Decoupling of size and shape fluctuations in heteropolymeric sequences reconciles discrepancies in SAXS vs. FRET measurements

Unfolded states of proteins and native states of intrinsically disordered proteins (IDPs) populate heterogeneous conformational ensembles in solution. The average sizes of these heterogeneous systems, quantified by the radius of gyration (R_G), can be measured by small-angle X-ray scattering (SAXS). Another parameter, the mean dye-to-dye distance (R_E) for proteins with fluorescently labeled termini, can be estimated using single-molecule Förster resonance energy transfer (smFRET). A number of studies have reported inconsistencies in inferences drawn from the two sets of measurements for the dimensions of unfolded proteins and IDPs in the absence of chemical denaturants. These differences are typically attributed to the influence of fluorescent labels used in smFRET and to the impact of high concentrations and averaging features of SAXS. By measuring the dimensions of a collection of labeled and unlabeled polypeptides using smFRET and SAXS, we directly assessed the contributions of dyes to the experimental values R_G and R_E. For chemically denatured proteins we obtain mutual consistency in our inferences based on R_G and R_E, whereas for IDPs under native conditions, we find substantial deviations. Using computations, we show that discrepant inferences are neither due to methodological shortcomings of specific measurements nor due to artifacts of dyes. Instead, our analysis suggests that chemical heterogeneity in heteropolymeric systems leads to a decoupling between R_E and R_G that is amplified in the absence of denaturants. Therefore, joint assessments of R_G and R_E combined with measurements of polymer shapes should provide a consistent and complete picture of the underlying ensembles.