Fractal dimension of an intrinsically disordered protein: Small‐angle X‐ray scattering and computational study of the bacteriophage λ N protein

Abstract

Small-angle X-ray scattering (SAXS) was used to characterize the bacteriophage k N protein, a 107 residue intrinsically disordered protein (IDP) that functions as a transcriptional antitermination factor. The SAXS data were used to estimate both the average radius of gyration and the fractal dimension, a measure of the protein's internal scaling properties, under a variety of solution conditions. In the absence of denaturants, the radius of gyration was 38 6 3.5 Å and the fractal dimension was 1.76 6 0.05, slightly larger than the value predicted for a well-solvated polymer with excluded volume (1.7). Neither the radius of gyration nor the fractal dimension changed significantly on the addition of urea, further indicating that the protein is extensively unfolded and well solvated in the absence of denaturant. The addition of NaCl or D 2 O was found to promote aggregation, but did not appear to affect the properties of the monomeric form. The experimental SAXS profiles were also compared with those predicted by a computational model for a random-coil polypeptide, with an adjustable solvation energy term. The experimental data were well fit to the model with the solvation energy close to zero. These results indicate that the k N protein is among the more expanded members of the broad class of IDPs, most likely because of its high content of charged residues and a large net charge (115 at neutral pH). The expanded nature of the conformational ensemble may play a role in facilitating the interactions of the protein with other components of the dynamic transcriptional complex.

Small-Angle X-ray Scattering and Single-Molecule FRET Spectroscopy Produce Highly Divergent Views of the Low-Denaturant Unfolded State

“…The extent to which the scattering from an unfolded polymer reflects an expanded, random coil state or a more compact conformation can also be ascertained from the relationship between scattering intensity, I , and scattering angle, q , at larger scattering angles ( q > 1/ R g ), where: $$I\left(q\right)\propto q^{-\mathit{Dm}}$$ In this relationship, which holds for many particle types, D m , is a constant that reflects the “fractal dimension” of the scattering particle [see (30, 31) and references therein]. For polymers D m ranges from unity for a fully extended, one-dimensional chain to 3 for a compact globule.…”

“…( middle ) Guinier representations of the scattering data likewise suggest that equilibrium unfolded protein L undergoes little if any change in dimensions down to at least 3.5 M GuHCl. ( bottom ) Finally, analysis of the fractal dimensions (30, 31) of unfolded protein L likewise suggests that its unfolded state remains expanded from 7 to 3.5 M GuHCl, as the slopes of log( I ) versus log ( q ) plots (corresponding to the fractal dimension, D m ) collected under these conditions all fall between 1.52±0.01 to 1.62±0.01. The observed slopes approximate the 1.7 expected for an excluded volume random coil and fall far below the value of 3 expected for a compact globule.…”

“…Fractal dimensions (Figs. 2, 4) were determined as outlined in the literature (30, 31). The chemical melts (plots of equilibrium R g versus denaturant concentration-Fig.…”

Describing sequence–ensemble relationships for intrinsically disordered proteins

“…If |f + –f − | < 0.2, then the sequences are most likely to be globule formers and for values of |f + –f − | larger than 0.2, one observes a continuous transition into non-globular, expanded coils, where the precise power law followed by quantities such as 〈 R g 〉 as a function of N or 〈 R ij 〉 as a function of sequence separation |j–i| depends on the value of |f + –f − |. These findings were converged upon by different groups through a combination of single molecule FRET measurements [58], synergy between molecular simulations and fluorescence spectroscopies [146], NMR measurements of hydrodynamic sizes [147], and SAXS [123]. …”

Consistent View of Polypeptide Chain Expansion in Chemical Denaturants from Multiple Experimental Methods

“…With some exceptions 18–20 , several studies using SAXS and SANS experiments did not find a statistically significant change in unfolded state R g over the experimentally accessible range of denaturant concentration, for two-state folding proteins 20–24 and for an IDP 25 . For larger proteins, collapse upon denaturant dilution has been observed in time-resolved SAXS experiments, but in those cases the presence of stable folding intermediates modulating the observed R g cannot be excluded 26–28 .…”