Modeling

To theoretically test our Decyclifier system, and to find ways to improve it, we have constructed two separate computer models. By modelling our system in Simbiology we aim to obtain a further understanding of the parameters that rule the whole Decyclifier system. These parameters can be analyzed separately for each part, or for the system as a whole. By modelling the effect of the rhamnolipids in our system in Java we aim to create a visual and analytical tool for the extracellular reactions of the system during various time spans and concentrations of PAHs, laccases and rhamnolipids.

The data generated by these models will make it possible to optimize the Decyclifier, thus theoretically maximizing the breakdown rate of PAHs. With this information, we hope to both improve our current project and provide guidance for any future related projects. Moreover, we seek to prove that our concept is valid and gauge the efficiency of the system.

SimBiology

Whole system analysis

The first model was built and simulated in the Matlab extension SimBiology. This extension made it possible to create a system of correlated reactions and to regulate their interactions graphically and mathematically. Doing so saved us from having to deal with the convoluted differential equations that inevitably follow from a system as complex as ours.

For the most part we used Henri-Michaelis-Menten approximations for our enzymatic reactions. Due to the fact that most of these reactions are catalyzed with a single substrate, this serves as a fair approximation. Moreover, as far as we are aware, none of the reactions involved are inhibited to any significant degree or otherwise affected by exterior substances. For the diffusion and gene regulation reactions, other novel approximations are used.

The enzymatic values used are theoretical and obtained from the online enzyme database Brenda. Using this source we found most of the Km values that we needed. In some cases, the data pertaining to the enzyme with our substrate in Pseudomonas putida was not available, and we had to resort to using related values. When a choice had to be made, we decided to use data concerning the correct substrate in the wrong bacterium rather than the opposite. This decision was based on the assumption that the enzyme works in approximately the same way in different bacteria and that the efficiency varies more in relation to the used substrate than it does with the bacterium. The Decyclifier has been tested/developed with genes encoding three different laccases. We have used theoretical values for the laccase CotA in the SimBiology-model.

There are three different versions of the SimBiology model. One main model where the Decyclifier’s whole system is represented, one where the naphthalene degrading pathway is represented and one where the salicylate-induced pathway is represented. This enabled analysis of the system as a whole with a slight focus on two of the different parts of the system. The main model has the initial value of 5 moles of naphthalene and 50 moles of dissolved benzo-a-pyrene. The naphthalene degrading model has the initial value of 5 moles of naphthalene. The salicylate induced pathway has the initial value of 5 moles of salicylate and 50 moles of dissolved benzo-a-pyrene. The initial values for the remaining substrate related components of the system was set to zero. These values are strictly arbitrary and serve only to create an initial outlook as to how the system behaves.

Java

Our Java-model was built to specifically study the effects of rhamnolipids on our PAH degradation. drJava allows us to form a visual and analytical tool that models the extracellular reactions with alterable initial conditions. The model is a simple representation of our system with Rhamnolipids, BaPs and Laccases, where BaPs represent PAHs and Laccases represent both laccases and dioxygenases. This model will allow the user to get an overview of the laccase/rhamnolipid/PAH - system and how it works in theory as well as collecting data about the degraded PAHs over time during different conditions. The collected data can give us an insight as to what degree the rhamnolipids improves the action of the laccase, and also what ratios that give the optimal enzyme activity.

BaPs, laccases and rhamnolipids are introduced in the model with random positioning and for every time step they move randomly. Rhamnolipids can attach to the BaPs, and BaPs can form aggregates with other BaPs. Rhamnolipids are less likely to stick to BaPs if there is already a rhamnolipid attached. BaPs are less likely to form aggregates with other BaPs if rhamnolipids are attached to the BaPs. Laccases degrade BaPs with higher probability if they are not in aggregates due to the increased probability of the enzyme's active site to reach the BaP.

To study whether the introduction method of laccases and rhamnolipids into the system affect degradation of PaHs, different variations of our model were constructed. Laccases and rhamnolipids were either introduced continuously to the system, at the same time as the BaPs or some time steps after BaPs are introduced in the system.

Due to the complexity of the real system, strictly arbitrary values regarding association, dissociation and breakdown of the respective components had to be decided. As such, the model only serves as a theoretic representation of the actual in vivo system but should still follow a similar pattern.

Last but not least, the speed and accuracy of the molecules was generated randomly. This in itself is not unrealistic, but since the maximum speed was chosen arbitrarily it does not necessarily represent reality.

In addition, the relationship in amount between the BaPs and the laccases have merely been estimated and the size ratio in our visual representation is completely unrealistic. This is mainly due to the fact that the laccase in reality is so much larger than the BaPs, which would make a visual representation very hard to interpret. Another major difference is that in our model, degraded BaPs simply disappear, as opposed to turning into the degradation product. In reality there would be an accumulation of product, which we have not taken into account in this model.

The number of BaPs in the system was studied during 500 time steps under different conditions; size of the interaction area, number of laccases, number of rhamnolipids and introduction method of laccases and rhamnolipids. For every set of conditions 100 simulations were run and data collected for every five timesteps. Graphs were produced using the mean value of the number of BaPs in the system for every measured time step.

Our results and data

Both of our models yielded data that helped us optimize the Decyclifier system. The Simbiology model showed us the rate-limiting step of our system, whilst the Java model showed that the system will indeed be improved by the presence of rhamnolipids.

Simbiology

Figure 2 shows how the concentrations/proportions between the different components vary over time in relation to its initial values.

From Figure 2, it is clear to see that our model successfully visualizes the degradation of naphthalene to salicylate. This in turn causes the induction of our main system which finally results in the degradation of dissolved benzo-a-pyrene. Figure 2 also shows that benzo-a-pyrene is degraded at a similar rate compared to naphthalene which indicates an effective system.

The Simbiology model of the whole system proved the rate limiting enzymes in our system to be 2-hydroxybenzalpyruvatealdolase and 1,2-dihydroxynaphthalene dioxygenase, both parts of the naphthalene degrading pathway. A future modification to the Decyclifier should therefore be to increase production of these enzymes in proportion to the rest of the enzymes in the pathway.

Naphthalene degrading pathway analysis

Figure 4 shows the relationship between the different components of our naphthalene degrading pathway. Concentration of naphthalene decreases over time at a slightly higher rate than the formation rate of salicylate. A slight accumulation of intermediate products prove that there is a rate limiting step present somewhere within the pathway The intermediates are identified as trans-o-Hydroxy-benzylidenepyruvate and 1,2-Dihydroxy-naphthalene where the first reaches the highest concentration. The rate limiting enzymes are therefore primarily the reaction catalyzed by 2-hydroxybenzalpyruvatealdolase (NahA) and secondarily the reaction catalyzed by 1,2-dihydroxynaphthalene dioxygenase (NahC). This was to be expected as these enzymes had the greatest Km values and the lowest Vmax values.

Analysis of salicylate-induced pathway

Figure 6 shows how the amount of free salicylate i.e. salicylate that is not bound to the repressor-protein decreases with the increase in output of the protein encoding genes. The amount of dissolved benzo-a-pyrene decreases as well while the amount intermediate breakdown product and the dioxygenase product, here annotated as unknown product increases. This also follows expectations.

drJava

In figures 8 to 12 we see the effect of varying rhamnolipid concentrations in the system. In all graphs the breakdown rate increases with increasing rhamnolipid concentration. Figure 9 shows how the breakdown rate of BaP depends on laccase and rhamnolipid concentration. Not surprisingly, the degradation rate is higher the more laccases is present in the system. It is clear from figure 9 that the ratio of laccase/BaP causes a greater degradation rate effect of BaP than the ratio of rhamnolipid/BaP. Therefore the priority should be in optimizing laccase production, although the presence of rhamnolipids will also improve the system.

Figure 10 shows that degradation of 100 BaP is faster in a smaller space (650x650 pixels) compared to in a larger space (1000x1000 pixels) when all other settings are the same, BaP/laccase ratio is 5 and rhamnolipid/BaP ratio is 0, 0.2 or 0.5. This is likely due to the increased probability of two molecules encountering each other in a smaller space. Figure 10 also shows that decrease in space from 1000x1000 pixels to 650x650 pixels gave a greater BaP degrading rate effect than increase of rhamnolipid/BaP ratio from 0 to 0.5.

Figure 11 shows that the BaP degrading rate is not significantly affected by laccases and rhamnolipids being introduced in the system at time step 0 or 20. In figure 12 introduction method A with laccases and rhamnolipids introduced to system at time step 0 is compared to B, continuous supply of laccases and rhamnolipids to the system, 1 laccase and 0, 1 or 2 rhamnolipids added every 5 time steps. As expected BaP degrading rate is higher in the beginning of the simulation for model A because of higher concentration of laccases and rhamnolipids. BaP degradation rate decreases when BaP concentration decreases. BaP degradation rate for B is very low at the beginning because of low concentration of laccases and increases as the concentration of laccase increases.