Intrinsically disordered proteins (IDPs) have fluctuating heterogeneous conformations, which makes their structural characterization challenging. Although challenging, characterization of the conformational ensembles of IDPs is of great interest, since their conformational ensembles are the link between their sequences and functions. An accurate description of IDP conformational ensembles depends crucially on the amount and quality of the experimental data, how it is integrated, and if it supports a consistent structural picture. We used integrative modeling and validation to apply conformational restraints and assess agreement with the most common structural techniques for IDPs: Nuclear Magnetic Resonance (NMR) spectroscopy, Small-angle X-ray Scattering (SAXS), and single-molecule Förster Resonance Energy Transfer (smFRET). Agreement with such a diverse set of experimental data suggests that details of the generated ensembles can now be examined with a high degree of confidence. Using the disordered N-terminal region of the Sic1 protein as a test case, we examined relationships between average global polymeric descriptions and higher-moments of their distributions. To resolve apparent discrepancies between smFRET and SAXS inferences, we integrated SAXS data with NMR data and reserved the smFRET data for independent validation. Consistency with smFRET, which was not guaranteed a priori, indicates that, globally, the perturbative effects of NMR or smFRET labels on the Sic1 ensemble are minimal. Analysis of the ensembles revealed distinguishing features of Sic1, such as overall compactness and large end-to-end distance fluctuations, which are consistent with biophysical models of Sic1’s ultrasensitive binding to its partner Cdc4. Our results underscore the importance of integrative modeling and validation in generating and drawing conclusions from IDP conformational ensembles.

Single-molecule Förster resonance energy transfer (smFRET) is an important tool for studying disordered proteins. It is commonly utilized to infer structural properties of conformational ensembles by matching experimental average energy transfer ⟨E⟩exp with simulated ⟨E⟩sim computed from the distribution of end-to-end distances in polymer models. Toward delineating the physical basis of such interpretative approaches, we conduct extensive sampling of coarse-grained protein chains with excluded volume to determine the distribution of end-to-end distances conditioned upon given values of radius of gyration Rg and asphericity A. Accordingly, we infer the most probable Rg and A of a protein disordered state by seeking the best fit between ⟨E⟩exp and ⟨E⟩sim among various (Rg,A) subensembles. Application of our method to residues 1-90 of the intrinsically disordered cyclin-dependent kinase (Cdk) inhibitor Sic1 results in inferred ensembles with more compact conformations than those inferred by conventional procedures that presume either a Gaussian chain model or the mean-field Sanchez polymer theory. The Sic1 compactness we infer is in good agreement with small-angle X-ray scattering data for Rg and NMR measurement of hydrodynamic radius Rh. In contrast, owing to neglect or underappreciation of excluded volume, conventional procedures can significantly overestimate the probabilities of short end-to-end distances, leading to unphysically large smFRET-inferred Rg at high [GdmCl]. It follows that smFRET Sic1 data are incompatible with the presumed homogeneously expanded or contracted conformational ensembles in conventional procedures but are consistent with heterogeneous ensembles allowed by our subensemble method of inference. General ramifications of these findings for smFRET data interpretation are discussed.

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 prejudgement, 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 R g . 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 R g of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that R g of unfolded Protein L is highly sensitive to [GuHCl], but data from small-angle X-ray scattering (SAXS) suggested a near-constant R g irrespective of [GuHCl]. Strikingly, the present analysis indicates that although the reported E 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 g 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.

Proteins with intrinsic or unfolded state disorder comprise a new frontier in structural biology, requiring the characterization of diverse and dynamic structural ensembles. Here we introduce a comprehensive Bayesian framework, the Extended Experimental Inferential Structure Determination (X-EISD) method, which calculates the maximum log-likelihood of a disordered protein ensemble. X-EISD accounts for the uncertainties of a range of experimental data and back-calculation models from structures, including NMR chemical shifts, J-couplings, Nuclear Overhauser Effects (NOEs), paramagnetic relaxation enhancements (PREs), residual dipolar couplings (RDCs), hydrodynamic radii (Rh), single molecule fluorescence Förster resonance energy transfer (smFRET) and small angle X-ray scattering (SAXS). We apply X-EISD to the joint optimization against experimental data for the unfolded drkN SH3 domain and find that combining a local data type, such as chemical shifts or J-couplings, paired with long-ranged restraints such as NOEs, PREs or smFRET, yields structural ensembles in good agreement with all other data types if combined with representative IDP conformers.

Conformational states of the metastable drkN SH3 domain were characterized using single-molecule fluorescence techniques. Under nondenaturing conditions, two Förster resonance energy transfer (FRET) populations were observed that corresponded to a folded and an unfolded state. FRET-estimated radii of gyration and hydrodynamic radii estimated by fluorescence correlation spectroscopy of the two coexisting conformations are in agreement with previous ensemble x-ray scattering and NMR measurements. Surprisingly, when exposed to high concentrations of urea and GdmCl denaturants, the protein still exhibits two distinct FRET populations. The dominant conformation is expanded, showing a low FRET efficiency, consistent with the expected behavior of a random chain with excluded volume. However, approximately one-third of the drkN SH3 conformations showed high, nearly 100%, FRET efficiency, which is shown to correspond to denaturation-induced looped conformations that remain stable on a timescale of at least 100 μs. These loops may contain interconverting conformations that are more globally collapsed, hairpin-like, or circular, giving rise to the observed heterogeneous broadening of this population. Although the underlying mechanism of chain looping remains elusive, FRET experiments in formamide and dimethyl sulfoxide suggest that interactions between hydrophobic groups in the distal regions may play a significant role in the formation of the looped state.