# Team:NCTU Formosa/Modeling

### From 2012.igem.org

# Modeling

As we know, isobutanol is toxic to E.coli. So, we wonder how much E.coli can tolerate isobutanol. Therefore, we make a model to calculate the doubling time. According to the following figures, we realize that the maximum concentration of isobutanol that seriously hinder E.coli growth is 1.3%. The figure gives us an important information to help us understand the growing condition of E.coli and to adjust the incubation time in our project.

**Figure 1.**

**Figure 2.**

According to the equation of Thomas Robert Malthus, we can get the doubling time of E.coli in the following table.

**Figure 3.**

**Figure 4.**

Theoretically, through calculation with the Thomas Robert Malthus equation, we supposed to have a higher doubling time in higher concentration. However, there was an unexpected data occurred as shown in the table above. This phenomenon occurred in the doubling time of E.coli when it was cultured in 2% isobutanol concentrated medium. According to the equation we utilized, the doubling time should be higher than that of 1.3% isobutanol concentrated medium. We pondered this phenomenon may be because in 2% isobutanol concentrated medium, the E.coli appeared to have a shorter lag phase than that of the other lower concentrated medium, therefore affecting the algebra of the function S(t). But overall, despite the phenomenon described above, our modeling meet our expectation.

In addition to the isobutanol tolerance, we also made a model to calculate the doubling time under different temperature(40°C, 42°C, 44°C). The reason why we choose this three temperature is that the best isobutanol production yield is under 42°C in our previous experiment. We tried to figure out the relationship between isobutanol production and the amount of bacterium? We supposed that the higher amount of E.coli, the higher production yield we got. However, the assumption did not fit the observed data.

**Figure 5.**The OD value under three different temperature（Ave=Average of three OD value

We did a three repeated experiment. E. coli was incubated in 37°C until OD= 0.2, then transferred to three different temperature for 40 hours incubation.

**Figure 6.**Simulation diagram and doubling time.

We can realize that amount of E.coli is the most under 40°C and the least under 44°C. However, the growth rate of E.coli under 44°C is the fastest. According to our previous data, the highest yield of isobutanol is under 42°C~44°C incubation. We observed that the isobutanol yield in E.coli is the most under 42°C , even though the amount of E.coli is not the most. It shows that there is no direct relationship between the isobutanol production and the amount of bacterium. We also do qPCR to figure out the expression of mRNA under different temperature.