In Assignment 8 you upgraded your microscope to make two-color images, and fabricated a microfluidic device that we used to switch the flow through the device from two fluid reservoirs. In Assignment 10, we'll use this new setup to replicate part of the experiment described in the following paper:
In preparation for this experiment, we're going to write the analysis code needed to extract the Hog1 protein's response from images of yeast cells.
To get started, read Mettetal's paper.
Our goal for assignment 10 is to reproduce the bode plot in the paper (Figure 2 B and C), and fit it to a model second-order system. We will only measure the 'wild type' yeast strain, since measuring the mutant would take too much time.
- What mathematical model did Mettetal, et. al. use for the yeast response network? Express the model in the following forms: transfer function (TF), poles and zeros (ZPK), single differential equation (SDE), and coupled differential equations (CDE). Express the TF, SDE, and ZPK models in terms of the undamped natural frequency, $ \omega_0 $, damping ratio $ \zeta $, and/or damped natural frequency $ \omega_D $.
- Find an expression for the step response and plot it over a range of values of $ \omega_0 $ and $ \zeta $. A hand-drawn plot is fine, but you should probably look into MATLAB's step function.
- Plot the frequency response (i.e. make a Bode plot) of the system over a range of $ \omega_0 $ and $ \zeta $ values that includes over damped, critically damped, and under damped.
- What are two questions that you have about the paper's methodology or how we're going to implement the experiment in 20.309?
Next, head over to Part 1 of this assignment, where you'll answer some questions about the paper and write your analysis code:
Submit your work on Stellar in a single PDF file with the naming convention <Lastname><Firstname>Assignment9.pdf.
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