Assignment Date: Thursday, March 15, 2018
Due Date: Thursday, March 29, 2018 @ 11:59pm
In this assignment, you will analyze gene expression data and learn how to make several kinds of plots in the environment of your choice. (We suggest Python or R.) Make sure to show your work/code in your writeup! As before, any questions about the assignment should be posted to Piazza.
This file contains pre-normalized expression values for 100 genes over 10 time points. Most genes have a stable background expression level, but some special genes show increased expression over the timecourse and some show decreased expression.
a. Cluster the genes using an algorithm of your choice. Which genes show increasing expression and which genes show decreasing expression, and how did you determine this? What is the background expression level (numerical value) and how did you determine this? [Hint: K-means and hierarchical clustering are common clustering algorithms you could try.]
b. Calculate the first two principal components of the expression matrix. Show the plot and color the points based on their cluster from part (a). Does the PC1 axis, PC2 axis, neither, or both correspond to the clustering?
c. Create a heatmap of the expression matrix. Order the genes by cluster, but keep the time points in numerical order.
A typical human cell has ~250,000 transcripts, and a typical bulk RNA-seq experiment may involve millions of cells. Consequently in an RNAseq experiment you may start with trillions of RNA molecules, although your sequencer will only give a few million to billions of reads. Therefore your RNAseq experiment will be a small sampling of the full composition. We hope the sequences will be a representative sample of the total population, but if your sample is very unlucky or biased it may not represent the true distribution. We will explore this concept by sampling a small subset of transcripts (1000 to 5000) out of a much larger set (1M) so that you can evaluate this bias.
In this file with 1,000,000 lines we provide an abstraction of RNA-seq data where normalization has been performed and the number of times a gene name occurs corresponds to the number of transcripts sequenced.
a. Randomly sample 1000 rows. Do this simulation 10 times and record the relative abundance of each of the 15 genes. Plot the mean vs. variance.
b. Do the same sampling experiment but sample 5000 rows each time. Again plot the mean vs. variance.
c. Is the variance greater in (a) or (b)?, and explain why. What is the relationship between abundance and variance?
d. Suppose you had received data where the number of times a gene name occurs corresponds to the number of reads mapped to that gene. In a few sentences explain how would you normalize the data, and what additional information would you need? [Hint: why is read count not enough?]
a. Using the file from question 2 along with this file, randomly sample 1000 rows from each file. Sample 5 times for each file (this emulates making experimental replicates) and conduct a paired t-test for differential expression of each of the 15 genes. Which genes are significantly differentially expressed at the 0.05 level?
b. Now sample 1000 rows 10 times from each file, equivalent to making more replicates. Which genes are now significant at the 0.05 level?
c. Perform the simulations from parts a, b but sample 5000 rows each time from each file. Which genes are significant?
d. For the four experiments you have conducted, create a bar plot that illustrates the differences in expression between the two files observed in each experiment. [Hint: The design of the plot is up to you, but you may find a stacked bar plot or a logarithmic axis useful.]
e. Now examine the complete files: which genes actually had different relative abundance? In a few sentences, explain your results for parts a,b,c in the context of this information. Address replicates and the size of the random sample. If you want, you can perform additional simple simulation experiments with this data - describe what you did and how it informed your answer to this question.