Team:BGIC-Global/Model
Background
Being high school students, it is a little challenging for us to understand the concept & principle of modeling. Under the instruction of our supervisors, previously, we planned to use the data (growth curve of E.coli vs concentration curve of the dosed formaldehyde) collected from our project experiments to estimate the optimized product cycle.
However, facing the experiment failure again and again, there was a serious lag of our lab progress. While we were still trying hard to improve our experiments, we started to consider the possibility of building a new model with available data. After several rounds of discussion and some additional research, we decided to design a model, which could provide a relevant accurate application reference to our end-users, to improve the user experience.
The problem that our model tackles – a colorimetric chart for our end users!
As introduced in our product design, we provide a special culture medium, MacConkey broth purple to grow the engineered E.coli in our product. With a mild PH indicator, the liquid (mixture of bacteria and culture medium) will be colored yellow below pH 5.2, and violet above pH 6.8. Through the observation of the color change, we expect our end users could identify whether the bacteria is growing and when to replace the kit, with certain instructions.
When the bacteria E.coli B21 (which we use for our product) start to grow, they will metabolise lactose as their energy source, and produce lactic acid, which lowers the PH level of the liquid. Therefore, we need to provide a reference to our end users so that they’ll be able to confirm the product is working properly. There’s certain term of bacteria growth cycle. We also need to give instructions to our end-user, when the bacteria are almost disfunctional therefore they need to replace the kit.
However, facing the experiment failure again and again, there was a serious lag of our lab progress. While we were still trying hard to improve our experiments, we started to consider the possibility of building a new model with available data. After several rounds of discussion and some additional research, we decided to design a model, which could provide a relevant accurate application reference to our end-users, to improve the user experience.
The problem that our model tackles – a colorimetric chart for our end users!
As introduced in our product design, we provide a special culture medium, MacConkey broth purple to grow the engineered E.coli in our product. With a mild PH indicator, the liquid (mixture of bacteria and culture medium) will be colored yellow below pH 5.2, and violet above pH 6.8. Through the observation of the color change, we expect our end users could identify whether the bacteria is growing and when to replace the kit, with certain instructions.
When the bacteria E.coli B21 (which we use for our product) start to grow, they will metabolise lactose as their energy source, and produce lactic acid, which lowers the PH level of the liquid. Therefore, we need to provide a reference to our end users so that they’ll be able to confirm the product is working properly. There’s certain term of bacteria growth cycle. We also need to give instructions to our end-user, when the bacteria are almost disfunctional therefore they need to replace the kit.
Step 1: Detecting the relationship of PH level and the concentration of bacteria cells
Here we ultilized a group of data from our previous experiments and publicized research. The data show the PH level and cell concentration (converted from the OD600 value) every different hour.
For better data fitting effect, we firstly processed the data with the following formulas:
X = Conc. (cell/ml) / 10^9
Y = 7.5-PH
According to our observation, we found the curve most likely exponential, the function of which is,
Y = a * X ^ b
Then under the guidance of our modeling supervisors, we tried the R - Nonlinear Least Square Function. After deleting a few interfering dots, we eventually got the estimated coefficient and the exponent for our exponential function:
Y = 0.5552 * X ^ 1.9984
For better data fitting effect, we firstly processed the data with the following formulas:
X = Conc. (cell/ml) / 10^9
Y = 7.5-PH
Y = a * X ^ b
Then under the guidance of our modeling supervisors, we tried the R - Nonlinear Least Square Function. After deleting a few interfering dots, we eventually got the estimated coefficient and the exponent for our exponential function:
Y = 0.5552 * X ^ 1.9984
Step 2: Creating the colorimetric chart of MacConkey showing PH levels
We got the color references of 6 different PH levels of MacConkey.
We took the RGB color values from the center points of each reference picture, with which we were able to generate a list of gradients, using the linear interpolation function of Python. (Yes, we learnt more programming skills than mathematics knowledge through modeling.) Then we coded in Python to draw the colorimetric chart which contains 500 gradients.
Step 3: Marking the checkpoints
We decided to mark 3 checkpoints for our end users,
1. The product has started to work!
2. It’s suggested to replace the kit now…
3. The product is not working any more, please replace your kit at once!
Due to the lack of experiment result, we currently set the values according to the experience of our lab supervisors. The OD600 values of these 3 checkpoints were suggested to set as 0.3, 1.1 and 1.2.
After coding in Python, the 3 checkpoints were marked accordingly. And here’s the final chart!
1. The product has started to work!
2. It’s suggested to replace the kit now…
3. The product is not working any more, please replace your kit at once!
Due to the lack of experiment result, we currently set the values according to the experience of our lab supervisors. The OD600 values of these 3 checkpoints were suggested to set as 0.3, 1.1 and 1.2.
After coding in Python, the 3 checkpoints were marked accordingly. And here’s the final chart!
Impact to our project
1. We noticed that currently the checkpoints on the color bar is quite difficult to distinguish. It indicated us to adjust the initial PH level lower, maybe 7.0 will be much better.
2. With chart, our product will be even more user friendly and responsible.
2. With chart, our product will be even more user friendly and responsible.
Future improvements
1. We could apply more accurate data when we have new progress from the lab work, to improve the function of cell concentration and PH level.
2. We will try to mark more distinguishable checkpoints after optimizing our initial conditions, as well as conducting more tests.
2. We will try to mark more distinguishable checkpoints after optimizing our initial conditions, as well as conducting more tests.