Lkelly9 Week 6

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• Lauren M. Kelly
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Purpose

• The purpose of this assignment is to hypothesize what the impact of ammonium feet rate is on a quantity of interest in a chosen journal article and devise a system of differential equations that captures the important behaviors using state variables that are necessary to the process.

Workflow/Methods

• First, i picked one of the "Gaining a Better Understanding of the Fermentation/Respiration Switch" project and read the Albertin et al (2011) paper. Attached is a PDF of the notes that I took on this paper as I was reading it. I used these notes to better understand how different variables were related and write a system of differential equations.
  • Notes on Albertin et al Article
• Based on the reading, I concluded that the relationship between nitrogen concentration, K (population limit), CO2 production (Vmax) was important in regards to the fermentation respiration switch.

Results

Hypothesis

• Based on the findings in the Albertin et al (2011) paper and our work in previous assignments, it can be inferred that the nitrogen consumption is positively correlated to K (maximum population) and Vmax (maximal CO2 production rate). Increasing K will increase the amount of nitrogen the yeast can consume and the amount of CO2 the yeast can produce. A multiplicative nutrient use model will be utilized to display this relationship.
• It is assumed that the yeast are being grown in a chemostat.

State Variables

• q = dilution rate
• u = concentration of nutrient fed into the reactor (nitrogen or glucose)
• Nt = population of yeast at time t
• K = carrying capacity
• V = CO2 concentration
• Vmax = maximum CO2 production
• y = concentration of yeast
• c = concentration of nutrient (nitrogen or glucose)
• t = time

Differential Equations

Explanation

• Nitrogen Consumption
  • qu1 represents the nitrogen being fed into the reactor
  • qc1 represents the nitrogen being taken out of the reactor
  • y[(c1c2/K)] represents the amount of nutrient being assimilated by the yeast
• Glucose Consumption
  • qu2 represents the glucose being fed into the reactor
  • qc2 represents the glucose being taken out of the reactor
  • y[(c1c2)/K] represents the amount of nutrient being consumed by the yeast
• Yeast Population Growth
  • yR[(c1c2)/K] represents the growth rate of the yeast in the reactor as they consume the nutrients.
  • qy represents the yeast being taken out of the reactor at a constant rate
• CO2 Productions
  • Vmax = the maximum CO2 production
  • V = the concentration of CO2
  • The CO2 concentration is limited by the carrying capacity (K)

Acknowledgements

• Worked with Cameron M. Rehmani Seraji in Seaver 120 on February 22nd.
• Referenced the Week 5 Assignment in order to figure out a set of equations.
• Except for what is noted above, this individual journal entry was completed by me and not copied from another source.

Lauren M. Kelly 21:56, 22 February 2017 (EST)

References

• Dahlquist, Kam D. (2017) BIOL398-05/S17:Week 6. Retrieved from http://www.openwetware.org/wiki/BIOL398-05/S17:Week_6 on 22 February 2017.
• Albertin, W., Marullo, P., Aigle, M., Dillmann, C., de Vienne, D., Bely, M., & Sicard, D. (2011). Population Size Drives Industrial Saccharomyces cerevisiae Alcoholic Fermentation and Is under Genetic Control . Applied and Environmental Microbiology, 77(8), 2772–2784. http://doi.org/10.1128/AEM.02547-10