Team:Brasil-USP/Modeling/EnzymaticReaction

Enzymatic Reactions

Modeling results


So far, we have modeled the production of enzymes that are capable of breaking rubber polymers, namely Lcp and RoxA. During the rubber degradation, however, no other products will be formed, only a bunch of small polymers with variable lengths. This means that, in a Michaelis-Menten fashion, our substrate and our product are the same. Then, we can ask which is the best way to model such behavior? Is Michaelis-Menten suitable? The result is partially yes, as we show below.

Figure 1- During the rubber degradation, Lcp and RoxA will break rubber polymers into smaller polymers. In a Michaelis-Menten fashion, our substrate and our product are the same. How can we solve it?

The main idea

This problem is not new, and in a similar way was studied before [1]. Since both our enzymes break polymers only in certain points, we can consider the substrate every breakable point in the system. See figure 2 to visualize this idea. In the figure, a polymer S has 3 breakable points. RoxA and Lcp will act on those points.

Figure 1- During the rubber degradation, Lcp and RoxA will break rubber polymers into smaller polymers. In a Michaelis-Menten fashion, our substrate and our product are the same. How can we solve it?

The only difference between Lcp and RoxA is simply how they break the polymer. RoxA has a kind of ruler: it always breaks at the lose ends of the polymer, generating one small piece and leaving the rest intact [2]. Lcp seems to break the polymer at random breakable points, creating a mixture of polymers with different sizes.

We will use this to find the proper kinetic of our enzymatic reaction.

Dynamics of the enzymatic reaction

Discussions and references

1- Cheng and Prud`Humme. Enzymatic Degradation of Guar and Substituted Guar Galactomannans, Biomacromolecules, 2000, vol 1, p.782.
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