An Adequate Account of Excluded Volume Is Necessary To Infer Compactness and Asphericity of Disordered Proteins by Förster Resonance Energy Transfer.

Single-molecule Förster resonance energy transfer (smFRET) is an important tool for studying disordered proteins. It is commonly utilized to infer structural properties of conformational ensembles by matching experimental average energy transfer ⟨E⟩exp with simulated ⟨E⟩sim computed from the distribution of end-to-end distances in polymer models. Toward delineating the physical basis of such interpretative approaches, we conduct extensive sampling of coarse-grained protein chains with excluded volume to determine the distribution of end-to-end distances conditioned upon given values of radius of gyration Rg and asphericity A. Accordingly, we infer the most probable Rg and A of a protein disordered state by seeking the best fit between ⟨E⟩exp and ⟨E⟩sim among various (Rg,A) subensembles. Application of our method to residues 1-90 of the intrinsically disordered cyclin-dependent kinase (Cdk) inhibitor Sic1 results in inferred ensembles with more compact conformations than those inferred by conventional procedures that presume either a Gaussian chain model or the mean-field Sanchez polymer theory. The Sic1 compactness we infer is in good agreement with small-angle X-ray scattering data for Rg and NMR measurement of hydrodynamic radius Rh. In contrast, owing to neglect or underappreciation of excluded volume, conventional procedures can significantly overestimate the probabilities of short end-to-end distances, leading to unphysically large smFRET-inferred Rg at high [GdmCl]. It follows that smFRET Sic1 data are incompatible with the presumed homogeneously expanded or contracted conformational ensembles in conventional procedures but are consistent with heterogeneous ensembles allowed by our subensemble method of inference. General ramifications of these findings for smFRET data interpretation are discussed.