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. 2007 Jan 30;104(5):1528-33.
doi: 10.1073/pnas.0607097104. Epub 2007 Jan 24.

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

Kusai A Merchant  1 , Robert B Best, John M Louis, Irina V Gopich, William A Eaton
Affiliations

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

Kusai A Merchant et al. Proc Natl Acad Sci U S A. .

Abstract

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.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Structures of dye-labeled protein L. (A) Cartoon. (B) Space-filled heavy atoms. (C) Bead model used in Langevin simulations.
Fig. 2.
Fig. 2.
FRET efficiency histograms for protein L (Left) and CspTm (Right) for several denaturant concentrations. The peaks at high and intermediate Em correspond to the folded and unfolded state populations, respectively. The green and blue lines are Gaussian fits to the folded and unfolded subpopulations. Molecules lacking an active acceptor (yellow) appear at Em ≈ 0. The Poissonian shot-noise contribution (29) to the folded and unfolded peak widths (black dashed lines) is shown at 0 M and 6 M GdmCl.
Fig. 3.
Fig. 3.
Dependence of FRET efficiency and Rg on denaturant concentration. (A) Mean FRET efficiencies 〈E〉 for the unfolded states of protein L (blue triangles) and CspTm (red inverted triangles) after γ correction. (B) Rg for protein L and CspTm in the unfolded state determined from 〈E〉 assuming slow chain dynamics and a Gaussian chain model for the end-to-end distribution. The Rg values previously determined by equilibrium SAXS at 4 M GdmCl (green circle) and by time-resolved SAXS at 1.4 M GdmCl (green square) are also shown (20).
Fig. 4.
Fig. 4.
Langevin simulation results for protein L and CspTm. (A) Donor–acceptor distance distributions for folded protein L (black line) and CspTm (red line). The N- and C-terminal α carbons are separated by 38 Å and 13 Å in the structures of protein L and CspTm, respectively. (B) Decay of correlation functions for donor–acceptor distance (black line), reorientation of the donor (green line) and acceptor (red line), and κ2 (blue line). (C) Decay of donor fluorescence in protein L calculated with (red lines) and without (black lines) the assumption of complete orientational averaging; curves for the folded and unfolded states are solid and broken, respectively, and the isolated donor decay is shown for reference in green.
Fig. 5.
Fig. 5.
Comparison of measured (blue lines) lifetimes for CspTm (Left) and protein L (Right) at 2.5 M (Top), 4 M (Middle), and 7.2 M (Bottom) GdmCl with those calculated assuming no chain dynamics during the donor lifetime for several Peq(R): Gaussian chain (red lines) and bead models with only excluded volume (green lines) and both excluded volume and attractive interactions (black dashed lines).
Fig. 6.
Fig. 6.
Expansion of denatured states in simulations. All-atom molecular dynamics simulations of protein L (blue) and CspTm (red) in explicit urea/water solutions show an increase in Rg with urea concentration.
Fig. 7.
Fig. 7.
Differences in donor fluorescence decays within the unfolded state FRET peaks at 4 M GdmCl for protein L (A) and CspTm (B). The donor photons in the green and red curves are from bursts on the high-efficiency (green) and low-efficiency (red) side of the unfolded peak, respectively (see Insets). The donor fluorescence decays faster for bursts with higher 〈E〉.
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