Polyproline and the “spectroscopic ruler” revisited with single-molecule fluorescence

Results

Energy transfer from the green-fluorescing donor dye (Alexa Fluor 488) at the carboxyl terminus to the red-fluorescing acceptor dye (Alexa Fluor 594) at the amino terminus was measured by determining the fraction of acceptor photons in bursts from individual molecules containing ≥100 detected photons and constructing histograms of FRET efficiencies [E ≡ n_A /(n_A + n_D ), where E is the transfer efficiency and n_D and n_A are the numbers of counts in the donor and acceptor channels, respectively] calculated from the individual bursts. Fig. 1 shows the results for a subset of the polyproline peptides investigated. As expected, the mean transfer efficiencies decrease with increasing peptide length. The histograms show a maximum at transfer efficiencies ranging from ≈0.95 for the six-residue peptide to 0.2 for the 40-residue peptide (Figs. 1 and 2). The additional peak at a transfer efficiency close to zero is thought to be caused by molecules lacking an active acceptor chromophore and was not included in the calculation of mean transfer efficiencies. The peak near zero efficiency increases with increasing laser intensity and with the size of the molecule, whereas in previous experiments (16) it was found to be virtually absent when the solution was flowed. These observations suggest that the acceptor chromophore undergoes a photochemical change before entering the confocal volume to a form that does not accept excitation energy from the donor. Nevertheless, comparison of the FRET efficiency in the first and second half of individual bursts shows no difference, indicating that acceptor photobleaching does not influence the results.

Surprisingly, even for peptides with >30 residues, a large amount of transfer was observed. Assuming the same rigid geometry of polyproline as observed in the crystal structure (28), these peptide lengths would correspond to end-to-end distances of >10 nm, and the resulting transfer efficiencies calculated for the dye pair used would be <3%, which would be inseparable from the peak near zero efficiency. A comparison with the Förster curve assuming a fixed distance r between the dyes, illustrates the dramatically increased FRET efficiencies for long polyproline peptides (Fig. 2 A ), where R ₀ = 5.4 nm is the Förster radius (the distance of 50% excitation energy transfer) for this dye pair calculated assuming complete orientational averaging of the dye transition dipoles (25). This discrepancy raises two questions. Are the single-molecule FRET efficiencies accurate? Is it valid to assume that polyproline is a rigid rod for the longer peptides?

A potential complication in single-molecule experiments arises from differences in the photon-collection efficiencies of the two detection channels corresponding to donor and acceptor emission. This effect can be corrected for by introducing into the equation used to calculate the transfer efficiency from the experimental data a factor γ that accounts for differences in the detection efficiencies of the emission channels and fluorescence quantum yields of the dyes (33), i.e., E = n_A /(n_A + γn_D ); γ must be determined for the particular experimental setup and pair of chromophores. For the instrument and dyes used here, we previously compared single-molecule and ensemble FRET efficiencies measured with a calibrated spectrofluorimeter to show that γ ≈1 (13). To further test this approximation, we performed time-correlated single-photon counting measurements on bulk samples of labeled polyproline to determine FRET efficiencies from the fluorescence lifetime of the donor chromophore as a function of peptide length. The FRET efficiency is given by [1 – (τ _DA /τ _D )], where τ _DA and τ _D are the donor lifetimes in the presence and absence of acceptor, respectively. As shown in Fig. 2, the efficiencies from the lifetime measurements are in good agreement with those from the single-molecule intensity measurements, eliminating the possibility of the high efficiencies arising from γ < 1.

For the shortest peptides, a significantly lower transfer efficiency than expected is observed experimentally. Polarization measurements point to a possible reason for decreased energy transfer. For the shortest polyproline peptides, an increase in the steady-state residual anisotropy is observed for the donor, from 0.05 for the longest peptides to 0.11 for the hexaproline peptide: the decrease in the lifetime of the excited state of the donor caused by the very rapid energy transfer to the acceptor no longer permits complete orientational averaging of the chromophores. Consequently, the value of 2/3 for the orientation factor κ² derived assuming rapid orientational averaging, and most commonly used for the analysis of FRET experiments in solution, is not applicable. As a limiting case, we calculated the distance dependence of the mean transfer efficiency 〈E〉 for dyes with a fixed separation and random but static relative transition dipole orientations from the isotropic probability density p(κ²) using†† The result shows a decreased FRET efficiency for small distances (Fig. 2 A ), providing an upper bound on the influence of a lack of orientational averaging.

The larger discrepancy with Eq. 1 is observed for the longer polyprolines (Fig. 2 A ). To investigate the influence of the polypeptide bending, which would bring the dyes closer together, providing an explanation for the higher FRET efficiency of the long polyprolines, we performed Langevin molecular dynamics simulations. Trajectories of several microseconds were computed for a range of polypeptide lengths. The simulations included the glycine and cysteine residues at the termini but not the dyes. The starting structure was a polyproline type II helix modeled according to the crystal structure (28). The simulations reveal considerable bending of the peptides, especially for the higher oligomers. Because of the strong distance dependence of Förster transfer, this bending will make a significant contribution to an increase in transfer efficiency between the dyes on the termini, particularly for the longer peptides. The ends of the polypeptide containing 40 proline residues, which has a contour length of ≈12 nm, can get to within ≈6 nm in the simulation (Fig. 3), corresponding to an increase in the (instantaneous) transfer rate by a factor of ≈2⁶.

The end-to-end (Gly nitrogen atom to Cys sulfur atom) distance distributions obtained from the simulations are very similar to those of a worm-like chain. To obtain an estimate of the persistence length, the distributions were fit with the equation of Thirumalai and Ha (34), which provides a good approximation for the end-to-end distance distribution P(r) of a semiflexible chain, where r is the end-to-end distance, l_c and l_p are the contour length and the persistence length of the chain, respectively, and N is a normalization constant. The fits of the worm-like chain model to the data give a persistence length of 4.4 ± 0.9 nm (Fig. 3). The apparently smaller persistence lengths for the shortest peptides may be due to the larger deviations of the fits at the short distance ends of the distributions.

A quantitative determination of the influence of chain bending on the mean FRET efficiency also requires consideration of the time scale of the end-to-end distance fluctuations and the donor fluorescence lifetime (35, 36). Fig. 4 summarizes the relevant times. The typical duration of a photon burst in our experiments is ≈1 ms, much longer than the donor fluorescence lifetime or the end-to-end distance correlation time, resulting in complete conformational averaging during the observation time for an individual molecule. The fluorescence lifetimes of the donor, as determined by time-correlated single-photon counting measurements, range from ≈0.4 to 3.6 ns for the different labeled peptides. The reorientational correlation time of the donor chromophore is ≈0.3 ns as determined from the anisotropy decay of donor-labeled peptide in the absence of transfer. Chain dynamics were quantified from the molecular dynamics simulations by calculating the autocorrelation functions of the end-to-end distance fluctuations and fitting them with single-exponential decays. The resulting relaxation times are between ≈0.2 ns for the proline decamer to ≈10 ns for the longest peptides (Fig. 4). Chain dynamics and fluorescence decay are in a very similar range for all peptides, and for the shortest chains, the donor fluorescence lifetime approaches the reorientational correlation time, as expected from the corresponding increase in residual anisotropy mentioned above. Therefore, we should consider all three physically plausible limits for the possible averaging regimes:

1. If the rotational correlation time τ _c of the chromophores is small relative to the fluorescence lifetime τ _f of the donor and the dynamics of the polyproline chain (with relaxation time τ _p ) are slow relative to τ _f , where P(r) is the normalized interdye distance distribution and a is the distance of closest approach of the dyes.

2. If τ _c ≪ τ _f and τ _p ≪ τ _f ,

3. If τ _c ≫ τ _f and τ _p ≫ τ _f ,

In all cases we used the normalized end-to-end distance distributions from the molecular dynamics simulations, P(r) (Fig. 3) and the theoretical isotropic probability density p(κ²) to calculate the mean transfer efficiencies for the polyproline peptides studied by simulation.^†† The results are plotted in Fig. 2B and illustrate that the flexibility of the chains results in markedly increased transfer efficiencies compared to those calculated for rod-like molecules (Fig. 2 A ). Moreover, they demonstrate the strong influence of the different dynamic regimes. Considering that τ _c ≪ τ _f and τ _p ≈ τ _f for the longer oligomers, we expect the corresponding experimental results to be in the range of the values calculated with Eqs. 4 and 5. The static limit (Eq. 6) will only be relevant for the shortest peptides. All in all, chain flexibility and dynamics account well for the experimentally observed mean transfer efficiencies.‡‡

Discussion

To determine whether FRET measurements can provide quantitative distance information in single-molecule fluorescence experiments, we have measured the FRET efficiency for donor and acceptor dyes attached to the ends of freely diffusing polyproline molecules of various lengths. Polyproline, the stiffest homooligopeptide (37), forms a type II trans helix with a pitch of 0.31 nm per residue in aqueous solution (28), and its conformation does not change after addition of denaturants (13). However, our experimentally observed interdye-distance dependence of the mean FRET efficiency differs greatly from the predictions of the simplest Förster formula, Eq. 1, assuming a perfectly rigid rod for the polyproline spacer and fast, isotropic rotational averaging of the chromophores (Fig. 2 A ). For peptides with a length much shorter than the size of the Förster radius, too low a transfer efficiency is observed; for longer peptides, the transfer efficiency is substantially higher than expected for a rod-like behavior of polyproline. The differences are not a result of inaccuracies in the single-molecule measurements, because the mean efficiencies have been confirmed with ensemble lifetime measurements.

Two factors may contribute to the deviations for the smallest oligomers. One factor is the lack of orientational averaging during the donor lifetime, as indicated by the decay of the anisotropy (Fig. 4 Inset), so that the average angular factor κ² < 2/3. Our calculations (Eqs. 2 and 6) provide an upper bound on this effect, and the experimental data are well within the expected range (Fig. 2). The second factor is the breakdown of the point-dipole approximation of Förster theory, which requires that the size of the donor and acceptor be small compared to their intermolecular separation. In the present case, the lengths of both donor (0.7 nm) and acceptor (1.2 nm) dyes are not small compared to the length of the 10-residue polyproline spacer of ≈3 nm. The point-dipole approximation leads to the important property of the theory that all the parameters can be calculated directly from experimental measurables; if this is not true, the rate must be calculated from a detailed quantum mechanical treatment of the Coulomb interaction between the charge distributions (38–40), which is not nearly as reliable and could lead to either a faster or slower rate of excitation energy transfer (i.e., either a higher or lower FRET efficiency than predicted by using the point-dipole approximation).

For the long peptides, Langevin molecular dynamics simulations show that the difference can be explained by the flexibility of polyproline. The decay of the autocorrelation function indicates that the end-to-end distance distribution is sampled completely within the 1-ms collection time of photons from individual molecules. By considering the averaging regimes relevant for the reorientation of the dyes and the fluctuations of the end-to-end distances of the chains, the main components contributing to the enhancement of the mean FRET efficiencies are accounted for (Fig. 2B ). A more complete analysis would include the donor and acceptor dyes and their linkers in simulations with explicit solvent and a direct calculation of the FRET efficiency, as was done, for example, in the case of Förster transfer of excitation energy from tryptophan to heme, calculated by using an all-atom molecular dynamics trajectory of myoglobin (41).

Polyproline peptides were first used in the context of FRET in the work of Stryer and Haugland (1), who experimentally observed the distance dependence of the transfer efficiency predicted by Förster (26), assuming polyproline to be a rigid rod. For the longer polyprolines used in the present work, however, the end-to-end distance distributions obtained from Langevin molecular dynamics simulations are not those of a rigid rod but are much more like the distributions of a worm-like chain (42). To extract an apparent persistence length, the end-to-end distributions were fit with the model function of Thirumalai and Ha (34), Eq. 3 (Fig. 3). The persistence length obtained from the fits is 4.4 ± 0.9 nm, significantly less than the textbook value of 22 nm (37, 42), indicating greater flexibility than previously estimated by assuming a fixed value of the backbone dihedral angle φ (37). However, in the range of the small peptide lengths used by Stryer and Haugland (up to the dodecamer), polyproline can be approximated by a rigid rod.§§

Interestingly, since the experiments of Haugland and Stryer, there have been very few studies of the distance dependence of the FRET efficiency and no rigorous determination of the accuracy of Förster theory at distances for which the point-dipole approximation should apply. In the only previous single-molecule study of the distance dependence, Deniz et al. (43) used B-form, double-stranded DNA as a spacer between large donor and acceptor dyes. By using the reported R ₀ = 5.3 nm and an assumed correction factor γ = 1, the measured FRET efficiency was also found to be much higher than the predictions of Eq. 1, although flexibility is expected to play a very small role because the persistence length of DNA is ≈10-fold larger than the R ₀ of the donor–acceptor dye pair. However, a very recent reinvestigation found excellent agreement between measured and predicted FRET efficiencies, by including dye flexibility, by using alternating laser excitation of the donor and acceptor to eliminate the zero-efficiency peak (44), by determining a more accurate value for the correction factor γ, and by redetermining R ₀ from spectroscopic data to be 6.9 nm (N. K. Lee, A. N. Kapanidis, Y. Wang, X. Michalet, J. Mukhopadhyay, R. H. Ebright, and S. Weiss, personal communication).

Polyproline has been used as a spectroscopic reference for single-molecule fluorescence experiments (13), and because of the large number of potential photochemical complications in single-molecule studies on biomolecular dynamics, we expect labeled polyproline peptides to become an important standard for calibrating measurements and for testing and refining new experimental methods. For single-molecule FRET experiments on proteins, it is desirable to use a polypeptide-based reference molecule, because the type of attachment chemistry and the characteristics of the immediate molecular environment can influence the photophysical properties of fluorophores (45, 46). Single-molecule measurements have the advantage of providing distributions, and they can be used to separate subpopulations and to investigate their dynamics individually. Although the chromophores necessary for these studies are relatively large, our results show that, in principle, there are no additional complications in single-molecule experiments other than those arising from photodestruction due to multiple excitations at the high laser intensities used. As in ensemble FRET experiments, consideration of the dynamics is critical for extracting structural information.