A self-consistent description of the conformational behavior of chemically denatured proteins from NMR and small angle scattering

Abstract

Characterization of the conformational properties of unfolded proteins is essential for understanding the mechanisms of protein folding and misfolding. This information is also fundamental to determining the relationship between flexibility and function in the highly diverse families of intrinsically disordered proteins. Here we present a self-consistent model of conformational sampling of chemically denatured proteins in agreement with experimental data reporting on long-range distance distributions in unfolded proteins using small-angle x-ray scattering and nuclear magnetic resonance pulse-field gradient-based measurements. We find that standard statistical coil models, selected from folded protein databases with secondary structural elements removed, need to be refined to correct backbone dihedral angle sampling of denatured proteins, although they appear to be appropriate for intrinsically disordered proteins. For denatured proteins, pervasive increases in the sampling of more-extended regions of Ramachandran space {50 degrees <psi < 180 degrees} throughout the peptide chain are found to be consistent with all experimental data. These observations are in agreement with previous conclusions derived from short-range nuclear magnetic resonance data from residual dipolar couplings, leading the way to a self-consistent description of denatured chains that is in agreement with short- and long-range data measured using both spectroscopic and scattering techniques.

Figure 1

Correlation between experimental and theoretical values of (a) radius of gyration R_g, and (b) hydrodynamic radius R_h for the ensembles corresponding to the standard database. Dashed line represents slope equal to 1.0. Experimental values of R_g were obtained from Kohn et al. (11), and R_h values were obtained from Wilkins et al. (47) and Pan et al. (48).

Figure 2

Optimal percentage of extended conformations. Agreement of the overall parameters (a) R_g and (b) R_h upon increasing the percentage of extended conformations in the database. Correlation between the experimental and theoretical (c) R_g and (d) R_h at the optimal database found, X = 2.0, which corresponds to a 74.2% of extended conformations. Dashed line again represents slope equal to 1.0.

Figure 3

Reproduction of experimental residual dipolar couplings measured from urea unfolded ubiquitin at pH2 aligned in polyacrylamide gel using databases sampling different levels of extension. The χ² is measured over seven types of coupling: ¹D_NH, ¹D_CαHα, ¹D_CαC′, D_{HNHα (i,i-1)}, D_{HNHN (i,i+1)}, D_HNHN(i,i+2), and D_HNHα. Data taken from Meier et al. (25).

Figure 4

Relationship of the R_g (a) and R_h (b) values calculated using the standard database with the length of the protein chain N. From this correlation, the parameters of Flory's relationship (Eq. 1) were derived for both observables. From R_g, ν = 0.522 ± 0.01 and R₀ = 2.54 ± 0.01; and from R_h, ν = 0.449 ± 0.01 and R₀ = 3.53 ± 0.01. (c) R_g values compiled for protein τ (solid circles) and other IDPs (open circles), compared with the threshold values according to the calibration found in panel a (solid line). See the Supporting Material for the list of IDPs used in this plot.