Why Modeling?
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PET degradation by Chlamydomonas reinhardtii
A C. reinhardtii which expresses and secretes the enzymes PETase and MHETase could pose as a solution for the problem of micro-plastic polluted water. Nevertheless, the viability of PET degradation by C. reinhardtii at a larger scale is yet unknown. Models of biological systems allow us to design experiments in silico that are difficult to reproduce in vivo and give us special insights into the role that parameters might play in the given biological system. Therefore, to assess the efficiency of PET degradation by C. reinhardtii, a model of PET degradation in continuous culture of C. reinhardtii was designed.
The overall goal of the model is to determine the time needed to degrade 1 mg of PET. As we are building a bioreactor for C. reinhardtii, it is imperative to know the best parameters that have to be fulfilled by our bioreactor and our algae to achieve the successful degradation of PET. The expression rate, secretion rate and kinetics of the enzymes, such as also the cultivation density, influence the degradation rate of PET in the bioreactor. Based on this assumption, the model was designed to take these factors into account. The model was programmed in Tellurium (Choi et al., 2018) and encompasses six reactions. The reactions are as listed on Fig. 1 and Tab. 1.
"The overall goal of the model is to determine the time needed to degrade 1 mg of PET."
| Reaction | Rate | Value |
|---|---|---|
| R1: --> PETase_in | k1 | 0.01 µM/s |
| R2: --> MHETase_in | k2 | 0.01 µM/s |
| R3: PETase_in --> PETase_out | k3 | 1 |
| R4: MHETase_in --> MHETase_out | k4 | 1 |
| R5: PET + PETase_out --> MHET + PETase_out | k5 | 25 mg/(µMEnzyme*Day) |
| R6: MHET + MHETase_out --> TPA + EG + PETase_out | k6 | kcat*[E]*[S]/(km*(1+TPA/ki)+[S]) |
There are six reaction rates in the model, one for each reaction. There is the expression rates k1 and k2 of the enzymes and the secretion rates k3 and k4. The kinetics k5 of reaction numbre five are the kinetics of the PETase enzyme. The exact kinetics of the PETase are yet to be described in detail. Nevertheless, approximations can be found in literature. According to Ma et al., the optimized PETase I179F has a reaction rate of 25 mg per µM enzyme per day, which we used in this model (Ma et al., 2019). In contrast to the PETase, the kinetics of the MHETase are better studied. TPA seems to inhibit the functionality of the MHETase and its activity and inhibition can be described by michaelis menten kinetics (Palm et al., 2019). The reaction rates and their values are listed on Tab. 1.
Assumptions and Hypothesis
The reaction rate of the PETase enzyme is known to be one of the main limiting factors in PET degradation. It is a slow enzyme and because of this reason there have been efforts to optimize it (Ma et al., 2019). This was one of our main concerns while designing and programming our model. Our hypothesis was, that the process of PET degradation would be a slow process that is yet unviable for industrial application and that its speed could eventually be regulated to a certain degree by biological parameters and cultivation parameters. We decided to focus our simulations on two main parameters, one of them external to the biology of the cell, and the other of biological nature. The external parameter that we assumed could influence the degradation of PET was the cultivation density of C. reinhardtii. A higher cultivation density would lead to a higher concentration of the secreted enzymes PETase and MHETase and thus to a faster PET degradation. The biological parameter that we chose to variate was the enzyme kinetics of the PETase. By increasing the kinetics of the enzyme PETase by a factor of 1000, a significantly faster degradation of PET is expected. The arbitrary value of 1000 was chosen as an extremely optimistic optimization of the PETase to examine the effect of such a substantial change to the kinetic parameters.
Variation of the Cultivation Density
As a first approach, the cultivation density of the algae was varied to examine its effect on the degradation rate of PET. For the simulation presented in Fig. 2, the cell volume to culture volume ratio of 1:10 was examined. This means that of 10 ml culture, you would have 1 ml of cells. The time needed to degrade 1000 µg (or 1 mg) of PET was extracted from this simulation, leading to a total degradation time of 8200 s, or 2,27 hours. This is a very optimistic simulation for the cultivation of the alga C. reinhardtii because the cultivation density of 1:10 is very difficult to achieve and sustain. Even with this optimistic calculation, a PET plastic bottle weighing 40 g would need approximately 10 years to be completely degraded. According to Klein et al. (2105), the water of the Rhein river in Germany is polluted with micro-plastic up to 1 g per kg. This would mean that to clean one liter of water, assuming that all the micro plastic is PET, 94,5 days would be needed. To analyse a more realistic cultivation density, a simulation for a cultivation ratio of 1:100 was made, as can be seen on Fig. 3. This simulation led to the degradation of 1 mg of PET in 82000 s, or 22,7 h. According to this simulation, it would take approximately 100 years for a 40 g PET bottle to be completely degraded. These simulations show that even after altering the cultivation density parameter, an efficient degradation of PET on industrial scale is not in sight.
Results: Variating the Cultivation Density
Bereits 1874 hatte der Chirurg Theodor Billroth in Wien zweifelsfrei den das Wachstum von Bakterien hemmenden Effekt des Pilzes Penicillium erkannt.[8] Im Jahr 1923 erforschte in San José Clodomiro Picado Twight, ein ehemaliger Wissenschaftler des Institut Pasteur, die wachstumshemmende Wirkung auf Staphylokokken und Streptokokken. Seine Forschungsergebnisse wurden 1927 von der Société de biologie in Paris veröffentlicht.[9] Die weitaus öffentlichkeitswirksamere (Wieder-)Entdeckung der Penicilline begann mit einer verschimmelten Bakterienkultur ein Jahr darauf: Alexander Fleming, der sich am St. Mary’s Hospital in London mit Staphylokokken beschäftigte, hatte 1928 vor den Sommerferien eine Agarplatte mit Staphylokokken beimpft und dann beiseite gestellt. Bei seiner Rückkehr entdeckte er am 28. September 1928, dass auf dem Nährboden ein Schimmelpilz (Penicillium notatum) wuchs und sich in der Nachbarschaft des Pilzes die Bakterien nicht vermehrt hatten. Fleming nannte den bakterientötenden Stoff, der aus dem Nährmedium gewonnen werden konnte, Penicillin und beschrieb ihn für die Öffentlichkeit erstmals 1929 im British Journal of Experimental Pathology.[10] Er untersuchte die Wirkung des Penicillins auf unterschiedliche Bakterienarten und tierische Zellen; dabei stellte er fest, dass Penicillin nur grampositive Bakterien wie Staphylokokken, Streptokokken oder Pneumokokken abtötete, nicht aber gramnegative Bakterien wie beispielsweise Salmonellen. Auch gegenüber weißen Blutkörperchen und menschlichen Zellen oder für Kaninchen erwies es sich als ungiftig. Fleming kam trotz dieser Kenntnis offenbar nicht auf die Idee, Penicillin als Medikament einzusetzen. Fast zehn Jahre später – 1938 – machten sich Howard W. Florey, Ernst B. Chain und Norman Heatley daran, systematisch alle von Mikroorganismen gebildeten Stoffe zu untersuchen, von denen bekannt war, dass sie Bakterien schädigten. So stießen sie auch auf Flemings Penicillin. Sie reinigten es und untersuchten seine therapeutische Wirkung zunächst an Mäusen und dann auch an Menschen. Im Jahre 1939 isolierte René Dubos vom Rockefeller Institute for Medical Research aus menschlichen Tränen das Tyrothricin und zeigte, dass es die Fähigkeit besaß, bestimmte bakterielle Infektionen zu heilen. 1941 unternahmen Florey und Chain den ersten klinischen Test, der allerdings nur auf wenige Personen beschränkt war. Da die Herstellung von Penicillin noch sehr mühsam war, gewannen sie es sogar aus dem Urin der behandelten Personen zurück.[11]
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