Team:BIT-China/roGFP2-Orp1MichaelisEquationModel
In the previous model, we successfully obtained the relationship between intracellular H2O2 concentration and extracellular H2O2 concentration. Therefore, we were going to establish the relationship between intracellular H2O2 concentration and roGFP2-Orp1 in order to evaluate the antioxidant function signal output of our entire system.
1. The roGFP2-Orp1 is a fusion protein, and Orp1 is a catalase. Therefore, the reaction process of the protein with H2O2 can be considered as a classical enzymatic reaction meaning that this reaction is a roGFP2-Orp1 Michaelis Equations Model, and the oxidation state of roGFP2 is one of the reaction products.
2. The total intracellular concentration of roGFP2 is constant. And roGFP2 has two states, oxidative state and reductive state. And the intercellular protein concentration is depended on the transcription rate of promoter.
3. The two absorption peak values of roGFP2 at 405 nm and 488 nm are linear with the protein concentration in two states.
According to Hypothesis 1, we consider the reaction process of intracellular hydrogen peroxide with roGFP2 as an enzymatic reaction process, which is consistent with the roGFP2-Orp1 Michaelis Equations Model.
$$V=\frac{v_{max}[H_{2}O_{2}]}{K_{m}+[H_{2}O_{2}]}$$
Here we define a new parameter OxDroGFP2 to reflect the degree of oxidation of roGFP2. Meanwhile, facilitate subsequent calculations.
$$OxD_{roGFP2}=\frac{[roGFP2_{ox}]}{[roGFP2_{ox}]+[roGFP2_{red}]}$$
According to Hypothesis 3, we can correlate the redox state of roGFP2 with the fluorescence value measured by the macroscopic observables easily. To establish this relationship, several molecular quantities followed need to be defined. i405red, i405ox, i488red, and i488ox are the fluorescence intensities contributed by a single roGFP2 molecule at the indicated wavelength and redox state. Ntotal is the total number of roGFP2 molecules. Nred is the number of reduced roGFP2 molecules. Nox is the number of oxidized roGFP2 molecules. Based on the assumption that the overall fluorescence intensity is equal to the sum of the fluorescence intensities from the individual roGFP2 molecules, the relationships were given in Table 1.
Table 1. Relationships Between Fluorescence Intensities and Probe Molecules
| Condition | Formula |
|---|
| Limiting condition 1: | Ntotal = Nred | I405red = Ntotal · i405red |
| Complete reduction | Nox = 0 | I488red = Ntotal · i488red |
| Limiting condition 2: | Ntotal = Nox | I405ox = Ntotal · i405ox |
| Complete oxidation | Nred = 0 | I488ox = Ntotal · i488ox |
| Actual measurement | Ntotal = Nred + Nox | I405 = Nox · i405ox + Nred · i405red |
| I488 = Nox · i488ox + Nred · i488red |
By substituting the resulting equations (right column of Table 3) into OxDroGFP2=Nox/Ntotal, the relationship between OxDroGFP2 and the macroscopic observables can be deduced.[1]
$$oxD_{roGFP2}=\frac{I405\cdot I488_{red}-I405_{red}\cdot I488}{I405\cdot I488_{red}-I405\cdot I488_{ox}+I405_{ox}\cdot I488-I405_{red}\cdot I488}$$
After the above relationship is completed, since the absolute protein concentration determination is difficult, we define the relative reaction rate as
$$V^{'}=\frac{V}{[roGFP2_{ox}]+[roGFP2_{red}]}$$
$$OxD_{roGFP2}=\frac{[roGFP2_{ox}]}{[roGFP2_{ox}]+[roGFP2_{red}]}$$
$$V^{'}=\frac{OxD^{'}-OxD}{t^{'}-t}$$
At the same time, according to Hypothesis 2, roGFP2total is constant, but the protein concentration could not be measured by us. So we thought that under the same promoter conditions, the protein concentration was basically the same and according to the data provided in the previous literature, it is known that in yeast cells, the Eno2 protein concentration is around 0.5 mM.[2]
So we could get:
$$[roGFP2_{total}]=0.5\ mM$$
In order to obtain the two constants in the Michealis equation, we measured the reaction rate of the reaction in yeast cells by applying different concentrations of H2O2 and using the simulation results of the H2O2 Decomposition Model in combination with the function of roGFP2. The results were as follows:
Calculate two constants by double reciprocal mapping.
$$v_{max}=0.015207$$
$$K_{m}=0.451642$$
The relationship between the change in fluorescence intensity of roGFP2 and the concentration of intracellular H2O2 is set up successfully.
Our model has been successfully implemented. Different concentrations of intracellular H2O2 can change the spectral properties of our system's roGFP2, and successfully convert our selected ROS signal (Intercellular H2O2 concentration) into a visualized fluorescent signal that means we can evaluate the intercellular H2O2 concentration easily through calculate the OxD value. However, due to time and experimental limitation, our model is only a preliminary establishment, and its subsequent calibration work is limited by experiment and time, there is no enough time to continue optimization .We also hoped that there will be follow-up teams to continue to finish our models.
