Question

Use Matlab for all questions, include graphs and comment what you did and address all questions. Upload your m-files with your submission. In this portion of the homework you will reproduce the minimalistic cell cycle model of Goldbeter, published in PNAS in 1992, a publication posted under the "Biosim Resources" folder.

1) Use code from Berkeley Madonna listed below as a starting point to develop your own Matlab implementation. Use ode45 (RK4 solver) or your own RK4 solver from the previous homework to solve the set of ODEs, and graph the solutions for C, M and X over time. Of note, your solution might slightly divert from the one published in the PNAS paper.
2) Perform a sensitivity analysis to determine the parameter most sensitive to perturbation. We use a definition of the Sensitive Objective Function (SOF) suggested by Aldridge (see posted Nature paper on Physicochemical Modeling): SOF = (% change in outcome) / (% change of rate). Perturb each parameter/constant you use in the model (excluding the initial concentrations of C, M and X) by 5%, and determine the amount of the cyclin C at the end (last timepoint) of the simulation, to determine the SOF. Reset the parameter back to its original value and proceed to the next one. It is relevant to consistently increase or decrease by 5%. Produce a table in which you rank all parameters for their SOF sensitivity. What is the most sensitive parameter? Remark: Perform each perturbation manually, or program a loop to change parameters automatically.
3) Plot C dependent on X. This is called a phase plot revealing a limit cycle (see also Fig. 4 in the paper). Produce a second plot to demonstrate how a more dramatic perturbation of the initial conditions of C or X causes the system to not get back to cycle. This is a demonstration for the limit of robustness of the system.

Answer 1

To calculate the rate of cell division, measure the number of cells at different time points and calculate the change in cell number over time.

Step-by-step explanation:

In order to calculate the rate of cell division, you need to measure the number of cells at different time points and calculate the change in cell number over time. By dividing the change in cell number by the time interval, you can determine the rate of cell division.

An example calculation could be:

If you start with 100 cells at time t=0 and after 24 hours you have 200 cells, the change in cell number is 200 - 100 = 100 cells. The time interval is 24 hours. Therefore, the rate of cell division is 100 cells / 24 hours = 4.17 cells per hour.

This calculation can be repeated for multiple time points to determine how the rate of cell division changes over time.