Average conformations determined from PRE data provide high-resolution maps of transient tertiary interactions in disordered proteins

Abstract

In the last decade it has become evident that disordered states of proteins play important physiological and pathological roles and that the transient tertiary interactions often present in these systems can play a role in their biological activity. The structural characterization of such states has so far largely relied on ensemble representations, which in principle account for both their local and global structural features. However, these approaches are inherently of low resolution due to the large number of degrees of freedom of conformational ensembles and to the sparse nature of the experimental data used to determine them. Here, we overcome these limitations by showing that tertiary interactions in disordered states can be mapped at high resolution by fitting paramagnetic relaxation enhancement data to a small number of conformations, which can be as low as one. This result opens up the possibility of determining the topology of cooperatively collapsed and hidden folded states when these are present in the vast conformational landscape accessible to disordered states of proteins. As a first application, we study the long-range tertiary interactions of acid-unfolded apomyoglobin from experimentally measured paramagnetic relaxation enhancement data.

Figure 1

Overview of PRE and computer-designed ensembles. (A) Dependence of PRE intensity ratio I_ox/I_red on the distance between a paramagnetic center covalently attached to a residue (e.g., an MTSL label) and an amide group (¹H^N). Distances <∼10 Å are indistinguishable, as are those >∼25 Å. (B) Theoretical PRE intensity ratio for labels at residues 1 and 38 in an arbitrary protein conformation (blue spheres). Neighbors within ∼25 Å of the labeled residues appear as decreased intensities. The first label (attached to residue 1) yields information on interresidue interactions in the proximity of regions I–III, whereas the second label (attached to residue 38) provides long-range contact information on regions III′ and IV′. Intensity profiles for RC models are shown as dashed lines. (C) Representative structures containing designed interactions (red) are shown for ensembles of α-synuclein, ubiquitin, and Aβ42. Gray regions were not restrained and, as a consequence, behave like an RC (not shown for clarity). (D) PRE intensity ratios for several labeled residues in the Ub-unfolded-folded ensemble. PRE profiles of fitted (red) intensities to noise-corrupted (blue) intensities are shown. Intensities with no added error are shown in black.

Figure 2

High-resolution mapping of long-range tertiary interactions in complex disordered protein states as a function of ensemble size (N_rep). (A) Fit to synthetic PRE intensities (RMSD_work; standard deviation ∼0.01). (B) CV against PREs left out of the calculations (RMSD_free; standard deviation ∼0.05). The agreement with PREs derived by randomly chosen conformations from a pool of 10⁴ structures (20 repetitions were made for each ensemble size) is also shown (inset). (C) CV against SAXS for ensembles derived from PRE-restrained (solid lines) and unrestrained (inset) MC simulations. (D) Contact maps determined by rMC simulations as a function of ensemble size. Dashed boxes highlight the tertiary contacts designed for the disordered ensembles; those for Ub-unfolded-folded correspond to the native structure of ubiquitin. For Ub-unfolded-complex, these are numbered for clarity (see Fig. 1C). In all cases, synthetic PRE data (∼1 PRE label every 10 residues) calculated from target ensembles with a population of interresidue contacts at 5% were used. The interresidue contact maps were derived by pooling the results of 20 independent calculations (performed at each ensemble size). Additional target ensembles and maps are given in Figs. S1–S4. The residues labeled are listed in Table S2.

Figure 3

Evaluation of the optimal number of PRE labeling ratio required to recover at high-resolution long-range tertiary interactions in complex disordered states of proteins. (A) Fit to synthetic PRE intensities (RMSD_work). (B) CV calculations against PREs left out of the calculations (RMSD_free). Results for an ensemble size of 1 are shown (see Figs. S8 and S9 for an ensemble size of 5). (C) Contact maps determined for ubiquitin, Aβ, and α-synuclein target ensembles using different numbers of PRE labels for calculated ensembles of size 1 (see Fig. S9 for an ensemble size of 5). Dashed boxes highlight the tertiary contacts designed for the disordered ensembles; those for Ub-unfolded-folded correspond to the native structure of ubiquitin.

Figure 4

High-resolution determination of long-range interresidue tertiary interactions in denatured apomyoglobin. (A) Structure of holomyoglobin (51). (B) Fitting of PREs (black, 14 PRE labels) and CV (red) calculations using rMC simulations for ensembles of increasing size (N_rep). (C) Contact maps as a function of ensemble size (N_rep). The interresidue contact maps were derived by pooling the results of 20 independent calculations (performed at each ensemble size). The per-residue accessible area buried upon folding is shown. Note that in general, calculated structures of disordered systems from PRE data alone (at any ensemble size) cannot be interpreted in terms of representative conformations present in solution (work on this is in progress). Fitted PRE profiles and an illustration of the chimeric headphonelike fold derived by fitting PREs to one conformer are given in Figs. S10 and S11.