80 Analysis of microtubule catastrophe
Refresh yourself about the microtubule catastrophe data we have explored. The data set we used there was from a control experiment wherein Garner, Zanic, and coworkers compared measurements of microtubule catastrophe times for experiments using fluorescently labeled tubulin and unlabeled tubulin. In this problem you will investigate microtubule catastrophe using labeled tubulin for different concentrations of total tubulin.
You can download the data set for microtubule catastrophe times for various concentrations of tubulin here: https://s3.amazonaws.com/bebi103.caltech.edu/data/gardner_mt_catastrophe_only_tubulin.csv.
a) I shouldn’t have to say this, but perform an exploratory data analysis on the data set.
b) We will consider two models for microtubule catastrophe. In the first model, we consider catastrophe to be a Poisson process such that the time to catastrophe is Exponentially distributed. In the second model, the catastrophe times were Gamma distributed. Use the data set with 12 µM tubulin to compare these two models. Which model is preferred?
c) Using whichever model you favor based on your work in part (b), obtain parameter estimates for the other tubulin concentrations. Given that microtubules polymerize faster with higher tubulin concentrations, is there anything you can say about the occurrence of catastrophe by looking at the values of the parameters versus tubulin concentration?