Assessment of models for calculating the hydrodynamic radius of intrinsically disordered proteins

Abstract

Diffusion measurements by pulsed field gradient NMR and fluorescence correlation spectroscopy can be used to probe the hydrodynamic radius of proteins, which contains information about the overall dimension of a protein in solution. The comparison of this value with structural models of intrinsically disordered proteins is nonetheless impaired by the uncertainty of the accuracy of the methods for computing the hydrodynamic radius from atomic coordinates. To tackle this issue, we here build conformational ensembles of 11 intrinsically disordered proteins that we ensure are in agreement with measurements of compaction by small-angle X-ray scattering. We then use these ensembles to identify the forward model that more closely fits the radii derived from pulsed field gradient NMR diffusion experiments. Of the models we examined, we find that the Kirkwood-Riseman equation provides the best description of the hydrodynamic radius probed by pulsed field gradient NMR experiments. While some minor discrepancies remain, our results enable better use of measurements of the hydrodynamic radius in integrative modelling and for force field benchmarking and parameterization. SIGNIFICANCEAccurate models of the conformational properties of intrinsically disordered proteins rely on our ability to interpret experimental data that reports on the conformational ensembles of these proteins in solution. Methods to calculate experimental observables from conformational ensembles are central to link experiments and computation, for example in integrative modelling or the assessment of molecular force fields. Benchmarking such methods is, however, difficult for disordered proteins because it is difficult to construct accurate ensembles without using the data. We here circumvent this problem by combining independent measures of protein compaction to test several methods to calculate the hydrodynamic radius of a disordered protein, as measured by pulsed field gradient NMR diffusion experiments, and find the Kirkwood-Riseman model to be most accurate.