Difference between revisions of "Team:UMaryland/BCmodel"

The degradation of PET follows heterogeneous catalysis, where the reactants and the products [2] are in different phases. This creates difficulty in modeling the rate of degradation but teams such as Tianjin China has used Langmuir's Equation, secretion, and diffusion models to model the process of secretion, diffusion, adsorption, and degradation. However, while their models gave great insight into the mathematical relationships between these variables, it was not possible to obtain practical results as many of the variables used in the equation are not found in the literature and are difficult to obtain experimentally.

We have developed the “working cellulose” model which is more practical in predicting the rate of degradation when PETase with a cellulose binding domain is added to a degradation system. We modeled the rate of degradation of PETase as a zero-order system, where the concentration of the reactant is negligible to the rate of the reaction. This is present in many surface-limited chemical catalysis models, where the catalyst surface is saturated by the reactants, and the rate limiting step can be simplified in the surface area of the catalyst.

However, in our PET degradation model, the reverse holds true, where the concentration of PETase is the rate limiting variable compared to the surface area of the PET film when considering practical examples such as the degradation of a plastic bottle. We determined the following rate equation for the degradation of PET:

In our reduced and simplified zero order enzyme kinetics equation, we only need to know the product, time, and enzyme concentrations to determine the kinetic variable k to predict degradation. Through values obtained through the original PETase discovery paper by Yoshida et al, we were able to calculate the kinetic variable for both low-crystalline and high-crystalline PET.

At 30°C, pH 7.0, [PETase concentration] = 50nM, time = 18 hrs: PETase produced a total of 0.015 mM of product when fed high-crystalline PET and 0.3 mM of product when fed thin-sheet PET.

Using above data we can determine the rate constants.

Therefore, with the calculated local concentration of our enzyme and our enzyme kinetic parameter we were able to predict the rate of degradation of a plastic water bottle. If we desire 4 grams of PET to completely degrade to its subsequent product MHET, using the molecular weight of MHET (Mw = 210.185 g mol-1), we determine that the final concentration of MHET in a 1 L container would be 0.019 M. Since PET is not an aqueous substance, it is difficult to assign it a “concentration” value for our equation. Therefore we would determine the creation time of MHET rather than the degradation time of PET.

Using our equation:

With the following parameters:

- [PETase] = 3.41 µM

- k = 0.00463 s-1 for high crystalline PET

- [MHET] = 0.019 M

Solving for time, we predict that complete degradation of one PET bottle sandwiched between two bacterial cellulose sheets with 50% saturation of our PETase-CBD fusion protein will occur in 1.2 x 106 seconds, or approximately 14 days.

As degradation progresses, the appropriateness of our zero-order enzyme kinetics model will decrease as the surface area of PET available to our enzyme will become more significant. Therefore, a time to 50% degradation will be more indicative of the actual degradation of PET. We determined this value to be about 7 days.