  Single molecule Forster 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 (Rg) and the persistence length (lp) are less accurate.
The relative error in the inferred R-g and lp, 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 the Gaussian P(R) is inadequate. Analysis
of experimental data of FRET efficiencies for the cold shock protein shows that
at there are significant deviations in the DSE P(R) from the Gaussian model.
