Leanne Kuwahara-Week 14/15

Purpose

To model temperature dependence of a chemostat experiment at 15, 20, and 25C.
To investigate the glucose efficiency and waster "constant" for the glucose and ammonium-limited cultures.

Temperature dependence modeling:
- Arrhenius equations used:
  - (1) k = Ae^(-Ea/RT)
  - (2) Ea = (Rln(k1/k2))/(1/T1-1/T2)
    - k = rate (r)
      - k1 = r cold (0.08)
      - k2 = r hot (0.46)
    - A = frequency factor
      - related to molecular collision
      - dependent on reaction
    - Ea = energy of activation
    - R = gas constant (8.3145J/mol K)
    - T = temperature (K)
      - T1 = T cold (12C)
      - T2 = T hot (30C)
Determined Ea using equation 2 and then plugged into equation 1 to find A
Used equation 1 with T = 15, 20, 25C to determine r at these temperatures
Modeled temperature dependence in MATLAB
- Added three conditions/cases (T = 15, 20, 25C) to the TaiParams sheet
- Used C-limited conditions determined from paper for feed concentrations of glucose and ammonium, residual concentrations of glucose and ammonium, and Y(glu/x)

Efficiency/Waste Modeling:
- Yeast produce more waste (EtOH and CO2) when glucose is plentiful
- Waste is relatively equal between temperatures
  - Prefer fermentation vs. respiration
- Compared efficiency of glucose conversion to biomass in C-limited cultures vs. N-limited cultures
Used (y,E) of C-limited and N-limited at 12 or 30C
Solved for m using y-y = m(x-x)
Solved for b using y = mx+b
Solved for efficiency using my+b, where y is the residual glucose

Part 1. Temperature Dependence

Residual glucose decreases as temperature increases
All plots were generated under the assumption of the limiting nutrient being glucose
- Residual concentrations of ammonium and glucose were adjusted to be within the range provided by the Tai et al. (2007) paper to best fit the model

Part 2. Efficiency/Waste Modeling

top: Original model where E = 1/Y
- E(12C, C-lim) = 14.2857
- E(12C, N-lim) = 20.0000
- E(30C, C-lim) = 14.2857
- E(30C, N-lim) = 25.0000
bottom: Effciency modified, where E = my + b
- 12C: m = 0.364532365; y = residual glucose (g) b = 14.08867026
- 30C: m = 0.701234358; y = residual glucose (g) b = 14.24776322
- E(12C, C-lim) = 14.2741
- E(12C, N-lim) = 20.0089
- E(30C, C-lim) = 14.2879
- E(30C, N-lim) = 24.9987

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