SAXS versus FRET: A Matter of Heterogeneity?

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Determining how conformational properties of unfolded proteins vary as a function of denaturant concentration has important implications for understanding the early stages of protein folding, and for our understanding of protein-solvent interactions. Upon dilution from a high concentration of denaturant into native conditions, does an unfolded protein undergo collapse first followed by folding, or does the chain remain expanded before folding and collapse occur concomitantly? The global dimensions of a protein are captured by its radius of gyration (R_g), meaning that, in principle, this question should be simple to answer by measuring R_g as a function of denaturant concentration. However, for several proteins, R_g, as directly quantified by small-angle x-ray scattering (SAXS) experiments, shows minimal changes as a function of denaturant concentration (1, 2). In contrast, for the same set of proteins, inferences drawn from single-molecule Förster resonance energy transfer (smFRET) experiments suggest R_g undergoes a significant and continuous collapse as denaturant concentration is reduced (2, 3, 4). These results have led to questions as to whether the observed discrepancy is due to the high protein concentrations needed for SAXS experiments, the presence of the dyes in smFRET experiments, or some additional inherent shortcoming of either or both experimental methods (1, 2, 5, 6, 7). In this issue, Song et al. (8) demonstrate that the observed discrepancy is not necessarily due to an inherent problem with either SAXS or smFRET. Instead, the discrepancy emerges due to the use of the conventional inference strategy utilized to convert mean FRET transfer efficiencies (〈E〉) measured in smFRET experiments into estimates of R_g that can then be directly compared to R_g measured from SAXS.

What is the conventional inference strategy, and why does it lead to this discrepancy? The conventional inference strategy consists of two parts. First, a homogenous polymer model is utilized to infer the end-to-end distance, R_EE, from the measured 〈E〉. Second, a one-to-one mapping between R_EE and R_g is used to extrapolate R_g from R_EE (4). Both of these inferences rely on the assumption that the underlying conformational ensemble expands or contracts uniformly—an assumption that ignores the chemical heterogeneity associated with polypeptides. Such an assumption is likely reasonable at high denaturant concentrations where the solvent quality is such that proteins behave like homopolymeric self-avoiding random coils, and thus explains why inferences regarding conformational properties of proteins often agree between SAXS and smFRET measurements under these conditions (1, 2, 3, 4, 8, 9). However, as denaturant concentration is decreased, there is a reduction in the effective solvent quality. This leads to the formation of sequence-dependent interactions that introduces conformational heterogeneity not captured by mean-field homopolymer models. Thus, as the concentration of denaturant decreases, the conventional inference strategy becomes increasingly inappropriate for inferring R_g from 〈E〉 due to the inherent decoupling of R_g and R_EE.

Song et al. (8) demonstrate the decoupling of R_g and R_EE by extracting conditional R_g distributions from minimal C_α resolution, explicit-chain simulations given a specific experimental 〈E〉. The use of explicit-chain simulations allows for the construction of a large ensemble of physically realizable conformations. Here, conformational heterogeneity is introduced by extracting subensembles that are consistent with a given E value. The authors show that by accounting for heterogeneity in the underlying ensembles, large changes in E can be consistent with minimal changes in R_g. This decoupling of R_g and E, and thus consequently R_EE, is shown in Fig. 1, which reproduces the 2D distribution of E and R_g. For unconstrained simulations, this 2D space illustrates how relatively similar R_g values can be consistent with a wide range of E values. Focusing on the archetypal Protein L, Song et al. (8) calculated R_g values from subensembles that are consistent with experimentally derived 〈E〉 values for a range of denaturant conditions. Using these values, the authors demonstrate that R_g remains relatively constant as a function of denaturant concentration, consistent with SAXS results.

Figure 1.

2D distribution of transfer efficiency (E) and radius of gyration (R_g) demonstrates the decoupling of E and R_g. Insets depict cartoon representations of conformations with similar R_g values but different E values. The terminal residues are depicted by green and red circles. This figure was adapted from Fig. 3 from Song et al. (8). To see this figure in color, go online.

Importantly, Song et al. (8) are clear that their strategy only provides a general rationale for the SAXS-smFRET discrepancy, but cannot yield insights on the sequence-dependent source of the conformational heterogeneity for a given protein. The extent of conformational heterogeneity, and thus whether the conformational properties of an unfolded protein can be reasonably approximated using homopolymer models, will be sequence dependent and is typically unknown a priori. As a result, understanding the extent and type of sequence-dependent interactions that lead to deviations from homopolymer models represents an important next step in interpreting smFRET data.

The lack of a one-to-one mapping between fluctuations at the ends of chains, as quantified by 〈E〉, and global size, as quantified by R_g, for heterogeneous ensembles (i.e., unfolded proteins in low denaturant concentrations) suggests that caution must be taken when converting between conformational descriptors that interrogate a specific length scale (〈E〉) and conformational descriptors that average over all interresidue distances (R_g). SAXS can provide an accurate description of an unfolded protein’s global size (R_g) and shape, but cannot necessarily offer information regarding a specific length scale (e.g., R_EE) without the application of some kind of model. Similarly, smFRET can yield an accurate description regarding the distance between two residues of an unfolded protein. However, the conversion of interresidue distances into a globally averaged conformational descriptor (e.g., R_g) requires extrapolation using some model. Thus, if both length-scale-specific and globally averaged conformational descriptions are desired, then additional strategies should be pursued. For SAXS, methods that quantify intramolecular distances, such as anomalous SAXS combined with gold labels, can be deployed to determine length-scale specific properties (10). Equivalently, for smFRET, multiple interdye distance measurements can be used to infer globally averaged properties (11). Additionally, as demonstrated by Song et al. and others, combining SAXS and/or smFRET measurements with explicit-chain simulations can yield further insights regarding the conformational behaviors of unfolded proteins (2, 5, 6, 8).

Altogether, these results suggest that theories designed for homopolymers may be inadequate to simultaneously provide accurate globally averaged and length-scale-specific conformational descriptions of unfolded proteins using either SAXS-derived R_g or smFRET-derived transfer efficiencies alone. Instead, to develop complete conformational descriptions of heterogeneous ensembles, a combination of experimental measurements designed to extract distinct conformational properties, as well as the aid of computational methods, are needed.

Editor: Rohit Pappu.