20.309: Biological Instrumentation and Measurement
Signals and systems
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Fill out the table below. Match each system function with its Bode magnitude and phase plot, step response, and pole zero diagram. (Write one letter A-E in each box below.) In the row labeled “Description,” write a descriptive name of each system, such as “low-pass filter” or “overdamped second-order system.”
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System function
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$ \frac{1}{s+1} $
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$ \frac{s}{s+1} $
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$ \frac{s}{s^2+2s+1} $
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$ \frac{s}{s^2+0.1s+1} $
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$ \frac{1}{s^2+10s+1} $
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Magnitude plot
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Phase plot
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Step response
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Pole/zero plot
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Description
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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.. This paper will be the focus of exam 2. We will discuss the paper and the supporting information on Thursday and Friday.
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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.
f) Indicate which of the pole zero diagrams below corresponds to the wild-type strain and the mutant strain.
g) Indicate which curve in the Bode plots below corresponds to the wild-type strain and the mutant strain.
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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?
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Turn in all your MATLAB code in pdf format. No need to include functions that you used but did not modify.
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Navigation
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