Estimations of conformational fractions in a protein

When a system of interest is a mixture of two states that have each been characterized spectroscopically, then it is possible to calculate the fraction of each state within the mixture. As an example, let the system of interest be a protein comprised of a-helix and parallel -pleated sheet and let the observable be the molar ellipticity at a specified wavelength, [0]obs- Taking the characteristic molar ellipticities at the specified wavelength to be [0] and [0] p for the a-helix and the parallel 8-pleated sheet, respectively, the observed molar ellipticity may be expressed in terms of the mole fractions Xi of each of the conformations, i.e., 

This may be written in general for any number of states and for the general observable, a, as 

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