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Team:UIUC Illinois/Modeling
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Revision as of 19:00, 17 October 2014
Mathematical Modeling of Caffeine Degradation Pathway
To predict the result of bioreactor, we used mathematica to solve differential using Michaelis-Menton equation. The strength of utilizing mathematica rather than matlab was that it allowed us to set up the value of several constants as varying rather than setting it as invariant. Kcat & Km values were obtained through research papers by Swati & Sathyanarayana (2006), and Ryan M.Summers (2010).
This is caffeine demehtlyation pathway by demethlyase. It goes from Caffeine to theobromine to 7-methylxanthine to xanthine. The other pathway is caffeine dehydrogenase. It goes from Caffeine to Trimethyl Uric acid.
First equation corresponds to caffeine concentration at different time. Second corresponds to the concentration of next product at different time.
Parameters
| Name | Description |
|---|---|
| Vm | Maximum rate of system |
| Kcat | Maximum number of substrate molecules converted into products |
| Km | Substrate concentration where the reaction rate is half of maximum (depend on both enzyme and substrate) |
Fig1. Caffeine Demethylation Pathway.
Modeling Dog's intestine
Description:
In addition to the model of the degradation of caffeine through the two pathways as shown above, it is possible to model the transport of caffeine through two body compartments: blood, small intestine. By doing so, we could understand the optimal levels of bacteria that we would need in order to degrade the maximum concentration of caffeine. In the research book “Solving Ordinary Equations in R” by Soetaert (2012), they list two equations which could model any drug concentration in the intestine represented by y_1 and in the blood represented by y_2
a is the absorption rate of drug from the intestine , b is the removal rate of drug from the blood, and u(t) represent a time dependent dosage of the drug into the intestine. In our case, since bacteria is involved in degrading caffeine, there would be an extra variable in the equationy_1': the degradation rate from bacteria. With these equations, the model should have a similar behavior as below
Where initial concentration of the drug in the blood is 0 but rises exponentially until the drug gets absorbed by the intestine, in which case, concentration of the drug in the blood starts to fall. This pattern of increasing to decreasing concentration of drug in the blood over a period of time is a result of the daily dosage of drug given. Similarly, the concentration of drug in the intestine increases at a rapid rate once the drug is absorbed into the intestine and decreases over time as the drug is being removed from the system. However, in our case with the bacteria, the rate at which the concentration of the drug is decreasing will be faster.
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