r LoadRunningData, eval=TRUE, echo=FALSE, message=FALSE, warning=FALSE}
library(DESeq2)
# load("rdata/RunningData.RData")
```

> # Objectives {.unlisted .unnumbered}
> * 'Unblind' our sample IDs
> * Understand possible confounding factors
> * Understand the impact of batches or additional covariates
> * Filter count table

# Differential Expression Workflow {.unlisted .unnumbered}

Here we will proceed setting up the inputs needed to initialize DESeq2 before testing for differential expression.

![](./images/wayfinder/wayfinder-DESeq2Init.png){width=75%}

---

# DESeq2 objects

Bioconductor software packages often define and use custom classes within R to store data in a way that better fits expectations around biological data, such as illustrated below from [Huber et al. 2015](https://www.nature.com/articles/nmeth.3252).

![A breakdown of the SummarizedExperiment class.](./images/SummarizedExperiment.jpg)

These custom data structures have pre-specified data slots, which hold specific types/classes of data and therefore can be more easily accessed by functions from the same package.

To create the DESeqDataSet we need two tables:

1. A count matrix (which we already loaded and saved as the object `count_table`) and
2. A table that assigns the condition labels for each sample (which we will generate below).

# Sample Information

As introduced at the beginning of the workshop, we have downloaded and prepared data from an existing publication [(Zhang et al., 2019)](https://elifesciences.org/articles/46976), wherein one goal is to understand the gene expression differences in wild-type mice that are "iron replete" (we label these "plus") and "iron deficient" (we label these "minus").

![](images/Module00_top_down.jpg)

## Read Sample Table

Our next step will be to describe the samples within our R session, so that we make the proper comparisons with DESeq2. Let's check the sample names from the count table.

```{r ColumnNames}
colnames(counts_rounded)
```

Based on the sample names that are the columns of `counts_rounded`, our samples are blinded, e.g. the sample names don't clearly correspond to treatment groups. We will need to specify which sample IDs connect to which experimental conditions.

Typically sample phenotype data, including experimental conditions, are stored as Excel or CSV files that we can read into R, and then use when creating a DESeq2 object. If you are unfamilar with CSV files or how to generate them, there are [tutorials](https://www.wikihow.com/Create-a-CSV-File) available to guide you through the process.

> # Tip: Sample naming conventions {.unlisted .unnumbered}
> Use only alpha-numeric characters (A-Z, a-z, 0-9), and separate parts of the name with underscores (`_`) or dots (`.`). Do not begin sample names with numbers.

We'll load our 'pre-made' sample information sheet, `samplesheet.csv`, to unblind our samples.

```{r Samplesheet, echo = FALSE, eval = TRUE}
samplesheet = read.table("../data/samplesheet.csv",
                       sep = ",",
                       header = TRUE,
                       row.names = 1)
```

```{r Samplesheet2, eval = FALSE}
samplesheet = read.table("data/samplesheet.csv",
                       sep = ",",
                       header = TRUE,
                       row.names = 1)
```

We can look at the object by typing its name and hitting Enter. Note, for larger experiments, you may want to use `head()`.

```{r ShowSamplesheet}
samplesheet
```

**Checkpoint**: *If you have loaded `samplesheet`, please indicate with the green 'check' button. Otherwise, please use the red 'x' button to have the command repeated*



In this example data, all mice are wild-type and the iron replete mice are labeled as "plus" and the iron deficient mice are labeled as "minus". Again, for larger experiments, you may want to examine the coding of the samples by looking at the `unique()` values of the relevant columns.

```{r TreatmentGroupTable}
unique(samplesheet$condition)
```


### Replicates in RNA-seq experiments

A frequent question for RNA-seq projects is "How many replicates do I need?".

The general goal of our analyses is to separate the “interesting” biological contributions from the “uninteresting” technical or other contributions that either cannot be or were not controlled in the experimental design. The more sources of variation, such as samples coming from heterogenous tissues or experiments with incomplete knockdowns, the more replicates (>3) are recommended.

![Image of technical, biological, and experimental contributors to gene expression, from HBC training materials](images/de_variation.png){width=75%}

For a more in depth discussion of experimental design considerations, particularly for the number of replicates, please read [A Beginner’s Guide to Analysis of RNA Sequencing Data](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6096346/) and papers like this one by [Hart et al](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3842884/) that focus on estimating statistical power for RNA-seq experiments.

### Sequencing depth recommendations

A related experimental design consideration we often discuss with researchers is how much sequencing depth should be generated per sample. This figure shared by Illumina in their technical talks is helpful to understand the relative importance of replicates versus sequencing depth.

![Illumina's differential expression recovery across replicate number and sequencing depth](images/de_replicates_img.png){width=75%}

Generally, for human and mouse experiments the recommendation is 30-40 million reads per sample to capture both highly expressed (abundant) and lowly expressed (rarer) transcripts, assuming that ~25,000 protein-coding genes would be measured for a polyA library prep. However, as the image above shows, sequencing depth has less of an impact than number of replicates in detecting differentially expressed genes (DEGs).

### Sample table formatting

Next, we'll format our table so that we have the appropriate data type (an ordered [factor](https://swcarpentry.github.io/r-novice-inflammation/12-supp-factors/)) for DESeq2 to recognize our treatment groups and appropriately compare samples.

```{r echo = FALSE, eval = FALSE}
# Consider copying sample sheet & updating/mutating condition column to be a factor t
```

```{r SamplesheetFactor}
# tidy version
samplesheet_ready <- samplesheet %>% mutate(condition = factor(condition, 
                                          levels = c('plus', 'minus')))

# base version
samplesheet_ready <- samplesheet
samplesheet_ready$condition = factor(samplesheet_ready$condition,
                            levels = c('plus', 'minus'))

unique(samplesheet_ready$condition)
```

Notice that we set the levels in a particular order. This is important for setting the "Control" (or "Reference") group as the denominator in the default comparisons when we setup our DESeq2 model.

Before we proceed, we need to make sure that the sample labels (column names) in the count table match the sample information table (row names), including the order. If the sample labels don't match, then we will see an error and need to correct the labels prior to proceeding. Checking the sample information table is extremely important to ensure that the correct samples are grouped together for comparisons.

```{r CheckSamplesheet}
all(colnames(count_table) == rownames(samplesheet_ready))
```
This line of code checks if both the identity and order match between our `count_table` and our `samplesheet`. If, in the course of using your own data, this returns `FALSE`, try using the `match()` function to rearrange the columns of `count_table` (or the rows of `samplesheet`) to get them to match.

**Checkpoint**: *If you your sample info check returns `TRUE`, please indicate with the green 'yes' button. Otherwise, please use the red 'x' button to have the command repeated*

# Creating DESeq2 object

To create the `DESeqDataSet` we will need the `count_table` and the `samplesheet`. We will also need a **design formula** to specify our model.

## Making model choices

The design formula specified informs many of the DESeq2 functions how to treat the samples in the analysis, specifically which column(s) in the sample metadata table are relevant to the experimental design.

In this case, we aren't aware of any [covariates](https://methods-sagepub-com.proxy.lib.umich.edu/reference/encyc-of-research-design/n85.xml) that should be considered in our comparisons. However, if there are additional attributes of the samples that may impact the DE comparisons, like date of collection, sex, or patient of origin, these should be added as [additional columns](https://support.bioconductor.org/p/75309/) in the sample information table and [added to a design formula](https://support.bioconductor.org/p/98700/).

More complex questions, including adding "interaction terms" between multiple group labels are helpfully described in [this support thread](https://support.bioconductor.org/p/98628/) as well as in the [DESeq2 vignette](https://bioconductor.org/packages/release/bioc/vignettes/DESeq2/inst/doc/DESeq2.html#interactions), which is an excellent document.

The design formula specifies the column(s) in the metadata table and how they should be used in the analysis. For our dataset we only have one column we are interested in, that is `condition`. This column has two factor levels, which tells DESeq2 that for each gene we want to evaluate gene expression change with respect to these different levels.

```{r DESeq2Object}
## Create DESeq object, line by line
dds = DESeqDataSetFromMatrix(countData = counts_rounded,
                              colData = samplesheet_ready,
                              design = ~ condition)
dds
```

Notice that printing the `dds` object helpfully shows us some helpful information:

* The dimension (number of genes by number of samples),
* The gene identifiers,
* The sample identifiers,
* The additional column names giving information about the samples

**Checkpoint**: *If you see `dds` in your environment panel, please indicate with the green 'check' button. Otherwise, please use  use the red 'x' button in your zoom reaction panel to have this step repeated. You can use the red 'x' to be put in a breakout room for help*

---


# Pre-filtering

While not necessary, [pre-filtering](http://bioconductor.org/packages/devel/bioc/vignettes/DESeq2/inst/doc/DESeq2.html#pre-filtering) the count table helps to not only reduce the size of the DESeq2 object, but also gives you a sense of how many genes were reasonably measured at the sequencing depth generated for your samples.

Here we will filter out any genes that have less than 10 counts across any of the samples. This is a fairly standard level of filtering, but can filter data less/more depending on quality control metrics from alignments and sequencing depth or total number of samples.

```{r PreFilter}
keep = rowSums(counts(dds)) >= 10
dds_filtered = dds[keep,]
dds_filtered
```

Notice the `dds_filtered` object has less elements than the unfiltered `dds` object, indicating that a number of genes were not measured in our experiment.

**Checkpoint**: *Questions?*

# Optional content

<details>
    <summary>*Click for how to model batch effects with DESeq2*</summary>

    Differences between samples can also be due to technical reasons, such as collection on different days or different sequencing runs. Differences between samples that are not due to biological factors as called **batch effects**. We can include batch effects in our design model in the same way as covariates, as long as the technical groups do not overlap, or **confound**, the biological treatment groups.

    Let's try add some additional meta-data information where we have counfounding batch effects and create another DESeq2 object.

```{r Confounders}
samplesheet_batch = samplesheet_ready
samplesheet_batch$batch = factor(c(rep(c("Day1"), 2),
                       rep(c("Day2"), 2),
                       rep(c("Day3"), 2)),
                     levels = c("Day1", "Day2", "Day3"))

dds_batch = DESeqDataSetFromMatrix(countData = counts_rounded,
                      colData = samplesheet_batch,
                      design = ~ batch + condition)
```
</details>
<br>

# Summary

In this section, we:

* Loaded the necessary input files into our R session
* Discussed model design for DESeq2
* Initialized a DESeq2 data set
* Filtered our count data

Now that we've created our DESeq2 objects, including specifying what model is appropriate for our data, and filtered our data, we can proceed with assessing the impact of the experimental conditions on gene expression for our samples.

---

# Sources

Training resources used to develop materials:

* HBC DGE setup: https://hbctraining.github.io/DGE_workshop/lessons/01_DGE_setup_and_overview.html
* HBC Count Normalization: https://hbctraining.github.io/DGE_workshop/lessons/02_DGE_count_normalization.html
* DESeq2 standard vignette: http://bioconductor.org/packages/devel/bioc/vignettes/DESeq2/inst/doc/DESeq2.html
* DESeq2 beginners vignette: https://bioc.ism.ac.jp/packages/2.14/bioc/vignettes/DESeq2/inst/doc/beginner.pdf
* Bioconductor RNA-seq Workflows: https://www.bioconductor.org/help/course-materials/2015/LearnBioconductorFeb2015/B02.1_RNASeq.html
* CCDL Gastric cancer training materials: https://alexslemonade.github.io/training-modules/RNA-seq/03-gastric_cancer_exploratory.nb.html
* CCDL Neuroblastoma training materials: https://alexslemonade.github.io/training-modules/RNA-seq/05-nb_cell_line_DESeq2.nb.html



```{r WriteOut.RData, eval=TRUE, echo=FALSE, message=FALSE, warning=FALSE}
# Hidden code block to write out data for knitting
# save.image(file = "rdata/RunningData.RData")
```

---

These materials have been adapted and extended from materials listed above. These are open access materials distributed under the terms of the [Creative Commons Attribution license (CC BY 4.0)](http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
