Conformational Heterogeneity and FRET Data Interpretation for Dimensions of Unfolded Proteins.

A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule Förster resonance energy transfer (smFRET). Conformational dimensions inferred by conventional approaches that presume a homogeneous conformational ensemble can be unphysical. When all possible-heterogeneous as well as homogeneous-conformational distributions are taken into account without prejudgment, a single value of average transfer efficiency 〈E〉 between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration 〈Rg〉. Here we utilize unbiased conformational statistics from a coarse-grained explicit-chain model to establish a general logical framework to quantify this fundamental ambiguity in smFRET inference. As an application, we address the long-standing controversy regarding the denaturant dependence of 〈Rg〉 of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that 〈Rg〉 of unfolded Protein L is highly sensitive to [GuHCl], but data from SAXS suggested a near-constant 〈Rg〉 irrespective of [GuHCl]. Strikingly, our analysis indicates that although the reported 〈E〉 values for Protein L at [GuHCl] = 1 and 7 M are very different at 0.75 and 0.45, respectively, the Bayesian Rg2 distributions consistent with these two 〈E〉 values overlap by as much as 75%. Our findings suggest, in general, that the smFRET-SAXS discrepancy regarding unfolded protein dimensions likely arise from highly heterogeneous conformational ensembles at low or zero denaturant, and that additional experimental probes are needed to ascertain the nature of this heterogeneity.