Characterizing the unfolded states of proteins using single-molecule FRET spectroscopy and molecular simulations.

To obtain quantitative information on the size and dynamics of unfolded proteins we combined single-molecule lifetime and intensity FRET measurements with molecular simulations. We compared the unfolded states of the 64-residue, alpha/beta protein L and the 66-residue, all-beta cold-shock protein CspTm. The average radius of gyration (Rg) calculated from FRET data on freely diffusing molecules was identical for the two unfolded proteins at guanidinium chloride concentrations >3 M, and the FRET-derived Rg of protein L agreed well with the Rg previously measured by equilibrium small-angle x-ray scattering. As the denaturant concentration was lowered, the mean FRET efficiency of the unfolded subpopulation increased, signaling collapse of the polypeptide chain, with protein L being slightly more compact than CspTm. A decrease in Rg with decreasing denaturant was also observed in all-atom molecular dynamics calculations in explicit water/urea solvent, and Langevin simulations of a simplified representation of the polypeptide suggest that collapse can result from either increased interresidue attraction or decreased excluded volume. In contrast to both the FRET and simulation results, previous time-resolved small-angle x-ray scattering experiments showed no collapse for protein L. Analysis of the donor fluorescence decay of the unfolded subpopulation of both proteins gives information about the end-to-end chain distribution and suggests that chain dynamics is slow compared with the donor life-time of approximately 2 ns, whereas the bin-size independence of the small excess width above the shot noise for the FRET efficiency distributions may result from incomplete conformational averaging on even the 1-ms time scale.