Introduction: Questions and outline
Looking at synthetic biology and the iGEM-competition as a team participating for the first time, we were astonished by the sheer amount of parts and devices already existing. After forming an idea of how a part can look like and coming up with possible functions we can let C. reinhardtii perform, there was one question that arose: What other characteristics does a part - no matter if DNA-sequence or other hardware - need to perform its function optimally? This general engineering question comes up early in the Design phase, where ‘other characteristics’ is defined by parameters which influence or are assumed to influence the performance of the part.
The aim of our models is not only to provide an overview of all the single components and their interrelations, but in a next step to also provide us with engineering strategies and reveal possible experiments that need to be performed. Out of reasons described on the Design-Page, we at first thought a whole cell model based on already existing metabolic reconstructions would be the right way to go. As we realized throughout our project and literature research that time was scarce and our demands could be met better in a more specialized and less time consuming way, we instead decided to focus on more special aspects of the system instead of the system cell as a whole. These are namely the PET-degradation we aimed to achieve in C. reinhardtii, the illumination of the cultivation vessel and the first step of CO2 fixation through carbonic anhydrases. For these three aspects our models gave feedback to our design process and helped us in pinning down important parameters for the subsequent building, testing and learning stages in the lifecycle of a part.
Model of 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.
Results: 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: Improving the PETase Kinetics by Factor 1000
The results for the first simulations, shown in Fig. 2 and Fig. 3, confirmed that the PETase kinetics are slow, especially in comparison to the kinetics of the MHETase. On the aforementioned graphs, the curve describing the concentration of MHET stays constant at a value converging to zero. This means that the MHETase immediately converts all MHET to terephthalate (TPA) and ethylene glycol (EG), demonstrating a big difference between the kinetics of the PETase and MHETase. Because the enzyme PETase is much slower than MHETase, MHET can not be accumulated but is rather immediately degraded to TPA and EG. Advanced methods to improve enzymes, for example by directed evolution, have shown that it is possible to drastically improve the kinetics of an enzyme. To assess the effect of an optimistically enhanced and improved PETase on the degradation rate of PET, two simulations were made, where the kinetics of the PETase were improved by a factor of 1000. We are aware that such an optimization of the PETase would be very difficult, if not impossible to achieve. Nevertheless, the drastic improvement of the enzyme for these simulations is expected to serve as an exaggerated case that shows under what conditions, if any, PET degradation is applicable at an industrial scale.
One simulation was made for the cultivation density ratio of 1:10 and the other one for a ratio of 1:100. The results can be seen on Fig. 4 and Fig. 5 respectively. For the simulation shown in Fig. 5, the time needed to degrade 1mg of PET was 260 s, or 4,3 min, which is a substantial improvement to the simulations discussed in the previous section. According to this simulation, the time needed for the degradation of a 40 mg plastic bottle would be approximately 119 days. Still, the problem of achieving and sustaining a cultivation ratio of 1:10 prevails. Therefore, the simulation was repeated for a cultivation ratio of 1:100 with the optimized PETase by a factor of 1000 (Fig. 5). The results of this simulation show that for this cultivation setup a time of 2600 s, or 43 min, is needed to degrade 1 mg of PET. The time needed to degrade a 40 mg PET bottle would be approximately 3,3 years.
Conclusion: Model of PET degradation by Chlamydomonas reinhardtii
The inevitable conclusion of our model is that the PET degradation process by C. reinhardtii is for the moment a slow process which is difficult to optimize for industrial application. To be able to use a PET degrading alga at an industrial scale, there are several factors that need optimization. What became clear to us after the results of these simulations is the fact that we needed to improve all possible factors that might have an impact on the PET degradation rate. To achieve this, we took the following decisions regarding the improvement of PET degradation. First, we chose the light inducible promoter PsaD for the design of our parts and constructs. This promoter is the promoter for an abundant chloroplast protein of the Photosystem 1 complex (Fischer et al. 2001). By choosing the promoter of this abundantly expressed protein we expect to boost the expression of our parts and therefore a higher PET degradation. Our second improvement was the introduction of the Sp20 glycomodule to our secretion constructs, due to the fact that this module seems to drastically improve secretion yield in C. reinhardtii (Ramos-Martinez et al. 2017). By having a higher secretion rate of the enzymes, we expect a higher PET degradation rate. Third, we chose the C. reinhardtii strain UVM4 which was designed to allow efficient expression of transgenes (Neupert et al. 2009). Because the results of the model made clear that culture parameters are a decisive factor, we seeked help from experts on algae cultivation to improve the cultivation of our algae and the design of our own bioreactor. For this we visited the company MINT Engineering, focused on the construction of big scale algae bioreactors, and the algae farm Roquette Klötze.
Introduction: Modeling light limitation for C. reinhardtii cultivation
Because the model of PET-degradation revealed the need for high cultivation densities, we came to the conclusion that it would be necessary to optimize cultivation parameters. With help from Dr. Ralf Steuer (described on the Human Practices Page) who is an experienced researcher in the field of algae biotechnology, we were able to further conclude that we should aim for light-limited cultivation, meaning that the amount of photons is the single factor determining the growth rate of C. reinhardtii, while other substrates are supplied in excess. This is why we decided to simulate the self-shading of the culture to gain insight into the light intensity distribution in a cultivation vessel. From there on, we draw a first conclusion for our cultivation setup and further apply it to measurement of optical density.
Formulation of the model
For describing the interplay between vessel depth and culture density, we start from the two equations (Huisman et al., 2002) on the left. For other mathematical derivations, see (Barbosa et al., 2004). Equation (1) provides us with the light intensity gradient inside the culture vessel due to algae cell concentration \(c_X\). Important for us is the antiproportionality of \(\mathrm{d}I\) to \(\mathrm{d}z\), meaning that light intensity is declining as the light path through an algae culture increases. This will allow us to draw conclusions on the design of our setup pretty fast. Because we want to treat different species, we reformulate (1) later to get a more general form. Equation (2) can be understood by looking at the single terms being added to each other on the right hand side. It equates the temporal change of \(c_X\) to the sum of positive (growth with production rate per surface area \(P\) and negative (dilution \(D\) of the culture and maintenance \(\mu_e\) contributions. Dilution rate is the rate at which we pump out culture out of the vessel. The maintenance term is necessary because cells require energy to maintain non-growth associated processes, reducing our maximum achievable value (see later). For (2) it is also important to note that productivity \(P\) is a function of light intensity. For resolving the model further, we express it through the specific productivity (productivity per cell in \(\frac{mol Carbon}{s} \cdot \(\frac{L}{mol}\), which is a function of light intensity in the vessel.
For the sake of clarity, precise mathematical derivations for this model are given in a PDF supplement.
Results
testhingy
\begin{array}[l] \begin{equation} \frac{\partial I(\lambda, z, t)}{\partial z}= -I(\lambda, z, t) \cdot \sum_{i}^{n} \epsilon_i(\lambda)_ \cdot c_i \end{equation} \\ \[\newcommand\T{\Rule{0pt}{1em}{.3em}} \begin{array}{r l} I(\lambda, z): & \text{Light Intensity in}\: \frac{\mu mol}{m^2 \cdot s} \\ \epsilon(\lambda): & \text{specific light attenuation coefficient in}\: \frac{L}{mol \cdot cm} \\ c_i: & \text{concentration of \(i\)-th species. Index X for cell concentration}\: \frac{mol}{L} \\ z: & \text{light path in}\:cm \end{array} \] \\ \begin{equation}\frac{\mathrm{d}c_X}{\mathrm{dt}}= \frac{Y}{z} \cdot p(\tilde p, c_X) - D \cdot c_X - \mu_e \cdot c_X \end{equation}\\ \begin{array}{r l} c_X:& \text{algae cell concentration in }\: \frac{mol}{L} \\ p(\tilde p, c_X):& \text{production rate per surface area}\: \frac{mol \: carbon}{m^2 \cdot h} \\ Y: & \text{yield of algae cells on carbon}\: \frac{mol Cells}{mol \: carbon \cdot } \\ \mu_e : & \text{maintenance rate in}\: \frac{1}{h} \end{array} \] \end{array}
Describing the light gradient
Text for the two column thingy here
Conclusion: Modeling light for C. reinhardtii cultivation
Conclusion Text
Sources
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