How accurate are polymer models in the analysis of Förster resonance energy transfer experiments on proteins?

Single molecule Förster resonance energy transfer (FRET) experiments are used to infer the properties of the denatured state ensemble (DSE) of proteins. From the measured average FRET efficiency, <E>, the distance distribution P(R) is inferred by assuming that the DSE can be described as a polymer. The single parameter in the appropriate polymer model (Gaussian chain, wormlike chain, or self-avoiding walk) for P(R) is determined by equating the calculated and measured <E>. In order to assess the accuracy of this "standard procedure," we consider the generalized Rouse model (GRM), whose properties [<E> and P(R)] can be analytically computed, and the Molecular Transfer Model for protein L for which accurate simulations can be carried out as a function of guanadinium hydrochloride (GdmCl) concentration. Using the precisely computed <E> for the GRM and protein L, we infer P(R) using the standard procedure. We find that the mean end-to-end distance can be accurately inferred (less than 10% relative error) using <E> and polymer models for P(R). However, the value extracted for the radius of gyration (R(g)) and the persistence length (l(p)) are less accurate. For protein L, the errors in the inferred properties increase as the GdmCl concentration increases for all polymer models. The relative error in the inferred R(g) and l(p), with respect to the exact values, can be as large as 25% at the highest GdmCl concentration. We propose a self-consistency test, requiring measurements of <E> by attaching dyes to different residues in the protein, to assess the validity of describing DSE using the Gaussian model. Application of the self-consistency test to the GRM shows that even for this simple model, which exhibits an order-->disorder transition, the Gaussian P(R) is inadequate. Analysis of experimental data of FRET efficiencies with dyes at several locations for the cold shock protein, and simulations results for protein L, for which accurate FRET efficiencies between various locations were computed, shows that at high GdmCl concentrations there are significant deviations in the DSE P(R) from the Gaussian model.