Homework 6.1: Surviving osmotic shock (40 pts)
In an investigation of how mechosensitive ion channels imbue a bacterial cell with the ability to withstand an osmotic shock, Chure, et al. did an experiment where they placed a collection of bacterial cells in a microfluidic chamber. They then exposed the cells to an osmotic shock and observed whether each cell exploded or survived the shock.
The cells they used had fluorescently labeled mechanosensitive ion channels (MscL). The McsL copy number was varied by varying the sequence in the ribosome binding site (RBS) for the mscL gene, thereby inhibiting translation of mscL. From the fluorescent intensity that was measured simultaneously with the osmotic shock, they could compute the effective number of ion channels.
So, for each cell they had a data pair, \((N, S)\), where \(S\) is one if the cell survived and zero if it exploded.
You task is to develop a generative model for this experiment and then to get parameter estimates for this model using the observed data.
You can download the data set here. Note that if you are using AWS, this data set is not in the machine image, so you will need to load it in directly, e.g., as
df = pd.read_csv('https://s3.amazonaws.com/bebi103.caltech.edu/data/chure_mscl_survival.csv')
This problem is quite open-ended. You will necessarily be modeling this phenomenologically, as it is difficult to know the particulars of how copy numbers of ion channels can impart survivability. Think about how you might do prior predictive checks and posterior predictive checks. You will almost certinaly have to come up with your own way of doing this. This is a good exercise in model building and estimation therewith.