# 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.

## Protocol

1. 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)
2. Determined Ea using equation 2 and then plugged into equation 1 to find A
3. Used equation 1 with T = 15, 20, 25C to determine r at these temperatures
4. 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)
1. 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
2. Used (y,E) of C-limited and N-limited at 12 or 30C
3. Solved for m using y-y = m(x-x)
4. Solved for b using y = mx+b
5. Solved for efficiency using my+b, where y is the residual glucose

## Results

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

## Acknowledgements

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