Model-independent decomposition of two-state data

Two-state models often provide a reasonable approximation of protein behaviors such as partner binding, folding, and conformational changes. Many different techniques have been developed to determine the population ratio between two states as a function of different experimental conditions. Data analysis is accomplished either by fitting individual measured spectra to a linear combination of known basis spectra or alternatively by decomposing the entire set of spectra into two components using a least-squares optimization of free parameters within an assumed population model. Here we demonstrate that it is possible to determine the population ratio in a two-state system directly from data without an a priori model for basis spectra or populations by applying physical constraints iteratively to a singular value decomposition of optical fluorescence, x-ray-scattering, and electron paramagnetic resonance data.