Relation between native ensembles and experimental structures of proteins

Abstract

Different experimental structures of the same protein or of proteins with high sequence similarity contain many small variations. Here we construct ensembles of "high-sequence similarity Protein Data Bank" (HSP) structures and consider the extent to which such ensembles represent the structural heterogeneity of the native state in solution. We find that different NMR measurements probing structure and dynamics of given proteins in solution, including order parameters, scalar couplings, and residual dipolar couplings, are remarkably well reproduced by their respective high-sequence similarity Protein Data Bank ensembles; moreover, we show that the effects of uncertainties in structure determination are insufficient to explain the results. These results highlight the importance of accounting for native-state protein dynamics in making comparisons with ensemble-averaged experimental data and suggest that even a modest number of structures of a protein determined under different conditions, or with small variations in sequence, capture a representative subset of the true native-state ensemble.

Fig. 1.

Leu side chains from the ubiquitin HSP ensemble with δ-methyl order parameters of 0.7 (L50) (a) and 0.2 (L8) (b).

Fig. 2.

Methyl group side-chain order parameters, S_axis², calculated over HSP ensembles (red lines) and NMR ensembles (blue lines) compared with experimental data (shaded black curves). The number of structures in the HSP and NMR ensembles are reported next to the name of the protein. Data for calmodulin and troponin C correspond to the N-terminal lobe only. The methyl group index on the x-axis is obtained by sorting in increasing order of residue number and methyl number (e.g., γ1 < γ2).

Fig. 3.

Methyl axis order parameters (S_axis²) for HIV-1 protease. (a–e) The following sets of S_axis² are compared with those determined from ²H relaxation experiments. (a) S_axis² calculated from HSP ensembles. (b) A separate set of experimental S_axis² from ¹³C relaxation. (c and d) S_axis² from ensembles of 50 structures generated by the RAPPER algorithm (27) before (c) and after (d) refinement against x-ray data. (e) S_axis² calculated from the NMR ensemble (PDB ID code 1BVE). Solid lines correspond to ideal coincidence of the two data sets; broken lines indicate ±0.2 from this value. Data points are color-coded by methyl type as follows: black, Leu δ1,δ2; red, Val γ1,γ2; green, Ile γ2; blue, Ile δ1; orange, Ala β. (f) rmsd between HSP and experimental order parameters as a function of HSP ensemble size.

Fig. 4.

χ₁ rotamer populations for representative residues in ubiquitin. Fractional populations calculated from RDCs (solid) (14) and from dynamic ensemble refinement (DER; hatched) (30) are compared. Full results are available in Table 2.

Fig. 5.

Distributions of RDC Q-factors for fits to NH RDCs from hen lysozyme (31). (a) Q factors for fits of individual HSP ensemble members to experimental RDCs. The solid line indicates the fit obtained from an ensemble average and the broken line the fit for the first member of the PDB ID code 1E8L NMR ensemble. (b) Q-factors for fits to structures generated from random normal mode displacements at 300 K to a set of synthetic RDCs derived from the minimum energy structure. Solid lines shows the Q-factors for RDCs ensemble-averaged over this set of structures.