Team:USP-EEL-Brazil/Model
Introduction
The creation of a model to describe a project is highly important since the model attended the system’s parameters, it’s possible to predict results and find a way to illustrate the functioning of the system, even before it’s finished. To develop a model, you should build on existing knowledge on what you’re trying to describe, understand these data, and then pick up some equations that may be used to each component of your project. The knowledge varies from source, you may base yourself on other people’s research or you can produce your own data to your model. On our iGEM Project the model was created based on Myceliophthora thermophila laccase rather than Pleurotus ostreatus and Phoma sp. laccases, because the MT laccase is well known and there’s a lot of data available, once the chosen for us are quite unknown and not so well described for estrogens and xenoestrogens removal, causing some trouble to develop some kind of prediction for our system.
Our project aims to develop a reactor system to the enzyme production, then, purify the enzyme, and apply the purified enzyme in another reactor to the effluent treatment. But we can’t simply apply all of this without a base of what to expect. On the modeling, we seek to analyze kinetic behavior, verifying the effective removal and the variation of its efficiency in different types of reactors.
Thus, we hope to find parameters to the choosing of the best application system, and how it's going to attend the water flux of our region, a small countryside city, really small, the city of Lorena.
Theory
The team has planned a system with a bioreactor to eliminate endocrines disruptors from the water. We modeled 2 of them: a fed-batch reactor and an enzymatic membrane reactor. Our main problem was finding data for all the situations we’re planning. The use of laccase for degrading endocrines disruptors isn’t yet a conventional process, and as described above, was pretty hard to find data about it.
Some laccases are known to follow the kinetics of Michaelis-Menten equation (AURIOL, 2007; SOARES, 2002; MICHNIEWICZ, 2008), described by the equation (1).
When [S]>>km, the expression (2) is obtained, and when km>>[S], the expression (3) is obtained.
Don’t worry, at the end of the section, we’ll have a table where all variables are described.
Most parts of the data we found were in removal rates, which were transformed from (% removal) to substrate concentration by equation (4):
Likewise, the derivative of expression (4) is considered by expression (5):
Being used to determinate the mass balances for each modelled reactor.
The choice of the best model to represent the data was based on Akaike information criteria (AIC). Akaike (1974) utilized the Kullback-Leiber Information to test the viability of a model. On the used software, the corrected AIC (AICc) (equation (6)) its available to be used with a simple command. This method compares all yours models and compare the maximized support function.
With all studies and model applications we found some conditions – like mediators concentration, pH or temperature – to focus and describe the enzyme behaviour.
Reactors
For each kind of reactor we have a different mass balance, that will influence on the kinetic degradation of the substracts. We plan to apply in two different reactors, so the models are described below.
BATCH REACTORS
Figure 1: Example of Batch Reactor. Source: Personal arquive.
For batch reactors we used the mass balance as the described by equation (5) when the data were based on removal ratio. Whenever the data was given in substrate concentration, the ordinary Michaelis-Menten was used, as above on equation (7)
And the boundary condition considered was that at t=0, the removal was 0 too.
Using the software Wolfram Mathematica, a nonlinear model was created to fit the data and find the km and the vmax.
FED-BATCH REACTORS
Figure 2: Example of Fed-Batch Reactor. Source: Personal arquive.
Our fed-batch reactor will be filled by n-feds, varying the volume inside the reactor, the model of batch reactor was used, using different vectors to each batch added on the software. The equation used was the number (7).
ENZYMATIC MEMBRANE REACTOR
Figure 1: Example of Enzymatic Membrane Reactor. Source: Personal arquive.
In this case, the mass balance is described by the equation (8):
The system considered a proportionality between the lost enzyme and the enzyme inside the reactor by the equation (9)
Integrating this function, the expression (10) is found
As described on the stationary model of Michaelis-Menten
And the (11) expression is found.
Each model considered the normal Michaelis-Menten equation (1), first order Michaelis-Menten equation (2) and order zero Michaelis-Menten equation (3).
REFERENCES
Auriol, M., Filali-Meknassi, Y., Tyagi, R. D., & Adams, C. D. (2007). Laccase-catalyzed conversion of natural and synthetic hormones from a municipal wastewater. Water Research, 41(15), 3281–3288. doi:10.1016/j.watres.2007.05.008
Michniewicz, A., Ledakowicz, S., Ullrich, R., & Hofrichter, M. (2008). Kinetics of the enzymatic decolorization of textile dyes by laccase from Cerrena unicolor. Dyes and Pigments, 77(2), 295–302. doi:10.1016/j.dyepig.2007.05.015
Soares, G. M. B., Amorim, M. T. P. esso., Hrdina, R., & Costa-Ferreira, M. (2002). Studies on the biotransformation of novel disazo dyes by laccase. Process Biochemistry, 37(6), 581–587. doi:10.1016/s0032-9592(01)00244-8
Different Mediators Test
Different mediators were used to evaluating their benefits use with laccase. The principal ones were Violuric Acid (VAC), Syringaldehyde (SRG), 2,2’-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid) (ABTS) and 1-hydroxybenzotriazole (HBT).
The most used mediator is ABTS, but this mediator is much expensive and toxic (SEI, 2007), for this reason, we found the possibility to use naturally occurring mediators (NOMs) like those cited above (syringaldehyde and violuric acid), that are much cheaper and non-toxic to the ecosystem.
Just 3 of the EDCs had data about the degradation using NOMs as mediators (SEI, 2007), the chose of the best of them will be based in the results around these 3. For each substrate the results chosen were the ones that achieved the best removal, using MT laccase. The x-axis will always be time, and y-axis will be removal. Although, papers have been published studying the application of Syringaldehyde as a mediator for BPA degradation (HOFMAN, 2015).
For EE2 (Figure 1), the best mediator was the Syringaldehyde, removing all the EE2 in solution ([EE2]0= 5mg/L and mediator’s concentration = 1mM) in less than 1 hour. For these conditions, the Vmax/km quotient found was 2725 h-1 by nonlinear model regression on Mathematica Wolfram software. The quotient was really high because all data measured with this mediator was kind of instantly degraded. Even at t=0, the value measured by Sei (2007) was 100% removal. In most part of the cases, the best model, chosen by Akaike information criteria, was the first order model, giving as a result only a quotient between Vmax and km.
Figure 1: EE2 degradation through time with 1mM – mediator. Source: Personal archive.
When the mediator’s concentration was reduced to 0.25mM, the values of vmax=1.513mg/Lh and km=0.032 were obtained, the model is shown on Figure 2.
Figure 2:EE2 degradation through time with 0.25 mM – mediator. Source: Personal arquive.
For the E2 degradation with mediator’s concentration = 1mM, the best results were obtained with the Violuric Acid (Figure 3.a) and with Syringaldehyde (Figure 3.b), showed on the picture below with the blue graph. Their results are almost the same, being very efficient and helping laccase to degrade the substrates even faster. For both of them the quotient Vmax/km = 2725.84 h-1 was found by nonlinear regression on the software.
Figure 3.a: : E2 degradation through time with 1mM Violuric Acid as mediator. Source: Personal arquive.
Figure 3.b: E2 degradation through time with 1mM Syringaldehyde as mediator. Source: Personal arquive.
When the mediator’s concentration was reduced to 0.25mM (Figure 4.a and 4.b), the Vmax/km=2932.86 h-1 for Syringaldehyde and Vmax/km=266.523 h-1 values were obtained.
Figure 4.a:E2 degradation through time with 0.25mM Violuric Acid as mediator. Source: Personal arquive.
For the E1 experiment the best results weren’t good enough. That’s the worst EDC to removal, with the lowest degradation efficiency of them all. With 1mM of mediator, the best results were obtained with Syringaldehyde (Vmax/ km=40.499h-1), showed in Figure 5.
Figure 4.b: E2 degradation through time with 0.25mM Syringaldehyde as mediator. Source: Personal arquive.
For the E1 experiment the best results weren’t good enough. That’s the worst EDC to removal, with the lowest degradation efficiency of them all. With 1mM of mediator, the best results were obtained with Syringaldehyde (Vmax/ km=40.499h-1), showed in Figure 5.
Figure 5.a: E1 degradation through time with 1mM Syringaldehyde as mediator. Source: Personal arquive.
When reducing the mediator’s concentration to 0.25mM (Figure 6) the new values of Vmax/ km= 2932 h-1, demonstrating better results than when using 1mM of the same mediator.
Figure 5.b: E1 degradation through time with 0.25mM Syringaldehyde as mediator. Source: Personal arquive.
The results published by Sei (2007) show that ABTS and HBT are really the most effective mediators, but as we’re solving environmental problems, the use of eco-friendly mediators is preferred in order to do no harm to the living beings around. Based on the removal of the 3 EDCs, the preferable NOM would be the Syringaldehyde, since it’s a NOM that can help with the EDCs removal.
REFERENCES
Sei, K., Takeda, T., Soda, S. O., Fujita, M., & Ike, M. (2007). Removal characteristics of endocrine-disrupting chemicals by laccase from white-rot fungi. Journal of Environmental Science and Health, Part A, 43(1), 53–60. doi:10.1080/10934520701750397
Optimum pH and Temperature
Proteins are macromolecular organic compounds and some of them have catalytic function, they’re known as enzymes. As they’re made up with amino acids, they have charge along their chain that changes as the pH varies. For this reason, with the variation of the pH the inter and intramolecular interactions can be increased or decreased, altering the tridimensional conformation of the molecule. All molecules have a more stable conformance, and when they’re not arranged this way, they can become very unstable, losing their activity and performance on their substrates.
The alteration on the conformation of the protein can change the affinity with substrates. Some substrates are preferable in low pH, and other may be preferable at high pH, for example.
As we’re using a model laccase (Myceliophthora thermophila), in this section we’ll discuss its properties around optimum pH and temperature. The 2 laccases we’re aiming to produce have poor data and we’ll use them to complement the discussion around the MT laccase.
MYCELYOPHTHORA THERMOPHILA LACCASE
For this laccase, the results obtained by Hollman (2008) about the optimum pH and the variation of the temperature around the enzyme’s stability are described in Figure 1.
These results show us that the optimum temperature may be around 50°C, and as more alkaline is the pH, more stable the enzyme gets. The pH 6 at 50°C appear to be the best conditions to the enzyme stability. Other researchers (Lloret et al.¸ 2010) studied the effects of pH separately at a temperature of 22,2°C on the stability of the lacMT (Fig. 2). We can notice that the enzyme has more stability when the pH is more alkaline (above pH 7) at a temperature near the room temperature.
PLEUROTUS OSTREATUS LACCASE
The studies around LacPO (LIBARDI JUNIOR, 2010) could describe its behavior with the variation of pH and temperature. On the figures below (3 and 4) these data can be analyzed.
In this study they used ABTS 20mM to determinate the activity using a McIlvain buffer with 1mL of the reactional mixture, at 25°C, containing 0.5U of laccase. Data show that the enzyme has more activity between pH 3 and 4.
For the temperature study the pH was maintained at 5, using ABTS 20mM to determinate the activity, using again a McIlvain buffer with 1mL of the reactional mixture and 0.5U of laccase. The best temperature for activity conservation was between 4 and 14°C.
PHOMA SP. LACCASE
LacPS was also studied by Nelson Libardi Junior (2010), at the same experimental conditions LacPO. Figure 5 can show the pH influence on the lacPS, and we can notice that the best results were obtained with acid pHs (3-5).
Differently from LacPO, this laccase is able to keep its activity in a wide range of temperature for a long period of time (4-28°C).
For the use of these laccases together we could set a system with ph 4 and temperature around 14°C.
REFERENCES
Hollmann, F., Gumulya, Y., Tölle, C., Liese, A., & Thum, O. (2008). Evaluation of the Laccase from Myceliophthora thermophila as Industrial Biocatalyst for Polymerization Reactions. Macromolecules, 41(22), 8520–8524. doi:10.1021/ma801763t
LIBARDI JUNIOR, Nelson. Estudo de lacases fúngicas para degradação de compostos interferentes endócrinos. 2010. 140 f. Dissertação (Mestrado) - Curso de Engenharia de Processos, Universidade da Região de Joinville, Joinville, 2010.
Lloret, L., Eibes, G., Lú-Chau, T. A., Moreira, M. T., Feijoo, G., & Lema, J. M. (2010). Laccase-catalyzed degradation of anti-inflammatories and estrogens. Biochemical Engineering Journal, 51(3), 124–131. doi:10.1016/j.bej.2010.06.005
Substrate Degradation
Our project aims to degrade 7 EDCs presented on the background page, so the models were made trying to predict their behaviors.
One of the reasons of the chose of the PL and PH enzymes was based on the available knowledge about its great potentials to degrade EDCs, but almost none study of the kinetic behavior of them. We aimed to express them and make it possible to study their kinetics. In Brazil, we found interesting data about its application on EDCs removal (LIBARDI JUNIOR, 2010; LACERDA, 2015). Lacerda (2015) has studied the application of both enzymes immobilized on Luffa cilindrica, reaching 75% of the initial activity in 30 days of immobilization for PO laccase and when analyzing the removal percentual with the immobilization, it was possible to achieve 64% of removal (initial concentration of 10mg/L) in pH 5 in a period of 24h.
Libardi Junior (2010) related that PL laccases are more effective than PH laccases to degrade NP, showing us that it was possible to reach more than 90% removal with the PL laccase in 72h. With BPA and EE2, its shown that 24h hours is enough to degrade at least 90% with both of the laccases.
During the modeling process, we determined data related to the rate of formation of degraded phenolic compounds, however, Uchida (2001) identifies a new stage of polymerization during laccases performance in the degradation of some compounds such as BPA. “BPA was metabolized by the laccase from the basidiomycete T. villosa to two kinds of compounds: one was high MW compounds, which were the main products, and other was low MW compounds. One of the high MW products was identified as a BPA dimer, 5,59-bis-[1-(4-hydroxyphenyl)-1-methyl-ethyl]-biphenyl-2,29-diol. FD–MS analysis showed some products had regularly increasing MWs. These results suggest that the laccase reaction may include, as one of its steps, the polymerization of BPA to form oligomers, followed by either the addition of phenol moieties or the degradation of the oligomer to release 4-isopropenylphenol.” As a result, we expect the rate of actual degradation of the endocrine disruptors to be lower than the predicted rate of degradation. And that may be a good thing. Whenever an EDC is polymerized, it may form granules that can be removed easily by unitary operations.
BATCH REACTOR
In this reactor the degradation of NP was studied. Using data published by Hofman & Schlosser (2015), we modeled the behavior of the laccase kinetic with NP as a substrate. The pH was maintained at 5 and the initial concentration of NP was 236.57 µg/L. Using a nonlinear model on the Mathematica Wolfram software, the best fit was obtained with the first order Michaelis Menten equation (equation number 3 on the “Theory” section).
The model obtained is illustrated at Figure 1. The quotient was Vmax/km=0.016 h-1.
Figure 1: concentration(µg/L) x time(h) of NP degradation through time, at 22°C and pH=5.
BPA was also documented by Hofman & Schlosser (2015) at the same conditions of NP (pH=5 and 22°C) in a batch reactor. The models were applied and a quotient of Vmax/km=1.579 h-1 and the result is shown by Figure 2.
Figure 2: concentration (µg/L) x time (h) of BPA degradation through time, at 22°C and pH=5.
FED-BATCH REACTOR
The studies performed by Lloret et al. (2012) were gratefully nice to model the kinetic behavior of MT laccase on a FBR. On the kinetic study, some parameters were evaluated to obtain knowledge about its influence on the enzyme kinetics. The initial activity (500 or 2000U/L), estrogens pulse frequency (1 or 2h) and oxygenation/aeration were varied. All experiments were performed at pH 7.
With the nonlinear model, the bigger quotient Vmax/km was used to chose the model with most conversion of EDC. The EDCs testes were E1 and E2.
The best conditions for E1 removal were stablished as a oxygenated reactor, estrogens pulse frequency of 2h and 500U/L of initial activity. The quotient Vmax/km=1.3379 h-1 was obtained (Figure 3).
Figure 3: concentration (mg/L) x time (h) of E1 degradation through time on the best FBR model.
Although, the best conditions for E2 removal were different. In its case, the reactor using oxygenation was maintained but an estrogen pulse frequency of 1h and initial activity of 2000U/L presented best results. The quotient Vmax/km=2.0018 h-1 was obtained (Figure 4).
Figure 4: concentration (mg/L) x time (h) of E2 degradation through time on the best FBR model.
ENZYMATIC MEMBRANE REACTOR
This kind of reactor provided us data about kinetic degradation of E1 and E2 using the MT laccase (LLORET et al., 2012). The parameters evaluated were oxygenation pulse frequency (0.5 or 1h), the hydraulic residence time (2 or 4h), estrogens addition rate (2 or 1mg/Lh). All tests used 500U/L of laccase. All experiments were performed at pH 7.
According to the nonlinear model made, the constant of enzymatic loss was significant to the system, and the reaction followed a first order kinetic. Thus, only the quotient Vmax/km was obtained. The bigger the quotient, best results of conversion are expected. On the experiment realized with estrogens addition rate of 1mg/Lh, hydraulic residence time of 4h and oxygenation pulse frequency of 0.5h. These conditions were considered the best for both of the EDCs tested. The E1 quotient Vmax/km=1.2515 h-1 (Figure 5) and E2 quotient Vmax/km=1.3756 h-1 (Figure 6) were determined.
Figure 5: concentration (mg/L) x time (h) of E1 degradation through time on the best EMR model.
Figure 6: concentration (mg/L) x time (h) of E2 degradation through time on the best EMR model.
REFERENCES
Hofmann, U., & Schlosser, D. (2015). Biochemical and physicochemical processes contributing to the removal of endocrine-disrupting chemicals and pharmaceuticals by the aquatic ascomycete Phoma sp. UHH 5-1-03. Applied Microbiology and Biotechnology, 100(5), 2381–2399. doi:10.1007/s00253-015-7113-0
Lloret, L., Eibes, G., Feijoo, G., Moreira, M. T., & Lema, J. M. (2012). Degradation of estrogens by laccase from Myceliophthora thermophila in fed-batch and enzymatic membrane reactors. Journal of Hazardous Materials, 213-214, 175–183. doi:10.1016/j.jhazmat.2012.01.082
LACERDA, Monike Fabiane Alves Ribeiro. DEGRADAÇÃO DE HORMÔNIO SINTÉTICO POR MEIO DE LACASES FÚNGICAS IMOBILIZADAS EM FIBRAS DE Luffa cylindrica. 2015. 83 f. Dissertação (Mestrado) - Curso de Engenharia do Meio Ambiente, Escola de Engenharia Civil e Ambiental, Universidade Federal de Goiás, Goiânia, 2015.
Uchida, H., Fukuda, T., Miyamoto, H., Kawabata, T., Suzuki, M., & Uwajima, T. (2001). Polymerization of Bisphenol A by Purified Laccase from Trametes villosa. Biochemical and Biophysical Research Communications, 287(2), 355–358. doi:10.1006/bbrc.2001.5593
Molecular Model
With a gentle collaboration with the Kazakhstan Team, we assembled a molecular model of the MT laccase binding site. We had a meeting and discussed the differences with each substrate, we provided our data and they provided their knowledge. On the document below we can see the discussion around the bonds and structure of the site.