Model

Mapping every possibility.

Michaelis-Menten Kinetics for T. Versicolor Laccase

Objective

By examining laccase activity and closely investigating its dependence on pH and temperature, we aim to gain deeper insights into the kinetic parameters of laccase from Trametes versicolor. With a solution-oriented approach, our goal is to enhance our understanding and open the way for future real-world applications.

Laccase Activity for Ibuprofen Degradation

For describing the rate of enzymatic reaction, we firstly used literature data [1] for illustrating the relationship between substrate concentration (ibuprofen) on the x-axis and the reaction velocity of laccase from T.versicolor on the y-axis, with a Michaelis-Menten model. As the ibuprofen concentration increases, the reaction velocity also tends to rise, demonstrating that laccase activity is positively correlated with the availability of the substrate.

The kinetic parameters of the laccase-catalyzed ibuprofen removal reaction were Km = 6.21 mM and Vmax = 2.56 M/h.

As substrate concentration continues to rise, the graph may show a trend towards saturation, where the increase in reaction velocity starts to plateau. This indicates that the laccase enzyme has reached its maximum catalytic capacity. At this point, the catalytic site may be occupied, and the reaction velocity levels off, reflecting that further increases in ibuprofen will not significantly enhance the degradation rate.

Fig 1
Fig 1) Michaelis-Menten Kinetics for T. Versicolor Laccase

Analysis of Laccase Activity

In our experiments, we investigated the activity of laccase in relation to pH and temperature, crucial factors influencing enzyme performance. The following sections summarize the findings from our data, literature, and sewage plant studies.

pH-Dependent Activity

The first graph illustrates the relationship between laccase activity, tested with ABTS, and pH levels. Our experimental data indicate that laccase exhibits optimal activity at a pH of 3, which is lower than what is typically reported in the existing literature [2]. Another paper suggests that laccase is highly effective under acidic conditions.[3] Notably, at pH levels above 6, we observe a significant decline in activity.

In sewage treatment plants, pH typically ranges from 6 to 8. To address the pH limitations and facilitate the use of laccase in these environments, we considered immobilizing the enzyme. This approach would help maintain laccase activity while preventing its release into the environment. Consequently, we standardized our subsequent experiments at a pH of 7.

Fig 1 Fig 1
Fig 2&3) pH-dependent activity with reference graph from literature

Temperature-Dependent Activity

The second graph depicts the dependence of laccase activity on temperature. Our experiments reveal that laccase activity peaks at approximately 65°C, which aligns closely with findings from relevant literature[3]. According to the literature, laccase remains active within a temperature range of 10–70°C.

In a sewage treatment plant, the temperature ranges from 10–12°C in winter to about 20°C in summer. This data indicates that laccase can function in a real-world scenario. However, at 10°C, the enzymes activity decreases, necessitating the use of higher enzyme concentrations.

Fig 1 Fig 1
Fig 4&5) temperature-dependent activity with reference graph from literature

Our Progress So Far

  • A real-world relevance, as it provides a practical context for understanding how laccase performs in actual environmental conditions
  • Model important for the validation of results, can also guide the development of more effective laccase-based solutions for environmental remediation

Future Steps for Our Model

  • Move from laboratory experiments to pilot-scale testing in a controlled wastewater treatment setup to evaluate laccase performance in real conditions
  • Test the treated effluent for toxicity levels before and after laccase treatment to demonstrate the enzyme's effectiveness in reducing harmful substances
  • By-product identification with analytical techniques like LC-MS/MS, NMR, or IR spectroscopy.
  • Toxicity assessment, by choosing the right assay.

Modelling the Enzymatic Reaction in a Plug Flow Reactor (PFR) with Immobilized Laccase

Our Objective

Our goal is to develope a model to simulate the conversion of a substrate in a PFR where the enzyme laccase is immobilized on a solid surface within the reactor. The model will predict substrate conversion efficiency, changes in flow rate, and reaction rates, while accounting for the effect of diffusion and enzyme immobilization.

Components of the Model:

1. Reaction Kinetics of Immobilized Laccase:

Our model assumes the laccase-mediated oxidation of a substrate [S] into a product [P]. We assume that the reaction rate r follows a Michaelis-Menten kinetic model but adjusted for immobilization.

For example:

r = (Vmax [S]) / (Km + [S]) * fimmobilization

Where:

  • [S] is the substrate concentration
  • Vmax is the maximum reaction rate of laccase.
  • Km is the Michaelis constant.
  • fimmobilization is a factor accounting for diffusion limitations and reduced enzyme flexibility due to the immobilization method.

2. Plug Flow Reactor Equations:

In a PFR, the substrate concentration changes along the length of the reactor as the reaction happens. You can calculate the material balance for the substrate S in a differential reactor volume dV by:

(d[S]) / dx = (-r) / v

[1]

Where:

  • [S] is the concentration of substrate S at a position x along the reactor.
  • r is the reaction rate.
  • v is the volumetric flow rate.

This equation tracks how the concentration of substrate decreases as it flows through the reactor.

3. Flow Rate and Conversion:

The volumetric flow rate in the reactor could change due to the reaction (e.g., if products have a different stoichiometry than the reactants). The conversion X is defined as the fraction of substrate S converted into products. It can be related to the concentration of S at the reactor inlet and outlet:

X = ([S]in - [S]out) / [S]in

fig6
Fig.6 Substrate Concentration and Conversion as a function of reactor length. Simulated parameters: Vmax: 1.5 mmol/s, Vmax immobilized: 1 mmol/s.,Km: 0.5 mM, flowrate: 10 ml/s, initial concentration: 10 mM reactor length: 200 cm, f: 1, simulated with python
fig11
Fig.7 A: Reactor length with 99% substrate conversion as a function of enzyme Vmax, B: Reactor length with 99% substrate conversion as a function of enzyme Km
fig12
Tab. 1 Reactor lengths with 99% Substrate Conversion under different kinetic enzyme parameters

Application of our Model:

By using a plug flow reactor model with immobilized laccase, you’ll be able to:

  • Predict substrate conversion along the length of the reactor.
  • Simulate how immobilization affects reaction kinetics and flow rates.
  • Optimize reactor conditions for improved enzyme efficiency and conversion rates.

For example, to optimize bioreactor design for enzymatic processes achieving 99% substrate conversion: High Vmax enzymes are preferred to reduce reactor size, though the benefit plateaus beyond a certain point. Low Km enzymes (high substrate affinity) are also critical to maintain efficient conversion, particularly in scenarios with lower substrate concentrations. Obvious strategies to improve the Km are to continue engineering the enzyme on a DNA or protein level and to predict affinities through programs like Alphafold. Due to time constraints we were not able to engineer a prototype and test our model out.

References

  1. https://www.sciencedirect.com/science/article/pii/S2214714422002355, 02.10.2024
  2. https://www.sciencedirect.com/science/article/pii/S1359511320300994?ref=pdf_download&fr=RR-2&rr=8cc468dfaaa65ba0
  3. https://amb-express.springeropen.com/articles/10.1186/2191-0855-3-63#Fig2, 01.10.2024