# Avalekander Week 14/15

## Purpose

The purpose of this week was using MatLab to simulate models showing temperature dependence of the chemostat reaction demonstrated in the Tai et al. (2007) and (2005) papers. Additionally, the efficiency constant E was altered to reveal how yeast's metabolization of nutrients changes under different conditions and with different levels of nutrient available.

## Methods

MatLab files were obtained here from Dr. Fitzpatrick (zipped package).

#### Temperature Dependence Modeling

Arrhenius equation used:

• r = Ae^(-B/RT)
• r = rate (r)
• A = frequency factor
• B = energy of activation
• R = gas constant (8.3145J/mol K)
• T = temperature (K)
• T1 = T (12C)
• T2 = T (30C)
• Determined B after canceling out the A's and then plugging the values for r, T, and the universal gas constant, R into the Arrhenius equation. Once B was solved for then the value could be plugged back in to solve for A.
• Used the same equation once A And B were solved for with T = 15, 20, 25C to determine r at these temperatures.
• Modeled temperature dependence in MATLAB

#### Investigating the Efficiency 'Constant'

• The y and E values were taken from the "taiParamsRevised" MATLAB file for all four cases.
• Using both point-slope and slope-intercept formulas, an equation for each temperature E(y) was created relating the points, y and E.
• The "chemostat_2nutrient_dynamics.m" file was modified to process the two developed equations.
• Results were compared to the previous ones.

Variables found from "taiParamsRevised" file:

12 degree C Glucose-Limited:

• r=0.08
• T=285.15K
• y=0.504504
• E=14.2857

30 degree C Glucose-Limited:

• r=0.46
• T=303.15K
• y=0.054054
• E=14.2857

12 degree C Ammonium-Limited:

• r=0.08
• T=285.15K
• y=16.2162
• E=20.0000

30 degree C Ammonium-Limited:

• r=0.46
• T=303.15K
• y=15.3333
• E=25.0000

Variables calculated using Arrhenius equation:

• A = 4.979 * 10^11
• B = 69,840.58946
• r(15 degrees C) = 0.1087
• r(20 degrees C) = 0.1787
• r(25 degrees C) = 0.289

Equations developed using point-slope and slope-intercept formulas:

• 12 degree C: E = 0.3637y + 14.1022
• 30 degree C: E = 0.7012y + 14.2483

## Results

#### Temperature Controlled Chemostat

• Plots simulated using glucose as the limiting nutrient
• Residual glucose decreases as the temperature increases

## Conclusions

• Changing the temperature did not affect the steady states
• For a future experiment maybe including temperatures outside of the 12 and 30 degree range could be done to see if that makes a bigger difference than using the intermediary 15, 20, 25 degrees.

## Acknowledgements

I would like to acknowledge my partner, Angela Abarquez with whom I worked on presenting this information with and met with twice (Monday and Wednesday) and texted with often. We also facetimed on Wednesday evening to finish up and practice presenting. In addition, I want to acknowledge Dr. Fitzpatrick for his assistance in office hours on Wednesday. I also texted with Leanne a few times about how her graphs looked and if they were similar to how Angela and my graphs were turning out. "Except for what is noted above, this individual journal entry was completed by me and not copied from another source." Avalekander (talk) 19:56, 8 May 2019 (PDT)