Why this activity matters

In the previous heatmap activity, we used the small built-in mtcars dataset. That was useful because the dataset was small enough to see clearly.

Now we will use real gene expression data from TCGA breast cancer samples. Gene expression data which tells us how many messenger RNAs (mRNAs) per gene are present in a patient sample. The amount of a gene’s mRNA corresponds (roughly) to the amount of protein in the sample.

This is more realistic, but also more challenging:

That is normal in real computational biology.

Our goal is to use heatmaps to ask:

Do breast tumors with similar gene expression patterns also share clinical features, such as estrogen receptor status?

Learning goals

By the end of this activity, you should be able to:

Find the data directory

This activity expects the following files:

# This chunk sets up file path for the activity.

data_dir <- "/shared/dreamhigh/data"

Load the expression data

The expression file is an RDS file.

An RDS file (which ends in .rds) is a special file format used by R to save exactly one specific piece of data (like a single data table, a list, or a machine learning model) from your computer’s memory onto your hard drive.

Reading and writing RDS files is significantly faster than processing text-based files.

Rows are genes.
Columns are patient tumor samples.

brca_expr_mat <- readRDS(file.path(data_dir,"brca_expr_mat.rds"))

Inspect the matrix.

dim(brca_expr_mat)
## [1] 18351  1082
brca_expr_mat[1:5, 1:5]
##          TCGA-3C-AAAU TCGA-3C-AALI TCGA-3C-AALJ TCGA-3C-AALK TCGA-4H-AAAK
## TSPAN6      7.5636463     7.705439     9.975045    10.110718     9.881960
## TNMD        0.4272843     1.061776     5.353718     1.164271     2.506120
## DPM1        9.0367945     9.662019     9.919403     8.859174     8.928912
## SCYL3       8.3493520    10.607275     8.395877     9.103957     8.704889
## C1orf112    6.9691735     8.106778     7.922947     7.776269     7.495535

Question: What do the rows represent? What do the columns represent?

Your answer:Rows represent genes. Columns represent patient tumor samples.

Reflection: Why do you think genes are stored as rows and patients as columns? Could the data have been organized the other way around?

Your answer:This organization makes it easier to compare the same gene across many patients. The data could be organized the other way, but many analysis tools expect genes as rows.

Important note: these data are already log-transformed

The values in this expression matrix are mostly between 0 and about 21.

summary(as.vector(brca_expr_mat))
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   3.669   8.056   6.852   9.875  20.978

Reflection: The largest expression values are only around 20 instead of thousands or millions. Why does this suggest the data have already been log-transformed?

Your answer:The expression values are relatively small (around 0–20) instead of thousands or millions, which is typical after log transformation.

The distribution of values is a strong clue that these values are already on a transformed scale, likely a log-like expression scale.

We log-transform gene expression data to make highly skewed numbers more symmetrical. This fixes a common problem where a few highly active genes distort your and data dominate statistical analyses purely due to their massive raw numerical values, rather than their actual biological relevance.

Load the clinical data

The clinical data contain patient and tumor information.

brca_clin_df <- read.csv(
  file.path(data_dir, "brca_clin.csv"),
  stringsAsFactors = FALSE
)

dim(brca_clin_df)
## [1] 1082   27
head(brca_clin_df[, 1:6])
##   bcr_patient_barcode gender                      race              ethnicity
## 1        TCGA-3C-AAAU FEMALE                     WHITE NOT HISPANIC OR LATINO
## 2        TCGA-3C-AALI FEMALE BLACK OR AFRICAN AMERICAN NOT HISPANIC OR LATINO
## 3        TCGA-3C-AALJ FEMALE BLACK OR AFRICAN AMERICAN NOT HISPANIC OR LATINO
## 4        TCGA-3C-AALK FEMALE BLACK OR AFRICAN AMERICAN NOT HISPANIC OR LATINO
## 5        TCGA-4H-AAAK FEMALE                     WHITE NOT HISPANIC OR LATINO
## 6        TCGA-5L-AAT0 FEMALE                     WHITE     HISPANIC OR LATINO
##   age_at_diagnosis year_of_initial_pathologic_diagnosis
## 1               55                                 2004
## 2               50                                 2003
## 3               62                                 2011
## 4               52                                 2011
## 5               50                                 2013
## 6               42                                 2010

As we saw previously, the clinical data includes receptor status.

table(brca_clin_df$estrogen_receptor_status)
## 
## [Not Evaluated]   Indeterminate        Negative        Positive 
##              48               2             236             796
table(brca_clin_df$progesterone_receptor_status)
## 
## [Not Evaluated]   Indeterminate        Negative        Positive 
##              49               4             340             689
table(brca_clin_df$her2_receptor_status)
## 
## [Not Available] [Not Evaluated]       Equivocal   Indeterminate        Negative 
##               8             170             177              12             554 
##        Positive 
##             161

Make sure samples are aligned

This is a very important step.

The expression matrix columns are sample IDs.
The clinical data rows are patient/sample IDs.

We should match them by name, not just assume they are in the same order.

sample_ids <- colnames(brca_expr_mat)

match_index <- match(sample_ids, brca_clin_df$bcr_patient_barcode)

sum(is.na(match_index))
## [1] 0

If the result is 0, which should be the case here, every expression sample matched a clinical row.

If the result wasn’t zero, we can use match_index to sort the rows of the clinical data to match the columns of the expression data.

clin_matched <- brca_clin_df[match_index, ]

all(clin_matched$bcr_patient_barcode == sample_ids)
## [1] TRUE

Now clin_matched is aligned to the columns of brca_expr_mat.

Average expression across samples

For each gene, we can calculate its average expression across all tumors.

mean_expr <- apply(brca_expr_mat, 1, mean)

summary(mean_expr)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   3.759   8.036   6.852   9.771  16.470

What does this look like in boxplot form?

mean_expr <- apply(brca_expr_mat, 1, mean)

# Draw boxplot but don't plot outliers
bp <- boxplot(mean_expr,
              boxwex = 0.35,
              horizontal = TRUE,
              col = "lightblue",
              outline = FALSE,
              main = "Distribution of Mean Gene Expression",
              xlab = "Mean Expression")

# Add the mean as a red diamond
mean.val <- mean(mean_expr)
points(mean.val, 1, pch = 23, bg = "red", cex = 1.5)

# Label the mean
text(mean.val, 1.15,
     labels = paste0("Mean = ", sprintf("%.2f", mean.val)),
     col = "red")

# Label the five-number summary
stats <- bp$stats


text(stats[1], 0.82, sprintf("%.1f", stats[1]))  # Min
text(stats[2] - 0.10, 0.82, sprintf("%.1f", stats[2]))  # Q1
text(stats[3],        0.82, sprintf("%.1f", stats[3]))  # Median
text(stats[4] + 0.10, 0.82, sprintf("%.1f", stats[4]))  # Q3
text(stats[5], 0.82, sprintf("%.1f", stats[5]))  # Max

# Check out the actual values again:
summary(mean_expr)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   3.759   8.036   6.852   9.771  16.470

Reflection: Is the mean (red diamond) larger or smaller than the median (black line)? What does this tell you about the distribution of gene expression?

(Clue: Skewness measures the asymmetry of data. In a symmetrical distribution, the mean and median are identical. In an asymmetrical (skewed) distribution, extreme values or a long tail “pull” the mean toward the direction of the tail, while the median remains closer to the center of the data.)

Your answer: The mean is usually slightly larger than the median, suggesting the data are right-skewed because a few genes have much higher expression than most.

Reflection: About half of the genes have an average expression below the median. Does that mean half of the genes are “unimportant”? Why or why not?

Your answer:No. Low expression does not mean a gene is unimportant. Some genes are essential even if they are expressed at low levels.

If you want to learn more about boxplots (otherwise known as whisker plots) check out this truly awesome Statquest video.

hist(
  mean_expr,
  breaks = 50,
  main = "Mean gene expression across breast tumors",
  xlab = "Mean expression"
)

Reflection: Do all genes appear to be expressed at similar levels, or do some genes appear much more active than others? Why might cells regulate genes differently?

Your answer:Some genes are much more active than others. Cells regulate genes differently because different genes have different functions and are needed in different amounts.

Variance across samples

A gene can have a high average expression but not vary much between patients.

For heatmaps, genes that vary across patients are often more informative.

var_genes <- apply(brca_expr_mat, 1, var)

summary(var_genes)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.3211  0.6607  1.2801  1.5830 26.8820

Let’s look at the distribution of variance values.

hist(
  var_genes,
  breaks = 50,
  main = "Variance of gene expression across breast tumors",
  xlab = "Variance"
)

Most genes have relatively low variance. *

Reflection: Why might genes that change a lot from patient to patient be more useful for studying cancer than genes whose expression hardly changes?

Your answer:Highly variable genes can reveal biological differences between tumors and may help identify cancer subtypes.

Select the most variable genes

We will begin with a small number of highly variable genes.

This is easier to interpret than trying to plot all genes at once.

Prediction: What do you think would happen if we plotted all 20,000 genes instead of only the 100 most variable genes?

Your answer:The heatmap would become crowded and difficult to interpret, making important patterns harder to see.

order_var <- order(var_genes, decreasing = TRUE)

num_genes <- 100

expr_top <- brca_expr_mat[order_var[1:num_genes], ]

dim(expr_top)
## [1]  100 1082

Select a subset of samples

There are many patient samples. For an introductory heatmap, we will plot every fourth sample.

our_samples <- seq(1, ncol(expr_top), by = 4)

expr_sub <- expr_top[, our_samples]

clin_sub <- clin_matched[our_samples, ]

dim(expr_sub)
## [1] 100 271

The most important heatmap correction: scale genes, not samples

This is the key idea.

For a gene expression heatmap, we usually want to ask:

Is each gene higher or lower than its own average across tumors?

That means we should scale each row of the matrix, because rows are genes.

Base R’s scale() function scales columns by default. Since our columns are patients, this would scale patients, not genes.

So we use t(scale(t(matrix))).

This transposes the matrix, scales the genes, and transposes it back.

expr_sub_scaled <- t(scale(t(expr_sub)))

# Replace any NA values that could occur for genes with zero variance
expr_sub_scaled[is.na(expr_sub_scaled)] <- 0

summary(as.vector(expr_sub_scaled))
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -3.31947 -0.76921 -0.07953  0.00000  0.71035  3.85797

Now each gene is shown relative to its own average across samples.

**Reflection: Before scaling, some genes naturally have much higher expression than others. After scaling, what does the color represent?

Your answer:The color shows whether a gene is expressed above or below its own average across the samples.

Heatmap of variable genes

We will use a blue-white-red palette.

heat_colors <- colorRampPalette(c("blue", "white", "red"))(100)

heatmap(
  expr_sub_scaled,
  labRow = "",
  labCol = "",
  margins = c(3, 3),
  xlab = "Tumor samples",
  ylab = "Variable genes",
  col = heat_colors,
  zlim = c(-2, 2),
  main = "Most variable genes in TCGA breast cancer samples"
)

Reflection: Do you think selecting only the most variable genes helped make patterns easier to see? Explain your reasoning.

Your answer:Yes. Using only the most variable genes reduces noise and highlights meaningful differences between tumors.

Reflection: If you saw two tumors with nearly identical expression patterns, what might you predict about those tumors? What additional information would you need before concluding they are biologically similar?

Your answer:I would predict they may belong to the same subtype. I would also need clinical information, mutation data, and patient outcomes before concluding they are biologically similar.

Add estrogen receptor status

Now we will add clinical labels.

We use:

er_status <- clin_sub$estrogen_receptor_status

er_label <- rep("", length(er_status))
er_label[er_status == "Positive"] <- "+"
er_label[er_status == "Negative"] <- "."

table(er_label)
## er_label
##       .   + 
##  13  57 201

Heatmap with ER labels

heatmap(
  expr_sub_scaled,
  labRow = "",
  labCol = er_label,
  cexCol = 0.5,
  margins = c(3, 3),
  xlab = "Tumor samples labeled by ER status",
  ylab = "Variable genes",
  col = heat_colors,
  zlim = c(-2, 2),
  main = "Gene expression heatmap with ER status labels"
)

Interpretation question: Do ER-negative tumors appear concentrated in any part of the heatmap?

Your answer:Yes, ER-negative tumors often cluster together, although the separation is usually not perfect.

Reflection: Suppose the ER labels matched the heatmap perfectly. Would that prove that estrogen receptor status causes the expression patterns? Why or why not?

Your answer:No. A perfect match shows a strong association but does not prove cause and effect.

Careful science note:
It is okay if the separation is not perfect. Real tumor data are complex. We are looking for patterns, not expecting every sample to behave perfectly.

Marker gene heatmap

Sometimes a small set of biologically meaningful genes is easier to interpret than the top 100 variable genes.

Here are several genes related to breast cancer subtype or tumor biology:

marker_genes <- c("ESR1", "PGR", "ERBB2", "FOXA1", "KRT5", "KRT14", "MKI67", "EPCAM")

marker_genes <- marker_genes[marker_genes %in% rownames(brca_expr_mat)]

marker_mat <- brca_expr_mat[marker_genes, our_samples]

marker_scaled <- t(scale(t(marker_mat)))
marker_scaled[is.na(marker_scaled)] <- 0

marker_genes
## [1] "ESR1"  "PGR"   "ERBB2" "FOXA1" "KRT5"  "KRT14" "MKI67" "EPCAM"
heatmap(
  marker_scaled,
  labRow = rownames(marker_scaled),
  labCol = er_label,
  cexRow = 0.9,
  cexCol = 0.5,
  margins = c(4, 8),
  xlab = "Tumor samples labeled by ER status",
  ylab = "Marker genes",
  col = heat_colors,
  zlim = c(-2, 2),
  main = "Breast cancer marker genes"
)

Question: How does ESR1 expression relate to ER status?

Your answer:ESR1 expression is generally higher in ER-positive tumors and lower in ER-negative tumors.

Reflection: Why is this heatmap easier to interpret than the heatmap containing 100 genes?

Your answer:It contains only a few well-known marker genes, making the biological patterns much easier to recognize.

This marker-gene heatmap may be easier to explain than the larger unsupervised heatmap.

CHALLENGE 1: PR status

Create labels for progesterone receptor status.

pr_status <- clin_sub$progesterone_receptor_status

pr_label <- rep("", length(pr_status))
pr_label[pr_status == "Positive"] <- "+"
pr_label[pr_status == "Negative"] <- "."

table(pr_label)
## pr_label
##       .   + 
##  13  81 177

Now plot the heatmap with PR labels.

heatmap(
  expr_sub_scaled,
  labRow = "",
  labCol = pr_label,
  cexCol = 0.5,
  margins = c(3, 3),
  xlab = "Tumor samples labeled by PR status",
  ylab = "Variable genes",
  col = heat_colors,
  zlim = c(-2, 2),
  main = "Gene expression heatmap with PR status labels"
)

Question: Does PR status look similar to ER status?

Your answer:Yes. PR status often shows a similar pattern because PR-positive tumors are frequently also ER-positive.

CHALLENGE 2: HER2 status

Create labels for HER2 status.

her2_status <- clin_sub$her2_receptor_status

her2_label <- rep("", length(her2_status))
her2_label[her2_status == "Positive"] <- "+"
her2_label[her2_status == "Negative"] <- "."

table(her2_label)
## her2_label
##       .   + 
## 108 125  38

Now plot the heatmap with HER2 labels.

heatmap(
  expr_sub_scaled,
  labRow = "",
  labCol = her2_label,
  cexCol = 0.5,
  margins = c(3, 3),
  xlab = "Tumor samples labeled by HER2 status",
  ylab = "Variable genes",
  col = heat_colors,
  zlim = c(-2, 2),
  main = "Gene expression heatmap with HER2 status labels"
)

Question: Does HER2 status separate as clearly as ER status?

Your answer:No. HER2 status usually does not separate the samples as clearly as ER status.

Reflection: Which receptor (ER, PR, or HER2) seems to show the strongest relationship with gene expression patterns? Were you surprised?

Your answer:ER generally shows the strongest relationship with gene expression patterns. This is expected because ER strongly influences many genes.Therefore; I wasn’t suprised but it is amazing to see the data.

CHALLENGE 3: triple-negative breast cancer

Triple-negative breast cancer means:

tnbc <- er_status == "Negative" &
  pr_status == "Negative" &
  her2_status == "Negative"

tnbc_label <- rep("", length(tnbc))
tnbc_label[tnbc] <- "TN"

table(tnbc_label)
## tnbc_label
##      TN 
## 244  27

Now plot the heatmap with TN labels.

heatmap(
  expr_sub_scaled,
  labRow = "",
  labCol = tnbc_label,
  cexCol = 0.5,
  margins = c(3, 3),
  xlab = "Tumor samples labeled by triple-negative status",
  ylab = "Variable genes",
  col = heat_colors,
  zlim = c(-2, 2),
  main = "Gene expression heatmap with triple-negative labels"
)

Question: Do triple-negative tumors appear as one clean group, or are they mixed with other tumors?

Your answer:They are often mixed rather than forming one perfectly distinct group.

Reflection: If triple-negative tumors do not all cluster together, what are two possible biological explanations?

Your answer:Different triple-negative tumors may have different genetic mutations, and they may belong to different biological subtypes despite sharing the same receptor status.

Final reflection

Final Reflection: Imagine you are a cancer researcher who has never seen these data before. Based on today’s analyses, what is one conclusion you feel confident making, and what is one question you would want to investigate next?

Your answer:One conclusion is that gene expression patterns are related to important clinical features, especially ER status. One question I would investigate next is whether these expression patterns can predict which patients respond best to different treatments.

The most important biological lesson is:

Gene expression patterns can reflect important tumor features, but real cancer data are complex and must be interpreted carefully.

Knit your report

Click:

Knit → Knit to HTML

Your final report should include: