# Difference between revisions of "Spring 2020 Assignment 9"

20.309: Biological Instrumentation and Measurement

## The Frequency Dependence of Osmo-Adaptation in Saccharomyces cerevisiae

Read The Frequency Dependence of Osmo-Adaptation in Saccharomyces cerevisiae and the supporting information.. This paper will be the focus of exam 2. We will discuss the paper and the supporting information on Thursday and Friday.

 Answer the following questions about The Frequency Dependence of Osmo-Adaptation in S. cerevisiae: What is the primary mechanism by which S. cerevisiae recovers from hyperosmotic shock? What model did Mettetal, et. al. use for Hog1 activation in response to a hyperosmotic shock? Mettetal, et. al. found that that the hyperosmotic shock response of wild-type yeast was (choose one): underdamped, critically damped, or overdamped. The response of the mutant (low Pbs) yeast was (choose one): underdamped, critically damped, or overdamped. In the plot below, indicate which step response corresponds to the wild-type strain and the mutant strain.

 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?

 Turn in all your MATLAB code in pdf format. No need to include functions that you used but did not modify.