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How can I calculate the alpha helix content (i.e. percent) in a protein from a given molar ellipticity of 222 nm, without using any software. I have tried the Greenfield-Fasman equation, but the answer doesn't seems to be correct.

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You can use the information at this site, especially section 3. (https://www.photophysics.com/resources/tutorials/circular-dichroism-cd-spectroscopy)

Notice the different CD spectra for alpha-helix, beta-sheets and random coil. If your protein is measured at 222nm you need to compare your measured values to the the spectra at 222nm, this will allow you to guestimate the secondary structure of the protein, but if you want to be accurate, you will need to measure at several wavelengths to determine the distribution of alpha helix, beta-sheet and random coil. This is because all three contribute to the measure spectra and as such you need several measurements to figure out the relative contributions of each secondary structure.

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