Objectives

  • Additional visualizations for gene/sample level QC assessment

Count boxplots

To evaluate the difference between the count distributions before and after normalization, let’s extract the raw counts and the rlog normalized counts, and coerce them to tibbles.

raw_counts = as_tibble(counts(dds), rownames = 'id')
norm_counts = as_tibble(assay(rld), rownames = 'id')

raw_counts
# A tibble: 16,249 × 7
   id                 SRR7777895 SRR7777896 SRR7777897 SRR7777898 SRR7777899 SRR7777900
   <chr>                   <int>      <int>      <int>      <int>      <int>      <int>
 1 ENSMUSG00000000001       1041        905       1296       3481       1283       1921
 2 ENSMUSG00000000028       1043       1232       1664       2690       1825       2720
 3 ENSMUSG00000000031       1819        914       1618       8618       1350       1222
 4 ENSMUSG00000000037         19         11         18         48         37         29
 5 ENSMUSG00000000049         18          1          4         24          1          1
 6 ENSMUSG00000000056      14972      14768      21026      22962      22263      23622
 7 ENSMUSG00000000078        888        607        911       1689        738       1180
 8 ENSMUSG00000000085        402        483        744        898        811       1261
 9 ENSMUSG00000000088        904       1212       1733       2434       1387       1267
10 ENSMUSG00000000093          7          8         16         23         17         29
# … with 16,239 more rows
# ℹ Use `print(n = ...)` to see more rows
norm_counts
# A tibble: 16,249 × 7
   id                 SRR7777895 SRR7777896 SRR7777897 SRR7777898 SRR7777899 SRR7777900
   <chr>                   <dbl>      <dbl>      <dbl>      <dbl>      <dbl>      <dbl>
 1 ENSMUSG00000000001      10.5       10.4       10.4       10.8       10.4       10.6 
 2 ENSMUSG00000000028      10.6       10.7       10.7       10.7       10.8       11.0 
 3 ENSMUSG00000000031      11.2       10.5       10.7       11.9       10.6       10.3 
 4 ENSMUSG00000000037       4.64       4.56       4.58       4.66       4.72       4.62
 5 ENSMUSG00000000049       3.02       2.82       2.84       2.94       2.81       2.81
 6 ENSMUSG00000000056      14.3       14.3       14.3       13.9       14.4       14.2 
 7 ENSMUSG00000000078      10.1        9.77       9.86       9.93       9.68       9.90
 8 ENSMUSG00000000085       9.28       9.41       9.53       9.23       9.60       9.80
 9 ENSMUSG00000000088      10.4       10.6       10.7       10.5       10.5       10.2 
10 ENSMUSG00000000093       3.88       3.89       3.93       3.91       3.94       3.99
# … with 16,239 more rows
# ℹ Use `print(n = ...)` to see more rows

Next, this is the perfect opportunity to use tidyr::pivot_longer() because we want to use ggplot() for the bar plots, but the data is currently in the wide form, not the tidy form!

tidy_raw = tidyr::pivot_longer(raw_counts, -id, names_to = 'sample', values_to = 'counts')
tidy_norm = tidyr::pivot_longer(norm_counts, -id, names_to = 'sample', values_to = 'counts')

We should also join in the sample metadata so that we can color on the sample groups.

samplesheet_tbl = as_tibble(colData(dds), rownames = 'sample')

tidy_raw = tidy_raw %>% left_join(samplesheet_tbl, by = 'sample')
tidy_norm = tidy_norm %>% left_join(samplesheet_tbl, by = 'sample')
raw_boxplot = ggplot(tidy_raw, aes(x = sample, y = log2(counts), fill = condition)) +
    geom_boxplot(notch = TRUE) +
    labs(
        title = 'Raw Counts',
        x = 'Sample',
        y = 'log2 Counts') +
    theme_bw() + theme(axis.text.x = element_text(angle = 90))
raw_boxplot
Warning: Removed 6656 rows containing non-finite values (stat_boxplot).

Question

Why did we get that warning about non-finite values?

norm_boxplot = ggplot(tidy_norm, aes(x = sample, y = counts, fill = condition)) +
    geom_boxplot(notch = TRUE) +
    labs(
        title = 'rlog Normalized Counts',
        x = 'Sample',
        y = 'rlog Counts') +
    theme_bw() + theme(axis.text.x = element_text(angle = 90))
norm_boxplot

Observe that the normalized plots truly do appear normalized; their means are more uniform. Let’s go ahead and save these plots in our outputs/figures folder.

ggsave(filename = 'outputs/figures/Boxplot_raw_condition.pdf', plot = raw_boxplot, height = 6, width = 6)
ggsave(filename = 'outputs/figures/Boxplot_rlog_condition.pdf', plot = norm_boxplot, height = 6, width = 6)

Heatmaps

Let’s create a heatmap based on the distance between pair-wise sample expression profiles. This is another vantage point of how similar and dissimilar the samples are from one another. To get started, we actually want a plain matrix, with out a column for the gene IDs, as we did for the boxplot.

norm_mat = assay(rld)
head(norm_mat)
                   SRR7777895 SRR7777896 SRR7777897 SRR7777898 SRR7777899 SRR7777900
ENSMUSG00000000001  10.514813  10.366709  10.419463  10.840373  10.410449  10.578771
ENSMUSG00000000028  10.604461  10.734506  10.735026  10.682714  10.820938  10.990999
ENSMUSG00000000031  11.160276  10.498747  10.742763  11.861617  10.578156  10.298022
ENSMUSG00000000037   4.642433   4.555500   4.578934   4.656950   4.719012   4.620204
ENSMUSG00000000049   3.017478   2.820198   2.843894   2.936455   2.814833   2.811619
ENSMUSG00000000056  14.321672  14.284652  14.337197  13.904238  14.393912  14.235971

Next, we’ll use the dist() function on the transpose of norm_mat to compute the distance. We will use the default Euclidean distance.

dist_mat = dist(t(norm_mat), upper = TRUE)

Next, we’ll plot a very simple pheatmap() using this matrix. But let’s check the class of dist_mat first, because the input to pheatmap() needs to be a matrix.

class(dist_mat)
[1] "dist"
# Have to coerce it
dist_mat = as.matrix(dist_mat)

dist_heatmap = pheatmap(
    mat = dist_mat,
    cluster_rows = TRUE,
    cluster_cols = TRUE,
    show_rownames = TRUE,
    show_colnames = TRUE
)
dist_heatmap

This is nice, but there are a few tweaks we might consider:

  1. The color scale used by default is divergent, but our distances are values in [0, Inf), so a linear color scale would be more appropriate here.
  2. We might like for the sample metadata to be included so that we can easily tell if the samples cluster by their condition.

To accomplish the first change, we’ll use the colorRampPalette() function from the RColorBrewer package. This is the package to use for creating color scales of all varieties. We highly recommend exploring the package website and documentation.

colors = colorRampPalette(brewer.pal(9, 'Blues'))(50)

Now let’s use that in the pheatmap() call using the color parameter:

dist_heatmap = pheatmap(
    mat = dist_mat,
    color = colors,
    cluster_rows = TRUE,
    cluster_cols = TRUE,
    show_rownames = TRUE,
    show_colnames = TRUE
)
dist_heatmap

This is a lot more reasonable. More distant samples are a deeper blue, while more similar samples are closer to white. Next, let’s add some annotation data.

annotation_tbl = samplesheet_tbl %>%
    dplyr::select(sample, condition) %>%
    column_to_rownames(var = 'sample')

dist_heatmap = pheatmap(
    mat = dist_mat,
    color = colors,
    cluster_rows = TRUE,
    cluster_cols = TRUE,
    show_rownames = TRUE,
    show_colnames = TRUE,
    annotation_col = annotation_tbl
)
dist_heatmap

And now we have our conditions as a colored annotation bar along the columns.

Session Info

sessionInfo()
R version 4.2.1 (2022-06-23)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Monterey 12.5

Matrix products: default
LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats4    stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] biomaRt_2.52.0              data.table_1.14.2           RColorBrewer_1.1-3          ggrepel_0.9.1              
 [5] DESeq2_1.36.0               SummarizedExperiment_1.26.1 Biobase_2.56.0              MatrixGenerics_1.8.1       
 [9] matrixStats_0.62.0          GenomicRanges_1.48.0        GenomeInfoDb_1.32.2         IRanges_2.30.0             
[13] S4Vectors_0.34.0            BiocGenerics_0.42.0         knitr_1.39                  rmarkdown_2.14             
[17] forcats_0.5.1               stringr_1.4.0               dplyr_1.0.9                 purrr_0.3.4                
[21] readr_2.1.2                 tidyr_1.2.0                 tibble_3.1.7                ggplot2_3.3.6              
[25] tidyverse_1.3.2             pheatmap_1.0.12            

loaded via a namespace (and not attached):
 [1] googledrive_2.0.0      colorspace_2.0-3       ellipsis_0.3.2         XVector_0.36.0         fs_1.5.2              
 [6] rstudioapi_0.13        farver_2.1.1           bit64_4.0.5            AnnotationDbi_1.58.0   fansi_1.0.3           
[11] lubridate_1.8.0        xml2_1.3.3             codetools_0.2-18       splines_4.2.1          cachem_1.0.6          
[16] geneplotter_1.74.0     jsonlite_1.8.0         broom_1.0.0            annotate_1.74.0        dbplyr_2.2.1          
[21] png_0.1-7              compiler_4.2.1         httr_1.4.3             backports_1.4.1        assertthat_0.2.1      
[26] Matrix_1.4-1           fastmap_1.1.0          gargle_1.2.0           cli_3.3.0              prettyunits_1.1.1     
[31] htmltools_0.5.3        tools_4.2.1            gtable_0.3.0           glue_1.6.2             GenomeInfoDbData_1.2.8
[36] rappdirs_0.3.3         Rcpp_1.0.9             cellranger_1.1.0       jquerylib_0.1.4        vctrs_0.4.1           
[41] Biostrings_2.64.0      xfun_0.31              rvest_1.0.2            lifecycle_1.0.1        XML_3.99-0.10         
[46] googlesheets4_1.0.0    zlibbioc_1.42.0        scales_1.2.0           vroom_1.5.7            hms_1.1.1             
[51] parallel_4.2.1         curl_4.3.2             yaml_2.3.5             memoise_2.0.1          sass_0.4.2            
[56] stringi_1.7.8          RSQLite_2.2.15         highr_0.9              genefilter_1.78.0      filelock_1.0.2        
[61] BiocParallel_1.30.3    rlang_1.0.4            pkgconfig_2.0.3        bitops_1.0-7           evaluate_0.15         
[66] lattice_0.20-45        labeling_0.4.2         bit_4.0.4              tidyselect_1.1.2       magrittr_2.0.3        
[71] R6_2.5.1               generics_0.1.3         DelayedArray_0.22.0    DBI_1.1.3              pillar_1.8.0          
[76] haven_2.5.0            withr_2.5.0            survival_3.3-1         KEGGREST_1.36.3        RCurl_1.98-1.8        
[81] modelr_0.1.8           crayon_1.5.1           utf8_1.2.2             BiocFileCache_2.4.0    tzdb_0.3.0            
[86] progress_1.2.2         locfit_1.5-9.6         grid_4.2.1             readxl_1.4.0           blob_1.2.3            
[91] reprex_2.0.1           digest_0.6.29          xtable_1.8-4           munsell_0.5.0          bslib_0.4.0           

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 11X: Bonus Content"
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("11X-")
```

```{r Modules, eval=TRUE, echo=FALSE, message=FALSE, warning=FALSE}
library(DESeq2)
library(ggplot2)
library(tidyr)
library(dplyr)
library(ggrepel)
library(pheatmap)
library(RColorBrewer)
```

> # Objectives {.unlisted .unnumbered}
> * Additional visualizations for gene/sample level QC assessment

# Count boxplots

To evaluate the difference between the count distributions before and after normalization, let's extract the raw counts and the rlog normalized counts, and coerce them to `tibble`s.

```{r RawCountsSetup}
raw_counts = as_tibble(counts(dds), rownames = 'id')
norm_counts = as_tibble(assay(rld), rownames = 'id')

raw_counts
norm_counts
```

Next, this is the **perfect** opportunity to use `tidyr::pivot_longer()` because we want to use `ggplot()` for the bar plots, but the data is currently in the wide form, not the tidy form!

```{r PivotLonger}
tidy_raw = tidyr::pivot_longer(raw_counts, -id, names_to = 'sample', values_to = 'counts')
tidy_norm = tidyr::pivot_longer(norm_counts, -id, names_to = 'sample', values_to = 'counts')
```

We should also join in the sample metadata so that we can color on the sample groups.

```{r JoinMetadata}
samplesheet_tbl = as_tibble(colData(dds), rownames = 'sample')

tidy_raw = tidy_raw %>% left_join(samplesheet_tbl, by = 'sample')
tidy_norm = tidy_norm %>% left_join(samplesheet_tbl, by = 'sample')
```

```{r RawBoxplot}
raw_boxplot = ggplot(tidy_raw, aes(x = sample, y = log2(counts), fill = condition)) +
    geom_boxplot(notch = TRUE) +
    labs(
        title = 'Raw Counts',
        x = 'Sample',
        y = 'log2 Counts') +
    theme_bw() + theme(axis.text.x = element_text(angle = 90))
raw_boxplot
```

> # Question {.unlisted .unnumbered}
> Why did we get that warning about non-finite values?

```{r NormBoxplot}
norm_boxplot = ggplot(tidy_norm, aes(x = sample, y = counts, fill = condition)) +
    geom_boxplot(notch = TRUE) +
    labs(
        title = 'rlog Normalized Counts',
        x = 'Sample',
        y = 'rlog Counts') +
    theme_bw() + theme(axis.text.x = element_text(angle = 90))
norm_boxplot
```

Observe that the normalized plots truly do appear normalized; their means are more uniform. Let's go ahead and save these plots in our `outputs/figures` folder.

```{r BoxplotsRawSave, eval = FALSE}
ggsave(filename = 'outputs/figures/Boxplot_raw_condition.pdf', plot = raw_boxplot, height = 6, width = 6)
ggsave(filename = 'outputs/figures/Boxplot_rlog_condition.pdf', plot = norm_boxplot, height = 6, width = 6)
```

# Heatmaps

Let's create a heatmap based on the distance between pair-wise sample expression profiles. This is another vantage point of how similar and dissimilar the samples are from one another. To get started, we actually want a plain matrix, with out a column for the gene IDs, as we did for the boxplot.

```{r NormCounts}
norm_mat = assay(rld)
head(norm_mat)
```

Next, we'll use the `dist()` function on the transpose of `norm_mat` to compute the distance. We will use the default Euclidean distance.

```{r DistanceMat}
dist_mat = dist(t(norm_mat), upper = TRUE)
```

Next, we'll plot a very simple `pheatmap()` using this matrix. But let's check the class of `dist_mat` first, because the input to `pheatmap()` needs to be a `matrix`.

```{r DistanceHeatmap}
class(dist_mat)

# Have to coerce it
dist_mat = as.matrix(dist_mat)

dist_heatmap = pheatmap(
    mat = dist_mat,
    cluster_rows = TRUE,
    cluster_cols = TRUE,
    show_rownames = TRUE,
    show_colnames = TRUE
)
dist_heatmap
```

This is nice, but there are a few tweaks we might consider:

1. The color scale used by default is divergent, but our distances are values in [0, Inf), so a linear color scale would be more appropriate here.
2. We might like for the sample metadata to be included so that we can easily tell if the samples cluster by their `condition`.

To accomplish the first change, we'll use the `colorRampPalette()` function from the `RColorBrewer` package. This is **the** package to use for creating color scales of all varieties. We highly recommend exploring the package website and documentation.

```{r ChooseColors}
colors = colorRampPalette(brewer.pal(9, 'Blues'))(50)
```

Now let's use that in the `pheatmap()` call using the `color` parameter:

```{r DistanceHeatmaColors}
dist_heatmap = pheatmap(
    mat = dist_mat,
    color = colors,
    cluster_rows = TRUE,
    cluster_cols = TRUE,
    show_rownames = TRUE,
    show_colnames = TRUE
)
dist_heatmap
```

This is a lot more reasonable. More distant samples are a deeper blue, while more similar samples are closer to white. Next, let's add some annotation data.

```{r DistanceHeatmapAnnotated}
annotation_tbl = samplesheet_tbl %>%
    dplyr::select(sample, condition) %>%
    column_to_rownames(var = 'sample')

dist_heatmap = pheatmap(
    mat = dist_mat,
    color = colors,
    cluster_rows = TRUE,
    cluster_cols = TRUE,
    show_rownames = TRUE,
    show_colnames = TRUE,
    annotation_col = annotation_tbl
)
dist_heatmap
```

And now we have our conditions as a colored annotation bar along the columns.

# Sources

* HBC QC tutorial: https://hbctraining.github.io/DGE_workshop/lessons/03_DGE_QC_analysis.html
* Detailed Heatmap tutorial from Galaxy: https://training.galaxyproject.org/training-material/topics/transcriptomics/tutorials/rna-seq-viz-with-heatmap2/tutorial.html

---

# Session Info
```{r SessionInfo}
sessionInfo()
```

---

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.
