BE/Bi 103, Fall 2018: Homework 8¶
Due 1pm or 7pm, December 2¶
(c) 2018 Justin Bois. With the exception of pasted graphics, where the source is noted, this work is licensed under a Creative Commons Attribution License CC-BY 4.0. All code contained herein is licensed under an MIT license.
This document was prepared at Caltech with financial support from the Donna and Benjamin M. Rosen Bioengineering Center.
This homework was generated from an Jupyter notebook. You can download the notebook here.
Problem 8.2: Microtubule catastrophe, 40 pts¶
Note: This problem is best done after the lecture November 22.
In this problem, we use data from Gardner, Zanic, et al., Depolymerizing kinesins Kip3 and MCAK shape cellular microtubule architecture by differential control of catastrophe, Cell, 147, 1092-1103, 2011. The authors investigated the dynamics of microtubule catastrophe, the switching of a microtubule from a growing to a shrinking state. In particular, they were interested in the time between the start of growth of a microtubule and the catastrophe event. They monitored microtubules in a single-molecule TIRF assay by using tubulin (the monomer that comprises a microtubule) that was labeled with a fluorescent marker. As a control to make sure that fluorescent labels and exposure to laser light did not affect the microtubule dynamics, they performed a similar experiment using differential interference contrast (DIC) microscopy. They measured the time until catastrophe with labeled and unlabeled tubulin. We will carefully analyze the data and make some conclusions about the processes underlying microtubule catastrophe.
In the file gardner_mt_catastrophe_only_tubulin.csv (which you can download here), we have observed catastrophe times of microtubules with different concentrations of tubulin. To start with, we will consider the experiment run with a tubulin concentration of 12 µM. So, our data set consists of a set of measurements of the amount of time to catastrophe. We will consider three models for microtubule catastrophe.
- Model 1: The time to catastrophe is Exponentially distributed.
- Model 2: The time to catastrophe is Gamma distributed.
- Model 3: The time to catastrophe is Weibull distributed.
Note that these descriptions are for the likelihood; we have not specified priors.
a) Describe the three models in words. Give physical descriptions of the meanings of their parameters. Describe how these models are related to each other. Tutorial 3c will be useful.
b) Perform parameter estimates for the respective models and make model comparisons. Comment on what this means with respect to our understanding of how microtubule catastrophe works.
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?