Model

For the construction of a mathematical model that could provide insight into the future implementation of the project R-DETOX, it was decided to construct an equation that would result in the time, in months, of detoxification that could be achieved by the Device 2 of our modified genetic circuit. As a software, Microsoft Excel was used since, according to Wu, Ako and Hu in “A Useful Microsoft Excel Add-in Program for Modeling Steady-state Enzyme Kinetics” (2011), Excel is a fast and reliable tool for enzyme kinematic data analysis. It is our project’s purpose to mitigate the contamination in the Anones Lagoon produced by biochemical remains and with this model we could see a clear picture of the quantity of enzyme needed to reduce enough RDX so that the lagoon’s water falls below toxicity levels established by the EPA.

Using the applications Google Earth and Google Maps, which provide detailed information and views about geographical regions worldwide, we could approximate length and width measurements in order to then calculate the estimated volume for the lagoon. We searched for the Anones Lagoon and found measurements for length (848.17 m) and width (313.31 m). For the depth measurement, we were not able to find trustworthy information through research. However, we asked various Vieques residents that knew the area and have previously been involved in investigations of it if they could give us an approximation of the lagoon’s depth. With their answers, it was concluded on average that the lagoon’s depth varied in intervals of 3 through 16 feet (1 through 5 meters) depending on craters in the lagoon’s soil that have been developing over the years. Given this depth approximation, we were able to calculate the lagoon’s volume according to five different depth values: 1 m, 2 m, 3 m, 4 m, and 5 m. Table 1 shows the data approximations for the volume calculation of the Anones Lagoon and Table 2 shows the values for volume calculations in cubic meters and liters according to the five different depth measurements selected.

Having estimated the different volume measurements, we were able to calculate the quantity of substrate molecules per liter according to the five different volume values recognized as levels. This body of water has controlled access, therefore, we were not able to get samples directly from the lagoon. We opted for utilizing five possible RDX concentration values to create Models A through E (see Table 3) for each one of them. The set of values selected for the implementation of our model were 1 mg/L, 2 mg/L, 3 mg/L, 4 mg/L, and 5 mg/L. These values were decided to be treated as molecules, hence the proper conversions were made using substrate characteristics (Table 4).

The RDX concentration value established by the EPA as the maximum concentration of RDX that can be present in drinking water without causing adverse effects is 0.1 mg/L, as stated by the Agency for Toxic Substances and Disease Registry. This being said, it is important to know how much enzyme is needed to degrade RDX until reaching a concentration value that is considerably acceptable. We calculated the number of substrate (RDX) molecules per liter by multiplying each of the selected substrate concentration levels by the five levels of volume measurements mentioned previously (refer to Tables 5-9).

The evaluation of the degradation capacity of a single enzyme molecule was done by computing the quotient of the division of number of substrate molecules by the catalytic constant K_cat (s^-1) , or turnover number. The catalytic constant Kcat describes the number of times each enzyme molecule will degrade substrate molecules into products per unit time (seconds). The K_cat value was assumed to be 3.33 s^-1 , as determined in the article “The 1.5-Å Structure of XplA-heme, an Unusual Cytochrome P450 Heme Domain That Catalyzes Reductive Biotransformation of Royal Demolition Explosive” (Sabbadin et al., 2009). The experiments held for the article shared our project enzyme, substrate, and aerobic conditions. By completing this division for each of the five concentration levels and volumes, we obtained the amount of substrate molecules that should be degraded by a single enzyme molecule per second. Thus, this result brings insight into how capable our modified genetic circuit will be on achieving the detoxification of the Anones Lagoon.

Considering the magnitude and scope of the project, a rate measured in months for each model was used for further calculations (refer to Tables 5-9). Having this conversion, we were able to establish an approximated range of desired detoxification time in months. For each RDX molecule, enzyme molecules needed to remediate RDX were quantified. In Graphs 1-5, a tendency is noticed that as time progresses, less enzyme is produced because of the fact that less RDX would remain in the lagoon as breakage of RDX rings is occurring. The data showing this behavior is shown in Tables 10-14.