# Spring 2020 Assignment 9

From Course Wiki

Revision as of 20:34, 26 April 2020 by Steven Wasserman (Talk | contribs)

## Signals and systems

System function | $ \frac{1}{s+1} $ | $ \frac{s}{s+1} $ | $ \frac{s}{s^2+2s+1} $ | $ \frac{s}{s^2+0.1s+1} $ | $ \frac{1}{s^2+10s+1} $ |
---|---|---|---|---|---|

Magnitude plot | |||||

Phase plot | |||||

Step response | |||||

Pole/zero plot | |||||

Description |

**Magnitude Plots**

**Phase Plots**

**Step Response Plots**

**Pole Zero Plots**

## Feedback systems

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

Read The Frequency Dependence of Osmo-Adaptation in Saccharomyces cerevisiae and the supporting information.. 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 mathematical model did Mettetal,
*et. al.*use for Hog1 activation in response to a hyperosmotic shock? Express the model in the following forms- transfer function (TF)
- poles and zeros (ZPK)
- single differential equation (SDE)
- coupled differential equations (CDE)
- What mathematical model did Mettetal, et. al. use to account for nonlinearities in the system?
- Plot the frequency response (i.e. make a Bode plot) of the model over a range of $ \omega_0 $ and $ \zeta $ values that includes over damped, critically damped, and under damped.
- 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. - 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.
- Which of the step responses below corresponds to Mettetal's model for the wild-type strain and the mutant strain (neglecting the nonlinear element).
- Which of the Bode plots below corresponds to Mettetal's model for the wild-type strain and the mutant strain.
- Which of the pole zero diagrams below corresponds to Mettetal's model for the wild-type strain and the mutant strain.
- What are two questions that you have about the paper's methodology?
</div> |