Lecture 2.4

Differential Gene Expression

Learning objectives

After this lecture, you should be able to do the following.

Explain what it means for a gene to be differentially expressed, and keep the size of a change separate from the evidence that it happened.

  1. Define a differentially expressed gene as one whose expected share of the RNA in a sample, averaged over repeats of the experiment, differs between two conditions.
  2. State the two separate answers an analysis gives for each gene: the evidence that its expression changed, and the size of that change.
  3. Interpret a whole-number \(\log_2\) fold change as a count of doublings or halvings, and state the fold change it stands for.
  4. Compare the noise in variant calling, sequencing error that repeated reads of one position average away, with the noise in differential expression, variation between replicates that only more replicates address.
  5. Given the \(\log_2\) fold changes of several genes, some of them negative, rank the genes by how large a change each reports, whichever way it runs.

Account for where the variation in the counts of a gene comes from, and for why biological replicates are needed to judge it.

  1. State that a count produced by random read sampling alone has a variance equal to its mean, the Poisson case.
  2. Define a biological replicate as an independent unit in the same condition, and a technical replicate as a repeated measurement of one unit.
  3. Given the mean count of a gene and its variance across replicates, classify the counts as consistent with Poisson noise alone or as overdispersed.
  4. Explain why replicate counts vary by more than Poisson noise predicts, as biological variation added to sampling noise, and what the dispersion, one number per gene, says about the size of that addition.
  5. Given a described design, classify each repeat as a biological or a technical replicate, and state how many biological replicates each condition has.
  6. Explain why only biological replicates show how much a gene varies between units treated alike, and why a test needs that amount to judge a difference.

Interpret the p-value that a differential expression test gives each gene, including what it does not tell you.

  1. State the null hypothesis a test holds for each gene: its true \(\log_2\) fold change is exactly zero.
  2. Explain a p-value as how often a difference at least as large as the one seen would turn up if the gene did not change.
  3. Explain why a small p-value is neither the probability that the gene is unchanged nor a measure of how large its change is.
  4. Given two genes with the same fold change, one whose replicates vary more than those of the other, predict which has the smaller p-value.

Account for why testing every gene at p < 0.05 fills a result with chance passes, and for what the false discovery rate controls.

  1. State that the false discovery rate is the expected share of false positives among the genes called.
  2. Explain why a gene that did not change still passes p < 0.05 about one time in twenty, so that testing many genes at once produces many chance passes.
  3. Given the number of genes tested and a statement that none changed, determine about how many pass a cutoff of p < 0.05 by chance.
  4. Given the number of genes called and a false discovery rate, determine about how many of the called genes are expected to be unchanged.

Read a table of differential expression results, and decide which genes belong on the hit list.

  1. Given the fold change and adjusted p-value of a gene, classify the gene by whether its change is large or small and its evidence is strong or weak.
  2. Predict whether a hit list grows or shrinks when the fold-change cutoff is raised, and when the adjusted p-value cutoff is tightened.
  3. Given a table of fold changes and adjusted p-values, a cutoff on the size of the change (up or down), and a cutoff on the adjusted p-value, determine which genes belong on the hit list.
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