A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule F\"orster 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 prejudgement, a single value of average transfer efficiency \langle E\rangle between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration \langle R_{\rm g}\rangle. 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 \langle R_{\rm g}\rangle of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that \langle R_{\rm g}\rangle of unfolded Protein L is highly sensitive to [GuHCl], but data from small-angle X-ray scattering (SAXS) suggested a near-constant \langle R_{\rm g}\rangle irrespective of [GuHCl]. Strikingly, the present analysis indicates that although the reported \langle E\rangle values for Protein L at [GuHCl] = 1 M and 7 M are very different at 0.75 and 0.45, respectively, the  R^2_{\rm g} distributions consistent with these two \langle E\rangle values overlap by as much as 75\\%DIF < . 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 will be needed to ascertain the nature of this heterogeneity.abstract %DIF > . 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.
A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule F\"orster 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 prejudgement, a single value of average transfer efficiency \langle E\rangle between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration \langle R_{\rm g}\rangle. 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 \langle R_{\rm g}\rangle of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that \langle R_{\rm g}\rangle of unfolded Protein L is highly sensitive to [GuHCl], but data from small-angle X-ray scattering (SAXS) suggested a near-constant \langle R_{\rm g}\rangle irrespective of [GuHCl]. Strikingly, the present analysis indicates that although the reported \langle E\rangle values for Protein L at [GuHCl] = 1 M and 7 M are very different at 0.75 and 0.45, respectively, the Bayesian R^2_{\rm g} distributions consistent with these two \langle E\rangle values overlap by as much as 75\\%DIF < . 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 will be needed to ascertain the nature of this heterogeneity.abstract %DIF > . 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.
A
Bayesian