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, ␣/␤ protein L and the 66-residue, all-␤ cold-shock protein CspTm. The average radius of gyration (R g) 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 R g of protein L agreed well with the R g 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 R g 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 Ϸ2 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. molecular dynamics ͉ protein folding ͉ denatured protein ͉ small-angle x-ray scattering ͉ radius of gyration T he role of the structure and dynamics of the unfolded states of proteins in determining the kinetics and mechanisms of protein folding is a relatively unexplored area. At high concentrations of chemical denaturants, unfolded proteins behave like random-coil homopolymers, and the average radius of gyration (R g ) depends only on the length of the polypeptide chain (1). However, at low denaturant concentrations where proteins fold and sequence matters, evidence for specific structure in the unfolded state has been observed for several proteins (2-4). Several experimental studies, moreover, suggest that native-like structure in the unfolded state may play an important role in the folding mechanism (5-7).Single-molecule FRET is well suited to investigate the structure and dynamics of unfolded proteins (8-14) because, unlike ensemble studies, it can resolve the folded and unfolded subpopulations in low denaturant regimes and also reveal information on structural distributions. Although single-molecule FRET has been mostly used in qualitative structural studies, quantitative distance information has been obtained for DNA (15,16) and polyproline (17). In the case of unfolded proteins, quantitative FRET analysis is complica...

Spectrally resolved infrared stimulated vibrational echo data were obtained for sperm whale carbonmonoxymyoglobin (MbCO) at 300 K. The measured dephasing dynamics of the CO ligand are in agreement with dephasing dynamics calculated with molecular dynamics (MD) simulations for MbCO with the residue histidine-64 (His64) having its imidazole epsilon nitrogen protonated (N(epsilon)-H). The two conformational substate structures B(epsilon) and R(epsilon) observed in the MD simulations are assigned to the spectroscopic A(1) and A(3) conformational substates of MbCO, respectively, based on the agreement between the experimentally measured and calculated dephasing dynamics for these substates. In the A(1) substate, the N(epsilon)-H proton and N(delta) of His64 are approximately equidistant from the CO ligand, while in the A(3) substate, the N(epsilon)-H of His64 is oriented toward the CO, and the N(delta) is on the surface of the protein. The MD simulations show that dynamics of His64 represent the major source of vibrational dephasing of the CO ligand in the A(3) state on both femtosecond and picosecond time scales. Dephasing in the A(1) state is controlled by His64 on femtosecond time scales, and by the rest of the protein and the water solvent on longer time scales.

Polyproline has recently been used as a spacer between donor and acceptor chromophores to help establish the accuracy of distances determined from single-molecule Fö rster resonance energy transfer (FRET) measurements. This work showed that the FRET efficiency in water is higher than expected for a rigid spacer and was attributed to the flexibility of the polypeptide. Here, we investigate this issue further, using a combination of single-molecule fluorescence intensity and lifetime measurements, NMR, theory, and molecular dynamics simulations of polyproline-20 that include the dyes and their linkers to the polypeptide. NMR shows that in water Ϸ30% of the molecules contain internal cis prolines, whereas none are detectable in trifluoroethanol. Simulations suggest that the all-trans form of polyproline is relatively stiff, with persistence lengths of 9 -13 nm using different established force fields, and that the kinks arising from internal cis prolines are primarily responsible for the higher mean FRET efficiency in water. We show that the observed efficiency histograms and distributions of donor fluorescence lifetimes are explained by the presence of multiple species with efficiencies consistent with the simulations and populations determined by NMR. In calculating FRET efficiencies from the simulation, we find that the fluctuations of the chromophores, attached to long flexible linkers, also play an important role. A similar simulation approach suggests that the flexibility of the chromophore linkers is largely responsible for the previously unexplained high value of R 0 required to fit the data in the classic study of Stryer and Haugland.fluorescence ͉ molecular dynamics ͉ persistence length ͉ polypeptide ͉ proteins F örster resonance energy transfer (FRET) has been a widely used tool for determining distances within and between biological molecules, and was called a ''spectroscopic ruler'' by Stryer and Haugland (1, 2). The basis of the technique is that the rate of energy transfer, k ET , between two chromophores depends on their separation in space R according to k ET ϭ k D (R 0 /R) 6 , as shown by Förster (k D Ϫ1 is the fluorescence lifetime of the ''donor'' chromophore and R 0 the distance at 50% transfer efficiency). The prediction of an R Ϫ6 dependence of k ET was initially confirmed in the experiment by Stryer and Haugland (1), who used a series of L-proline oligomers (Fig. 1A) as spacers of known length (3) between naphthyl and dansyl chromophores. Based on the early theoretical estimate by Schimmel and Flory (4) of 22 nm for the persistence length of poly-L-proline in the type II conformation, the spacers of 1-12 prolines were considered as rigid rods, resulting in a good fit of the theory to the experimental transfer efficiencies. An unexplained result, however, was that the fit required an R 0 significantly longer than the value determined spectroscopically.Advances in detector technology and the use of fluorophores with very high extinction coefficients, large quantum yields, and photochemical sta...