# Desireegonzalez Week 11

## Purpose

• The purpose of this assignment is to run a model of the nutrients and population growth seen in a chemostat experiment by running differential equations using MATLAB to produce a visual representation of the experiment; specifically visualization during steady state.

## Methods

### First Steps in Population/Nutrient Chemostat Modeling

1. Look at the following document for the weekly assignment and background on the chemostat experiment this document.
• Use the formulas and values in this document to calculate, by hand, the values for concentration of nutrient and yeast cells.
2. Next, use the MATLAB files chemostat_script.m and chemostat_dynamics.m to simulate a chemostat and compare the computations to a steady state outcome.
• Use the parameter values q = 0.10 (1/hr), u = 5 (g/L), E=1.5, r=0.8 (1/hr), K = 8 (g).
• Simulate the system dynamics using the MATLAB files and the parameters above.
• Be sure to save the graphs and upload them to your Openwetware journal.

## Results

1. What are the steady states of cell biomass and nutrient mass?
• Based on my hand calculations, the steady states of cell biomass and nutrient biomass are 1.143g and 2.57g respectively.
2. Assuming a 2 liter chemostat, what are the steady state concentrations of cells and nutrient?
• The steady state concentrations of cells and nutrient assuming a 2L chemostat are 0.5715g/L and 1.285g/L respectively.
3. Answer the following questions using the simulation created by MATLAB.
• Do the graphs show the system going to steady state?
• The graphs do show the system going to steady state, since the graph eventually levels off to a plateau. In steady state, the graph flattens out over time and looks like it is at equilibrium.
• The steady state values shown by the graph and the MATLAB calculations are very similar to the hand calculations that I did using the differential equations given.
• The MATLAB values calculated in the script were 1.1424g for cell biomass and 2.5724g for nutrient biomass.
• Be sure to save the graphs and upload them to your journal.
• BONUS: can you get two y-axes, with the second one to the right of the picture like in the journal articles you’ve read?
• I was unable to figure out how to get the two y-axis on one graph.

## Data Files and Images

• Attached in this zip file below are the MATLAB files I used, the graph that resulted from MATLAB, and a photograph of my hand calculations.

## Acknowledgements

• I communicated in person with my homework partner, Sahil to clarify what we needed to do for the assignment.
• In addition, I communicated with Leanne to ask a question about figuring out how to add the second axis for the bonus question.
• The MATLAB files needed for the completion of this assignment were provided by Dr. Dahlquist and Dr. Fitzpatrick.

Except for what is noted above, this individual journal entry was completed by me and not copied from another source.

Desireegonzalez (talk) 18:39, 10 April 2019 (PDT)

## References

Dahlquist, K. & Fitzpatrick, B.G. (2019, April 8). BIOL388/S19:Week 11. Retrieved from https://openwetware.org/wiki/BIOL388/S19:Week_11 on 8 April 2019.

Dahlquist, K. & Fitzpatrick, B.G. (2019, April 8). Biol 398/Math 388 Week 11 Assignment: A Simple Chemostat Model of Nutrients and Population Growth [PDF].

MATLAB (Version R2014b) [Computer software]. (n.d.). Retrieved 8 April 2019.

Below are the links to all the Assignments and Journal Entries of the Spring 2019 Semester.

User Page: user:desireegonzalez

Template Page: template:desireegonzalez

Weekly Assignment Pages:

Individual Journal Entry Pages:

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