Conor Keith Week 5
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Purpose
The purpose of this assignment is to further explore chemostat models with multiple nutrients, specifically in regards to equilibrium nutrient concentrations and yeast populations. Additive nutrient use, multiplicative nutrient use, and rate limited nutrient use are the multiple nutrient models covered.
Workflow
Problem 1
- For problem one I simply analyzed the additive model to determine why it may be insufficient.
Problem 2
- For problem two, I set the three equations in the multiplicative nutrient use model equal to zero, and solved the equations simultaneously to find equilibrium values for the two nutrients and yeast.
Problem 3
- For problem 3, a created a function in Matlab containing the differential equations in the multiplicative nutrient use model. I created globals for each of the parameters and made and c1, c2, and y were my state variables. I then wrote a script and set the parameters equal to the values given on the assignment page, but let u1 vary. I then plotted the solutions to the differential equations with u1 equal to the different concentrations used in the journal club paper.
Problem 4
- For problem 4 I repeated the proves used in problem 2, this time using the equations from the rate limited nutrient use model to obtain equilibrium values of the two nutrients and yeast population.
Results
- The additive model may not be the best choice because it assumes that the yeast only utilize one of the two nutrients for growth. If the glucose or ammonium supply were to be exhausted, the yeast would still grow. In reality, this is not very likely, as yeast rely on both nutrients.
- PDF of work for problems 2 and 4
- Script for problem 3
Conclusion
- Additive models for nutrient use are incomplete, as they assume the yeast in the chemostat can grow using either of the two nutrients. In reality glucose and ammonium are both needed for yeast growth. With fixed values for glucose concentrations as in the journal club paper, equilibrium yeast and glucose stay constant, while equilibrium ammonium changes with varying concentrations. The rate limited nutrient use model yields equilibria similar to the multiplicative nutrient use model.
Acknowledgements
- For this weeks assignment, I spoke briefly with each person from the class on campus. I received data and instructions from the Week 4 assignment page. Except for what is noted above, this individual assignment was completed by me and not copied from any other source.
References
- Week 4 Assignment
- Ter Schure, E. G., Sillje, H. H., Verkleij, A. J., Boonstra, J., & Verrips, C. T. (1995). The concentration of ammonia regulates nitrogen metabolism in Saccharomyces cerevisiae. Journal of bacteriology, 177(22), 6672-6675.
Conor Keith 23:30, 15 February 2017 (EST)
Assignment Pages:
- Week 1 Assignment
- Week 2 Assignment
- Week 3 Assignment
- Week 4 Assignment
- Week 5 Assignment
- Week 6 Assignment
- Week 7 Assignment
- Week 9 Assignment
- Week 10 Assignment
- Week 11 Assignment
- Week 12 Assignment
- Week 14/15 Assignment
Individual Journal Entries :
- Conor Keith Week 2
- Conor Keith Week 3
- Conor Keith Week 4
- Conor Keith Week 5
- Conor Keith Week 6
- Conor Keith Week 7
- Conor Keith Week 9
- Conor Keith Week 10
- Conor Keith Week 11
- Conor Keith Week 12
- Conor Keith Week 14/15
Shared Journal Pages:
