Team:Uppsala Universitet/Model
Introduction
For the organism to be able to degrade lignin it needs enzymes capable of doing this. Several non-specific peroxidase enzymes were considered such as manganese peroxidase (MnP), lignin peroxidase (LiP) and horseradish peroxidase (HRP). Modeling was used to compare the enzymes to see which one was the most suitable candidate to focus on with our project. For the system to function, it needs a source of hydrogen peroxide (H2O2) to fuel the reaction and the enzyme aryl alcohol oxidase (AAO) was chosen as the supplier of hydrogen peroxide.
To model the system a fundamental understanding of all the involved reactions was necessary. Reaction kinetics is a method which describes the rate at which reactions occur. Reaction kinetics can be used to derive a mathematical expression for how the enzymes used in the project would function together. Reaction kinetics can be simplified using Michaelis-Menten kinetics which yields an expression that can be solved mathematically.
Figure 1 shows that AAO uses the substrate such such as primary aromatic alcohols to produce H2O2 which HRP then uses to degrade lignin, a fraction of which can be used as a substrate. The substrate is not destroyed when it reacts to form H2O2 but is converted into a more stable form of the substrate which can be considered to be the final product.
The system of reaction can be described by the following equations [1]:
Table 1 describes the constants in the equations above. These equations form a system of nonlinear differential equations. The equations in the system can be restated using Michaelis-Menten equations:
The description of the constants and variables in the equation system can be found in table 1. They are solved using the numerical solving method ode45 that is built into the mathematical software Matlab. For this it is assumed that the solution is saturated with lignin and receives a constant influx of lignin.
Table 1: Descriptions of the variables and constants used in the model.
| Variable / Constant | Description |
|---|---|
| [S] | Concentration of Substrate |
| [H2O2] | Concentration of Hydrogen peroxide |
| [P] | Concentration of Product (Degraded lignin) |
| VX | The maximum velocity of the reaction |
| vX | The reaction velocity of the reaction |
| KM,X | The michaelis konstant |
| u | The fraction of product that also can be used as substrate. |
Due to the nonhomogeneous structure of lignin and the variation of possible substrates, a single substrate and lignin substitute was focused on to simplify the system. The substitute for lignin and the substrate was chosen to be veratryl alcohol due to it having a structure similar to that of lignin and that reactions with it has been studied with all of the enzymes of interest. The concentration of enzymes was derived from the expression levels of the enzymes and the expression levels of the peroxidases were set in a similar manner.
Table 2: The values of constants in the model for veratryl alcohol.
| Enzyme | KM /(mM) | kcat /(s-1) | Enzyme concentration /(10-5 mM) |
|---|---|---|---|
| Lignin peroxidase | 3.54 [3] | 13.72 [3] | 2.3 [2] |
| Manganese peroxidase | 5.3 [4] | 5.33 [4] | 2.3 [2] |
| Horseradish peroxidase | 2.74 [5] | 8 [5] | 2.3 [2] |
| Aryl-alcohol oxidase | 0.54 [7] | 114 [7] | 7.22 [6] |
Due to the nonhomogeneous structure and the variation of the size of lignin the degraded lignin derivatives may take a range of different forms that act as better or worse substrates for AAO, therefore an analysis of the effect of the degraded lignin that can be used as substrate was done. The value of u was varied to investigate the effect of how it would affect the system. There were also different starting concentrations of all components that could be taken into consideration. The starting concentrations used were [H2O2]=[S]=1 mM.
Results and discussion
The solution to the system of differential equations for the different enzymes yield three sets of data and three corresponding graphs, see figures 2-5. The fraction of degraded lignin that could be used as substrate was set to 0 (u=0). The reaction for AAO is much faster than that of the peroxidase due to the higher reaction rate and higher concentration of AAO. Therefore the concentration of substrate will be low for most of the reaction, it will be used up by AAO almost as soon as it is produced by the peroxidase.
Figure 5 shows that LiP reaches the maximum concentration first and MnP reaches it last which could also be expected from the values seen in table 2. The MnP reaches maximum after about 3 days, HRP reaches maximum after slightly more than a day and LiP reaches maximum after slightly less then a day. The time it takes for each enzyme to reach maximum concentration of degraded lignin is proportional to the reaction rates of the enzymes.
Figure 6 shows that the time it takes for the reaction to reach the maximum is dependent on the fraction of degraded lignin that can be used as substrate and shows that the amount of lignin that can be degraded increases with u.
Conclusion
The simulations show that only a small amount of hydrogen peroxide is needed for the lignin degradation reaction to complete within a reasonable time-frame. This suggests that the reaction does not need to be supplied with hydrogen peroxide to be self-sustaining. The simulations also show that the enzymes do not have to be concentrated for the system to work efficiently. All the peroxidases would work within a reasonable time-frame, meaning any of them are suitable candidates for the system of interest.
References
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[6] Viña-Gonzalez, Javier, et al. “Functional Expression of Aryl-Alcohol Oxidase in Saccharomyces Cerevisiae and Pichia Pastoris by Directed Evolution.” Biotechnology and Bioengineering, vol. 115, no. 7, July 2018, pp. 1666–74. DOI.org (Crossref), doi:10.1002/bit.26585.
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