Team:PuiChing Macau/Model
Food Waste Model
I. Objective
Our project goal is using
II. Assumptions
- E.coli grows best in LB broth
- Nutrient value is the only factor that affects the growth of E.coli
- Sugar, protein, and fat are the major factors that affect the growth of E.coli
- Linear (euclidean space) correlation between nutrient value and growth ofE.coli
III. Symbols
| SYMBOLS | MEANING |
|---|---|
| a to z | Amount of food waste in 100g |
| X | The nutrient value of food waste per 100g |
 |
The total nutrient value of combined food waste |
 |
The standardized total nutrient value of combined food waste |
 |
The nutrient value of LB broth |
IV. Modeling Process
IV.I. Gather data
The recipe of the LB broth contains 10g of Trypton, 5g of yeast extract, and 0.5g of Sodium Chloride [1]. We gathered the nutrient value of LB broth as shown in the following:
| Nutrient | Amount (gram per 100g of LB) |
|---|---|
| Total fat | 0.045 |
| Total Sugars | 0.08 |
| Total Protein (amino acids) | 11.195 |
Table 2. The nutrient value of LB Broth
Then, we divided common food waste into multiple categories, including staple food, meat, vegetables, and fruit, and obtained data from the U.S. DEPARTMENT OF AGRICULTURE, FoodData Central Data, FNDDS 2017-2018 for the nutrient value of different food waste.
Table 2. The nutrient value of LB Broth
IV.II. Compare the nutrient value of different combinations or stocks of food waste with LB broth using root mean squared error
- Sum up the nutrient value of different combinations or stocks of food waste
- Standardization by dividing the amount of food waste
- Using root mean square error mean absolute error to compare the nutrient value of LB broth with food waste
- Normalize our data by dividing the nutrient value of LB broth and calculate its relative root mean square error
- Finding out the minimum value of RMSE or RRMSE using the fmincon function in Matlab
- Using the minimum value of RMSE or RRMSE to find the corresponding amount of each food waste needed for optimal growth of E.coli
V. Result
Fig 1. RMSE value compared with LB broth (error bar=mean±SD)
Fig 2. The log ratio of food waste using RMSE (error bar=mean±SD)
Fig 3. RRMSE value compared with LB broth (error bar=mean±SD)
Fig 4. The log ratio of food waste using RRMSE (error bar=mean±SD)
We use both RMSE and RRMSE (Eq. 3 & Eq. 4 respectively, the smaller the better) to predict the optimal food waste ratio. In order to check, on average, which is the best combination of food waste types, we averaged the ratio and RMSE/RRMSE across the same type of food, as shown in the figures (Fig.1-4). When using the normalized RRMSE prediction, the combination of rice and vegetables, with 1 rice :10.59 vegetables (log10=1.025), can best mimic the LB Broth, implying that E.coli may grow the best under this combination of food waste mixture. Another reasonable group to mimic the LB Broth is the combination of vegetables and bread, as we can see that the average ratio is 10:4.16 (log10=-0.381). On the other hand, the model predicts that the mixture of beef and egg performs the worst in mimicking a suitable environment for E.coli to grow.
We use both RMSE and RRMSE (Eq. 3 & Eq. 4 respectively, the smaller the better) to predict the optimal food waste ratio. In order to check, on average, which is the best combination of food waste types, we averaged the ratio and RMSE/RRMSE across the same type of food, as shown in the figures (Fig.1-4). When using the normalized RRMSE prediction, the combination of rice and vegetables, with 1 rice :10.59 vegetables (log10=1.025), can best mimic the LB Broth, implying that E.coli may grow the best under this combination of food waste mixture. Another reasonable group to mimic the LB Broth is the combination of vegetables and bread, as we can see that the average ratio is 10:4.16 (log10=-0.381). On the other hand, the model predicts that the mixture of beef and egg performs the worst in mimicking a suitable environment for E.coli to grow.
VI. Conclusion and Outlook
Overall, we here use models to optimize and different combinations of food waste are able to mimic the LB and thus optimize the growth of E.coli . To the best of our knowledge, this kind of food waste optimizing modeling has not been done in the past. Therefore, We believe this model can not only help our project but also other studies in food waste optimization. Moreover, our models here can also be applied to optimize food waste from different stocks of food instead of different kinds, where nutrient value can be computed by averaging.
Due to time and resource limitations, we here did not use wet-lab experiments to further check which model (RMSE/RRMSE) can generate better predictions, which is one of the things we plan to do in the future. Also, further researchers can try to adapt non-euclidean distance error metrics [2], because we would expect a linear correlation of nutrient value and the actual growth. Here, although we have not yet built the model that can accurately optimize using food waste for growing microorganisms, our method can provide the basis for other researchers to further investigate.
Reference
[1] Sezonov, G., Joseleau-Petit, D., & D'Ari, R. (2007). Escherichia coli physiology in Luria-Bertani broth. Journal of bacteriology, 189(23), 8746–8749.
[2] Botchkarev, A. (2018). Performance metrics (error measures) in machine learning regression, forecasting and prognostics: Properties and typology. arXiv preprint arXiv:1809.03006.