Unfolded states of proteins and native states of intrinsically disordered proteins (IDPs) populate heterogeneous conformational ensembles in solution. The average sizes of these heterogeneous systems, quantified by the radius of gyration (R G ), can be measured by small-angle X-ray scattering (SAXS). Another parameter, the mean dye-to-dye distance (R E ) for proteins with fluorescently labeled termini, can be estimated using single-molecule Förster resonance energy transfer (smFRET). A number of studies have reported inconsistencies in inferences drawn from the two sets of measurements for the dimensions of unfolded proteins and IDPs in the absence of chemical denaturants. These differences are typically attributed to the influence of fluorescent labels used in smFRET and to the impact of high concentrations and averaging features of SAXS. By measuring the dimensions of a collection of labeled and unlabeled polypeptides using smFRET and SAXS, we directly assessed the contributions of dyes to the experimental values R G and R E . For chemically denatured proteins we obtain mutual consistency in our inferences based on R G and R E , whereas for IDPs under native conditions, we find substantial deviations. Using computations, we show that discrepant inferences are neither due to methodological shortcomings of specific measurements nor due to artifacts of dyes. Instead, our analysis suggests that chemical heterogeneity in heteropolymeric systems leads to a decoupling between R E and R G that is amplified in the absence of denaturants. Therefore, joint assessments of R G and R E combined with measurements of polymer shapes should provide a consistent and complete picture of the underlying ensembles.single-molecule FRET | intrinsically disordered proteins | denatured-state ensemble | protein folding | polymer theory Q uantitative characterizations of the sizes, shapes, and amplitudes of conformational fluctuations of unfolded proteins under denaturing and native conditions are directly relevant to advancing our understanding of the collapse transition during protein folding. These types of studies are also relevant to furthering our understanding of the functions and interactions of intrinsically disordered proteins (IDPs) in physiologically relevant conditions (1). Polymer physics theories provide the conceptual foundations for analyzing conformationally heterogeneous systems such as IDPs and unfolded ensembles of autonomously foldable proteins (2-4). Specifically, order parameters in theories of coil-toglobule transitions and analytical descriptions of conformational ensembles (5, 6) are based on ensemble-averaged values of radii of gyration (R G ) and amplitudes of fluctuations measured by end-toend distances (R E ).Estimates of R G are accessible through small-angle X-ray scattering (SAXS) measurements because scattering intensities are directly related to the global protein size (Fig. 1) (7, 8). At finite concentrations, assuming the absence of intermolecular interactions, R G is proportional to the square root o...

SummaryThe mechanisms by which intrinsically disordered proteins engage in rapid and highly selective binding is a subject of considerable interest and represents a central paradigm to nuclear pore complex (NPC) function, where nuclear transport receptors (NTRs) move through the NPC by binding disordered phenylalanine-glycine-rich nucleoporins (FG-Nups). Combining single-molecule fluorescence, molecular simulations, and nuclear magnetic resonance, we show that a rapidly fluctuating FG-Nup populates an ensemble of conformations that are prone to bind NTRs with near diffusion-limited on rates, as shown by stopped-flow kinetic measurements. This is achieved using multiple, minimalistic, low-affinity binding motifs that are in rapid exchange when engaging with the NTR, allowing the FG-Nup to maintain an unexpectedly high plasticity in its bound state. We propose that these exceptional physical characteristics enable a rapid and specific transport mechanism in the physiological context, a notion supported by single molecule in-cell assays on intact NPCs.

Understanding the function of intrinsically disordered proteins is intimately related to our capacity to correctly sample their conformational dynamics. So far, a gap between experimentally and computationally derived ensembles exists, as simulations show overcompacted conformers. Increasing evidence suggests that the solvent plays a crucial role in shaping the ensembles of intrinsically disordered proteins and has led to several attempts to modify water parameters and thereby favor protein-water over protein-protein interactions. This study tackles the problem from a different perspective, which is the use of the Kirkwood-Buff theory of solutions to reproduce the correct conformational ensemble of intrinsically disordered proteins (IDPs). A protein force field recently developed on such a basis was found to be highly effective in reproducing ensembles for a fragment from the FG-rich nucleoporin 153, with dimensions matching experimental values obtained from small-angle X-ray scattering and single molecule FRET experiments. Kirkwood-Buff theory presents a complementary and fundamentally different approach to the recently developed four-site TIP4P-D water model, both of which can rescue the overcollapse observed in IDPs with canonical protein force fields. As such, our study provides a new route for tackling the deficiencies of current protein force fields in describing protein solvation.