Hydrodynamic radii (Rh -values) calculated from diffusion coefficients measured by pulse-field-gradient nuclear magnetic resonance are compared for folded and unfolded proteins. For native globular proteins, the Rh -values increase as a power of 0.35 with molecular size, close to the scaling factor of 0.33 predicted from polymer theory. Unfolded proteins were studied under four sets of conditions: in the absence of denaturants, in the presence of 6 M urea, in 95% dimethyl sulfoxide (DMSO), and in 40% hexafluoroisopropanol (HFIP). Scaling factors under all four unfolding conditions are similar (0.49-0.53) approaching the theoretical value of 0.60 for a fully unfolded random coil. Persistence lengths are also similar, except smaller in 95% DMSO, suggesting that the polypeptides are more disordered on a local scale with this solvent. Three of the proteins in our unfolded set have an asymmetric sequence-distribution of charged residues. While these proteins behave normally in water and 6 M urea, they give atypically low Rh -values in 40% HFIP and 95% DMSO suggesting they are forming electrostatic hairpins, favored by their asymmetric sequence charge distribution and the low dielectric constants of DMSO and HFIP. While diffusion-ordered NMR spectroscopy can separate small molecules, we show a number of factors combine to make protein-sized molecules much more difficult to resolve in mixtures. Finally, we look at the temperature dependence of apparent diffusion coefficients. Small molecules show a linear temperature response, while large proteins show abnormally large apparent diffusion coefficients at high temperatures due to convection, suggesting diffusion reference standards are only useful near 25°C.
Keywords: Flory scaling factor; convection flow; diffusion-edited spectroscopy; dimethyl sulfoxide; fluorinated alcohols; protein folding; pulsed-gradient spin-echo NMR; translational self-diffusion coefficient.
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