Degradation Module

Overview

After detecting the presence of Δ9-THC, we need to design a degradation module to metabolise Δ9-THC to a sufficiently low concentration, which is harmless to human. Under the action of the enzyme, the Δ9-THC is degraded to Δ9-THC-COO-glu by the oxidation and glucuronization.

Description

The Metabolism of Δ9-THC

Concerning the metabolism of Δ9-THC, we design a metabolic pathway of Δ9-THC. The protein and enzyme related to the degradation, has been formed in the production of Pmr system in the detect module.

In phase 1, the majority of Δ9-THC is hydroxylated to 11-OH-Δ9-THC via CYP2C9 and CYP2C19. Then, the 11-OH-Δ9-THC is further oxidized to the psychoinactive Δ9-THC-COOH. This step is catalyzed by a microsomal aldehyde oxygenase whose affiliation to the CYP2C sub-family. In this step, we use the CYP2C9 to oxidize the 11-OH-Δ9-THC to the Δ9-THC-COOH.

In phase 2, the action of UGT enzyme glucuronizes the Δ9-THC-COOH to Δ9-THC-COO-glu, which is harmless to human body. In this step, we choose the enzyme UGT1A3 .Through this part, the Δ9-THC is finally degraded to harmless substance.

The pathway for Δ9-THC metabolism is as shown below:

ODE Model

The Michaelis-Menten Rate Law

To model the concentration of Δ9-THC and degradation substances, we use the Michaelis-Menten rate law, which used a quasi-steady-state assumption to simplify the following enzymatic reaction process:

This equation was converted into a quicker and more usable form, which described the reaction rate of a substrate becoming a product in the following way:

V_max is the maximum reaction rate based on the amount of enzyme present, K_m is the amount of substrate needed in order to achieve half of the maximum reaction rate, and [S] is the substrate concentration. We normalize V_max, K_m and [S] into the same units through dimensional analysis.

V_max is converted to the unit of nmol·min^-1·mg_-1. The mass of each enzyme can be exported by the detect module and be converted to the unit of mg. K_m and [S] are expressed in unit of nM.

In the parameter spreadsheet provided under "Parameter", parameter tables are provided which state the V_max and K_m values as they were found in the literature, which has been adjusted through dimensional analysis.

Assumptions

1. The process of Δ9-THC degradation by enzymes is basically not affected by inhibitors.
2. The enzymes are not degraded.
3. CYP2C9 and CYP2C19 possess the similar capacity to hydroxylate Δ9-THC.
4. Enzyme UGT is abundant and does not limit activation.

ODE Model

To simulate the degradation process of Δ9-THC, we build the ODE model by using the Michaelis-Menten rate law.
As what is said previously, the full ODE model is as followed:

Parameter

Parameter tables are provided as followed, which state the V_max and K_m values as they were found in the literature.

Results

To preliminarily test the rationality of ODE model, we estimated the concentration of Δ9-THC and the mass of the enzymes to obtain the initial result. From the figures above, we found that the degradation time of Δ9-THC is around 50 minutes, which was ideal and was close to the result experiment. Therefore, this ODE model can provide convincing simulation results for our Degradation Module.

Detection-Degradation Interaction

In our project, we want our pathway to work properly as follows:

1. Be sensitive to any sudden, high presence of Δ9-THC inside human body
2. Degrade the psychoactive ingredient as soon as possible
3. Stay deactivated when concentration of Δ9-THC is degraded to a safe level, thus preventing false triggering

Detailed explanation about each of the two modules above has proven that our pathway functions well in terms of the former 2 points. But it fails to provide any convincing proof about the last one, which could be the most important among all. So despite designing and testing them separately, it's of great significance to think of them as a whole as well. In this part, we are here to present our model for implementation of the interactions between detection and degradation.

What we do basically is adapt the ODE solving code of Degradation Module to an iteration-based version, and integrate it into the stochastic model for Detection Module. The time and concentration of THC taken in can be set manually. In our case we set the start time to 21600s (6hr), and as for the concentration, we refer to 2 different standards from the United States^[3] and Taiwan Province of China ^[4]. For the former, it's actually a standard for urine marijuana test proposed by University of Rochester, and considering the effect of urinary concentration, it's nearly impossible to meet this standard when taking medicine following medical advice. And for the latter, the news report indicates that it's a regulation on Δ9-THC for medical usage proposed by officials in Taiwan, China in recent years.

Simulation results for 2 standards respectively are shown above. It can be easily observed that the reporter protein spikes immediately and peaks at about 2~3 times of the average, and that the toxic ingredient and its psychoactive subsequent product, 11-OH-THC, have both been degraded to a much lower level that is harmless to human body in about 1 hour. These results have indicated a huge success of our design of both the detection and the degradation modules.