Team:Stuttgart/Model

Kinetic model

Models, especially kinetic simulations are a great way to explore the parameter space of the desired system. Based on established kinetic and thermodynamic laws, a few experimentally determined key values are enough to design a model that covers multiple environmental variables. Particularly during the Covid-19-situation, where lab time was severely limited, modeling is a great way to explore the system without the need of doing everything experimentally. Furthermore, the model can be extrapolated towards the proposed implementation of the system, to be able to evaluate possible applications in scientific and economic terms.

Model structure

Michaelis-Menten core

Our model is based on the Michaelis-Menten kinetic law. The required parameters vmax , Km, and kcat were determined experimentally and obtained from the literature for the substrate ABTS.1 This allows for adjustment of the substrate concentration and the amount of laccase used for degradation. The transition from a batch approach to a continuous system was reached by the implementation of an influx and an efflux. The influx contains the substrate (water pollutants) with a given concentration, and the efflux contains both undegraded and degraded substrate. Flow rates (Fin and Fout) can be easily adjusted towards the desired application. Thereby, the amount of laccase degraded substrate and the flow-through undegraded substrate can be determined.

Picture 1 of the simple michaelis-menten model

Consideration of MCF pores

Since our laccases are immobilized inside a mesocellular silica foam (MCF), the diffusion and flow conditions are complex and dependent on the size of the foam particles and their pore diameters. To simulate the flow conditions and concentration gradients in the foam, we split up the reaction volume into 20 successive compartments with individual substrate and product concentrations. We found 20 to be a limit value of compartments, over which more compartments would make no more difference in the kinetic behavior of the model. The laccase is equally distributed over all compartments. We decided to give the foam a total fixed volume of 1 liter and therefore 0.05 l per compartment.

Picture 2 of the simple michaelis-menten model with compartments

Protein decay

The immobilization allows for the recovery of the enzymes together with the MCF and prevents the washout by wastewater. Therefore, our laccases can be used over an extended time span. The degradation of laccases over time is discribed by an exponential decay.

Picture of laccase decay reaction.

Environmental conditions

Temperature, salt concentration, and pH-value are three critical factors affecting the activity of the laccase. Since wastewater treatment takes place all year, temperatures are fluctuating, the number of ions may vary from region to region and pH changes can occur. Therefore, it is important to consider these three environmental conditions and implement them into our model as factors, which scale the reaction rate directly.

Parameter estimation

Laccase degradation rate

To determine the exact decay rate, we set up a long-term stability ABTS-assay for the laccase from T. versicolor. We stored the laccase at 25 °C in Citrate-Na2HPO4 buffer at pH 5. The activity was measured over 10 days in triplicates to identify a degradation term that can be used in our model. The data was fit exponentially and used in our model to decrease the amount of active laccase with the time. The exponent 2.231∙10-6 was used as a degradation rate constant for the laccase.

Exponential fit of laccase decay

Environmental conditions

We used data from the literature that already represent the dependency of laccase activity on temperature, ion concentration, and pH value.2,3 With MATLAB, we fitted the experimental data from the literature to the best possible function with PolyFit of degree 3 for temperature and pH-value. For the ion concentration, we used exponential fitting.

Temperature fit

pH fit

Salt concentration fit

These functions represent the relative activity between 0 and 1 dependent on the respective condition and scale the activity of the laccase in our model as factors. These factors are calculated with the set parameters used in the above-determined equations. The single environmental factors are combined multiplicatively into an efficiency factor, which scales directly the reaction rate itself.

Environmental factors

Application of the model

In summary, the model allows for adjustment of:

  • Concentration of Laccase in the foam
  • Initial substrate concentration
  • Temperature of the system
  • pH-value inside the system
  • Ion concentration within the system
  • Flow of wastewater through the system

    • Depending on the set parameters, the model calculates the amount of degraded and flow-through substrate. This allows for the evaluation of desired applications. The given environmental conditions of a proposed implementation are entered into the model and the efficiency of our system is calculated. Degradation of other enzymes can be considered easily by adjusting the kinetic parameters within the model. Thereby, possible users of our system can check the efficiency of substrate degradation and then decide, if an implementation is worth it or not. The simulation is calculated over 700 000 seconds which corresponds to approximately 8 days.

    Wastewater treatment plant

    Exemplary, the model is applied to the wastewater treatment plant in Stuttgart Plieningen. The first step is to collect environmental conditions for the specific system. The wastewater treatment plant in Stuttgart Plieningen has an average dry-weather influx of 175 l/s, an average wastewater temperature of 17 °C, an average pH-value of 6, around 20 mM salt concentration, and a substrate concentration of Diclofenac of 1.33∙10-6 M.4 With this input values and almost no laccase (3∙10-8 M), the undegraded substrate (red) stays at the initial substrate concentration over the whole simulation time while there is no degraded substrate (green).

    Almost no reaction

    To achieve substrate degradation, the amount of laccase must be increased. At a laccase concentration of 3∙10-4 M there is an initial substrate degradation of 60 %, that is decreasing to 20 % after 8 days.

    60 % Degradation

    With a laccase concentration of 3∙10-3 M there is full substrate degradation for the first 3 days and still 85 % substrate degradation after 8 days.

    100 % Degradation

    In addition to laccase concentration, also the quantity of foam can be increased to improve substrate degradation. Since our model in the foam has a fixed volume of 1 l, this effect is introduced into the model by changing the absolute flux. Dividing the flux by two has the same effect as doubling the amount of foam and is easier adjustable in the model. With a low laccase concentration of 3∙10-8 M, 1000 l foam volume would be needed to achieve a substrate degradation comparable to a laccase concentration of 3∙10-4 M in 1 l foam.

    60 & Degradation

    Conclusion

    In our model, increasing the laccase concentration and increasing the theoretical amount of foam by decreasing the flux have the same effect and are directly proportional to each other. Admittedly, a flux of 200 l/s through 20 g of MCF are not realistic. We were not able to determine the important value of possible maximum flux through an MCF to be included as limit in our model. Therefore, an increase in substrate degradation should be achieved with a well-balanced increase in foam quantity and laccase concentration.

    Users of our filter system can therefore check before installation, how much substrate degradation is desired, and how much foam with a certain laccase concentration is needed for this amount of substrate degradation. With longer simulation times it should be also possible to determine the interval of replacement.

    Literature

    1. Frasconi, M., Favero, G., Boer, H., Koivula, A. & Mazzei, F. Kinetic and biochemical properties of high and low redox potential laccases from fungal and plant origin. Biochim. Biophys. Acta - Proteins Proteomics 1804, 899–908 (2010).
    2. Zdarta, J., Feliczak-Guzik, A., Siwińska-Ciesielczyk, K., Nowak, I. & Jesionowski, T. Mesostructured cellular foam silica materials for laccase immobilization and tetracycline removal: A comprehensive study. Microporous Mesoporous Mater. 291, (2020).
    3. Margot, J. et al. Bacterial versus fungal laccase: Potential for micropollutant degradation. AMB Express 3, 1–14 (2013).
    4. Loos, R., Marinov, D., Sanseverino, I., Napierska, D. & Lettieri, T. Directive 2008/105/EC, amended by Directive 2013/39/EU. (2018).
    © Christopher Adelmann, Fabian Klötzer, Jan Schlegel for iGEM Team Stuttgart 2020