Introduction
We plan to use the Michaelis-Menten (MM) equation to model the kinetics of the photoenzymatic repair of UV-induced pyrimidine dimers in E. coli. By understanding the reaction rate constants and enzyme kinetics, we aim to quantify the efficiency of photolyase in repairing DNA damage. This report serves as a foundational model for further investigating DNA repair mechanisms under UV stress.
Methods
To construct our model, we used the Michaelis-Menten equation, which sets the velocity of a reaction as a function of the maximum rate achieved by the system times the substrate concentration divided by the sum of a special Michaelis constant(Km) and the substrate concentration. Our assumptions were guided by the values we could grab from previous research, and we assumed the lower. Introducing our rate constants, which were calculated at room temperature[1], we assumed the lower bound for k₂, Km, and k3. The paper [1] only provides a lower bound for Km and k3 with no upper bound, so it seems justifiable to use the lower bound for them. The lower bound for Km also utilizes the lower bound for k₂ as Km = (k2+k3) / k1 justifying our use of its lower bound to keep consistency. k1 is the rate at which our substrate and enzyme react into the combined photolyase-pyrimidine dimer complex, and k₂ is the rate for the reverse reaction. Additionally, k3 is the rate at which the complex separates back into an enzyme and the repaired DNA, which is ultimately a function of some experimentally determined constant rate kp and the intensity of the light I. The paper [1] provided the following values of the constants:
- k₁ = 1.1 × 10⁶ M⁻¹s⁻¹: rate at which photolyase combines with pyrimidine dimers to form an enzyme-substrate complex
- ₂ = 1.9 × 10⁻³ s⁻¹: the rate of dissociation of the enzyme-substrate complex into photolyase and pyrimidine dimers
- k₃ = 10³ s⁻¹: the rate of photolyase catalysis (also equal to kI) for UV lesion repair.
Our final Michaelis Menten Equation was the following:
The substrate in our model is pyrimidine dimers, and enzyme concentrations represent the photolyase concentration, which was varied in our Michaelis-Menten equation. The Michaelis-Menten model was not developed for 6-4 photoproducts, but this model serves as a sufficient proof of concept.
There are two main types of damage after UV contact: Cyclobutane pyrimidine dimers (CPDs), which form when two adjacent pyrimidine bases (usually thymine or cytosine) become covalently bonded, creating a cyclobutane and their numerous occurrences are handled just fine with internal enzymes, while 6-4 photoproducts (6-4 PPs) occur when a covalent bond forms between the 6th carbon of one pyrimidine and the 4th carbon of an adjacent pyrimidine and require external help or photolyase treatment as they are not treated internally.
The general mechanisms between pyrimidine dimer repair and 6-4 photoproduct repair are similar to an extent as both utilize photolyase. Even though different types of photolyases are used for each repair, their general mechanism is the same. Lastly, our data is from E. coli, the species we worked on in our lab, further strengthening our model as a proof of concept.
In Figure 2, we can see the relationship between the substrate concentration - pyrimidine dimers - and the concentration of the photolyase enzyme together, affecting the reaction rate of the photolyase Enzyme. There is a positive, linear relationship between the concentration (in moles/liter) of the photolyase enzyme and the reaction rate, leading us to conclude that higher concentrations of the photolyase will result in faster repair of pyrimidine dimers. Most notably, however, is the effect - or lack of effect - of the concentration of pyrimidine dimers on photolyase Enzyme reaction rate. We can draw from our model that the reaction rate of the photolyase enzyme will be constant with respect to fixed concentrations of photolyase, and is not primarily affected by the presence of varying amounts of pyrimidine dimers-at least to the extent of which we tested the concentratio
Results and Analysis
The figures illustrate how the rate of DNA repair varies with different enzyme concentrations, amongst other variables and effects recorded. Following typical Michaelis-Menten behavior, we predicted the statistics to show the expected hyperbolic relationship between substrate concentration and repair rate.
In our Concentration Vs. Time graph, we used an initial value of photolyase concentration of 10-2 M in Figure 1. The graph indicates photolyase’s relative speed in the repair of pyrimidine dimers, caused by UV radiation. For a concentration of 10-2 moles of the photolyase enzyme, we can see a sharp decrease in the number of pyrimidine dimers due to the forming of photolyase-dimer complexes (shown through the sharp increase of the concentration of such complexes). In contrast, the number of free photolyase enzymes increases (due to the lack of dimers to repair), and the concentration of dimers and photolyase-dimer complexes decrease to 0 as time progresses, with the product of repaired DNA increasing as time progresses. The hyperbolic shape predominantly present in all the lines highlights typical Michaelis-Menten behavior.
Future Implementations
This model can be extended to calculate the effects of photolyase in various biological and environmental conditions. Refining the model with more specific data on enzyme concentrations and substrate types can be used to:
- Predict photolyase activity in other organisms or cellular environments.
- Investigate repair kinetics for other UV-induced lesions like 6-4 photoproducts.
- Explore how environmental factors like light intensity and temperature impact DNA repair.
Conclusion
Our current model using Michaelis-Menten kinetics provides a basic framework for studying photolyase activity and DNA repair efficiency. Since lower-bound estimates from multiple sources were used for critical parameters, the model's predictive capability can be enhanced by incorporating more accurate measurements from more integrated and recent studies. This is a solid first step to further exploring photolyase DNA repair mechanisms and their potential applications in biotechnology and medicine.
References
[1] Harm W. (1979). Analysis of photoenzymatic repair of UV lesions in DNA by single light flashes. XII. Evidence for enhanced photolysis enzyme-substrate complexes by a 2-photon reaction. Mutation research, 60(2), 121–133.
[2] Van Oudenaarden, A. (2004) I Michaelis-Menten kinetics, MIT OpenCourseWare.
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