1.1 Many variables are stored in one column

• Gene name e.g. SFB2. Note that not all genes have a name.
• Biological process e.g. “proteolysis and peptidolysis”
• Molecular function e.g. “metalloendopeptidase activity”
• Systematic ID e.g. YNL049C. Unlike a gene name, every gene in this dataset has a systematic ID.
• Another ID number e.g. 1082129. We don’t know what this number means, and it’s not annotated in the paper. Oh, well.

1. Use the appropriate function provided in the tidyr library to split these values and generate a column for each variable.

2. Once you separated the variables delimited by two “||”, check closer the new values: You will see that they might start and/or end with whitespaces which might be inconvinient during the subsequent use.
   • To remove these whitespaces, R base provides a function called trimws(). Let’s test how the function works:
   • dplyr allows us to apply a function (in our case trimws()) to all columns. In other words, we would like to modify the content of each column with the output of the function trimws(). How can you achieve this? Save the result in a tibble called cleaned_data.

# Creating test string with whitespaces:
s <- "  Removing whitespaces at both ends "
s

## [1] "  Removing whitespaces at both ends "

trimws(s)

## [1] "Removing whitespaces at both ends"

3. We are not going to use every column of the dataframe. Remove the unnecessary columns: number, GID, YORF and GWEIGHT.

Look at the column names.
Do you think that our dataset is now “tidy”?

1.2 Column headers are values, not variable names

• Keep care to build a tibble with each column representing a variable: At this point we are storing the sample name (will contain G0.05 …) as a different column sample associated to values in expression column. Save as cleaned_data_melt

Now look at the content of the sample column. We are again facing the problem that two variables are stored in a single column. The nutrient in the first character, then the growth rate.

Use the same function as before to split the sample column into two variables nutrient and rate (use the appropriate delimitation in sep.

1.3 Turn nutrient letters into more comprehensive words

Right now, the nutrients are designed by a single letter. It would be nice to have the full word instead. One could use a full mixture of if and else such as if_else(nutrient == "G", "Glucose", if_else(nutrient == "L", "Leucine", etc ...)) But, that would be cumbersome.

using the following correspondences and dplyr::recode, recode all nutrient names.

G = "Glucose", L = "Leucine", P = "Phosphate",
S = "Sulfate", N = "Ammonia", U = "Uracil"

1.4 Cleaning up missing data

Two variables must be present for the further analysis:

• gene expression named as expression
• systematic id named as systematic_name

delete observations that are missing any of the two mandatory variables. How many rows did you remove?

2.1 Plot the expression data of the LEU1 gene

Extract the data corresponding to the gene called LEU1 and draw a line for each nutrient showing the expression in function of the growth rate.

2.2 Plot the expression data of a biological process

For this, we don’t need to filter by single gene names as the raw data provides us some information on the biological process for each gene.
Extract all the genes in the leucine biosynthesis process and plot the expression in function of the growth rate for each nutrient.

2.3 Perform a linear regression in top of the plots

Let’s play with the graph a little more. These trends look vaguely linear.
Add a linear regression with the appropriate ggplot2 function and carrefully adjust the method argument.

2.4 Switch to another biological process

Once the dataset is tidy, it is very easy to switch to another biological process. Instead of the “leucine biosynthesis”, plot the data corresponding to sulfur metabolism.

3.1 Perform all linear models

Perform a linear regression of expression explained by rate for all group of name, systematic_name and nutrient. By sure to convert the linear models to a tibble using broom as saved as cleaned_lm

The computation takes ~ 60 sec on my macbook pro. For test purposes, you may want to subsample per group a small number of genes

• How many models did you perform?

• bonus question: you have observed a warning essentially perfect fit: summary may be unreliable, why? How can we clean up the dataset to avoid it?

3.2 Explore models, intercept values

For the gene LEU1, let’s look again at the linear models per nutrient and add as a dashed black line for mean of all intercepts.

LEU1 linear models per nutrient

We can see that when leucine is the limiting factor, the yeast expresses massively this gene LEU1 to compensate. Remember that all experiments are performed at constant growth rates in this chemostat.

Now, compute the difference between the intercept and the mean(intercept) per systematic name, so for all nutrient per gene. And select the top 20 highest intercept values to their means. Save as top_20_intercept

• merge those 20 genes with the cleaned_data_melt to retreived the original data points

• plot the data points and linear trends for those top 20 genes. Instead of the systematic name in the header, use the molecular function (MF)

• what can conclude?

3.3 Explore models, slope estimates

We can now have a look at the slope estimates.

• first, filter the term for slope estimate rate and remove p-value that are missing. Save as rate_slopes

• display the p-values histograms per nutrient

• looking at those histograms, how do you estimate the ratio of null and alternative hypotheses?

• how can retrieved the genes that belong most probably to the _alternative hypothesis?

• display the histograms of both p and q values per nutrient