The IC50 value represents the concentration of a substance that inhibits 50% of the target activity. In the case of the DPPH assay, the IC50 value represents the concentration of the antioxidant substance that is needed to scavenge 50% of the DPPH free radicals.

To determine the theoretical IC50 value for the DPPH assay, you can perform a dose-response curve using different concentrations of the antioxidant substance. The percentage of inhibition can be calculated by comparing the absorbance values of the sample and control (DPPH only). The data can be plotted as a graph of inhibition percentage against the concentration of the antioxidant substance. The concentration that causes 50% inhibition can be determined from the curve and is considered the theoretical IC50 value.

Here are the general steps to determine the theoretical IC50 value for the DPPH assay:

1. Prepare a series of dilutions of the antioxidant substance in a suitable solvent (e.g., methanol, ethanol, or water).

2. Prepare a DPPH solution in a suitable solvent at a fixed concentration (e.g., 0.1 mM).

3. Add a fixed volume of the DPPH solution to each well of a microplate.

4. Add a fixed volume of each dilution of the antioxidant substance to the corresponding wells of the microplate.

5. Incubate the microplate in the dark at room temperature for a fixed period of time (e.g., 30 minutes).

6. Measure the absorbance of each well at a suitable wavelength (e.g., 517 nm) using a microplate reader.

7. Calculate the percentage of inhibition using the following equation:

% inhibition = [(Acontrol – Asample) / Acontrol] x 100

where Acontrol is the absorbance of the DPPH solution without the antioxidant substance and Asample is the absorbance of the DPPH solution with the antioxidant substance.

8. Plot the percentage of inhibition against the concentration of the antioxidant substance.

9. Determine the concentration of the antioxidant substance that causes 50% inhibition (theoretical IC50 value) from the dose-response curve.

It's important to note that the theoretical IC50 value may differ from the actual IC50 value due to experimental variability and the specific conditions of the assay. Therefore, it's recommended to perform replicate experiments and statistical analysis to obtain more reliable results.