Article pubs.acs.org/JPCB
Conformational Dynamics of DNA Hairpins at Millisecond Resolution Obtained from Analysis of Single-Molecule FRET Histograms Roman Tsukanov, Toma E. Tomov, Yaron Berger, Miran Liber, and Eyal Nir* Department of Chemistry and the Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel S Supporting Information *
ABSTRACT: Here we provide high resolution study of DNA hairpin dynamics achieved by probability distribution analysis (PDA) of diffusion-based single-molecule Förster resonance energy transfer (sm-FRET) histograms. The opening and closing rates of three hairpins both free and attached to DNA origami were determined. The agreement with rates previously obtained using the total internal reflection (TIRF) technique and between free hairpins and hairpins attached to origami validated the PDA and demonstrated that the origami had no influence on the hairpin dynamics. From comparison of rates of four DNA hairpins, differing only in stem sequence, and from comparison with rates calculated using nearest-neighbor method and standard transition state theory, we conclude that the unfolding reaction resembles that of melting of DNA duplex with a corresponding sequence and that the folding reaction depends on counterion concentration and not on stem sequence. Our validation and demonstration of the PDA method will encourage its implementation in future high-resolution dynamic studies of freely diffusing biomolecules. reviewed here.1 An alternative approach based on maximum likelihood analysis has also been described.13 The PDA method has been used experimentally to analyze the dynamics of DNA hairpins,8,10,12 of LacY protein,14 and of DNA polymerase-I15 and was validated theoretically by demonstrating that the transition rates of numerically simulated two-state system can be obtained with high accuracy.8−10 However, because the shape of the E-histograms may be influenced by experimental artifacts, such as population mixing, photobleaching, and misalignment of the donor and acceptor detection volumes, experimental validation of the method is essential to demonstrate reliability under experimental conditions. In a recent study, we used TIRF to measure the opening and closing rates of two DNA hairpins with poly(dA) loops of 31 nucleotides (nt) and 6 base-pair (bp) stems.16 The stems differed by a single bp (G·C/A·T), which resulted in a slight difference in the thermodynamic stabilities of the hairpins. The hairpin closing rates were dependent on NaCl concentration but not on the stem sequence, and the differences in the opening rates were as expected on the basis of standard transition state theory (TST) and the difference in hybridization energy of the two stems estimated using the nearestneighbor method. The temporal resolution of the TIRF technique, however, limited the rates, stem thermodynamic
1. INTRODUCTION Single-molecule Förster resonance energy transfer (sm-FRET) is a powerful technique1 for measuring real-time conformational dynamics of biomolecules.2−4 The immobilization-based total internal reflection (TIRF) technique, in which each molecule is continually observed, provides direct information on the transitions between molecular states, and as a result, almost all sm-FRET measurements of transition rates to date have been conducted using this technique. Immobilizing the molecules, however, adds experimental complexity and may influence the dynamics, and the technique resolution is limited by the camera frame rate. The resolution can be substantially increased by using single-photon detectors;5 however, with this arrangement the experiments are somewhat tedious and slow. As a result, only a few systems with fast dynamics have been studied thus far.6 In diffusion-based approaches, the limitations due to immobilization are avoided and, due to the use of singlephoton detectors, the temporal resolution is potentially higher. To obtain the dynamics from the shape of the resultant FRET efficiency histogram (E-histogram) a semiempirical probability distribution analysis (PDA) method has been developed. The method includes statistical descriptions of the shot-noise contribution,7−9 and the dynamics are incorporated by calculating the expected distribution of mean E values of any assumed dynamics scenario.8,10−12 The PDA method and the relationship between the dynamics and the E-histogram are discussed in the Supporting Information (Figure S1) and © XXXX American Chemical Society
Received: November 16, 2013 Revised: November 21, 2013
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16. Use of the ALEX technique enabled us to remove the donor-only and acceptor-only populations that exist in small quantities in all histograms as a result of fluorophores bleaching and incomplete hybridization of the top and bottom strands. This enabled construction of E-histograms only from events (bursts) belonging to hairpins that had active (nonbleached) donor and acceptor fluorophores. In addition, in the case of hairpin-origami measurements, the ALEX technique enabled us to separate the hairpin-origami population from residual hairpin-only population16 (hairpins that detached from the origami), ensuring that the hairpin-origami histograms were constructed only from hairpin-origami events. This separation was made possible by an additional red fluorophore attached to the origami (Figure 1). 2.2. Experimental E-Histograms and the PDA Fitting. To illustrate the influence of the dynamics and the diffusion on the shape of the E-histogram and demonstrate how well the PDA method recapitulated various features of the histogram shape, selected E-histograms and best PDA fits are shown in Figure 2. All E-histograms in this study contained two peaks, corresponding to the hairpin open and closed states, and a bridge connecting the two peaks, which is due to hairpins that interconvert between the two states during transit through the confocal spot. The sizes of the open and the closed peaks and of the bridges depend on the stem sequence, on the NaCl concentration, and on whether the hairpins were free or attached to origami. As expected, as the NaCl concentration increased, the size of the open state peak decreased and that of the closed state peak increased. The hairpin-origami diffused more slowly than the hairpin-only (see the burst duration distribution, Figure S3, Supporting Information), increasing the probability that a transition between states would occur during transit; therefore, the hairpin-origami E-histograms have larger bridges than those of the hairpin-only. Similarly, because hairpin-1 has more thermodynamically stable stem (and a slower opening rate) than does hairpin-2 and because hairpin-2 has more stable stem than does hairpin-3, at the midpoints, where the opening and closing rates are equal for each hairpin, the hairpin-only-1 E-histogram shows a smaller bridge than that of hairpin-only-2, which shows a smaller bridge than that of hairpin-3. All the experimental E-histograms were fit well by a two-state model PDA (Figure 2, black dots, and see later discussion); therefore, a two-state model was used to analyze all data. For a detailed explanation of the PDA analysis procedure, see the Supporting Information. 2.3. Comparison of PDA and TIRF. The first experimental validation of the PDA method is presented in Figure 3. The opening and closing rates of coverslip immobilized hairpinorigami-1 measured using TIRF and calculated from dwell-time histograms16 (Figure 3A1) and the opening and closing rates of freely diffusing hairpin-origami-1 calculated using the PDA method (Figure 3A2) are compared in Figure 3B. For most of the NaCl concentrations tested, the rates of the freely diffusing hairpin were identical within experimental noise to those obtained for immobilized hairpin, demonstrating experimentally that the PDA method properly extracted the rates from the E-histograms. 2.4. Extending the Time Window Available for PDA Investigation using DNA Origami. Hairpin-1 and hairpin-2 were attached to DNA origami to slow their diffusion rates, resulting in increases in the sizes of the bridges in the Ehistograms. As is evident from the burst duration distribution (Figure S3, Supporting Information), the origami slowed the
stabilities, and NaCl concentrations that could be studied, preventing generalization of these conclusions to DNA hairpins of other sequences and to NaCl concentrations greater than 100 mM. Here we report two experimental validations of the PDA and the use of the PDA method to measure hairpin opening and closing rates that are more than an order of magnitude faster than we were able to monitor using TIRF.16 Three freely diffusing hairpins (hairpin-only) and hairpins attached to DNA origami (hairpin-origami) were studied (Figure 1), and
Figure 1. Names, sequences, and design of the hairpins studied in this work (hairpins 1, 2, 3) and of hairpin-0 studied previously,16 and the DNA origami design. The hairpins were designed to minimize possible interfering interactions between the fluorophores when the hairpins are closed, and the TT spacer was introduced to minimize interactions between the stem and the duplex. The origami was labeled with an additional acceptor to enabled separation of hairpin-only events from hairpin-origami using the ALEX technique.16
experiments were conducted with NaCl concentrations spanned from 25 to 600 mM. Each hairpin had 31-nt long poly(dA) loop and 6 bp stem; the stabilities of the stems were tuned by designing the stems with 4, 3, and 2 G·C pairs (hairpins 1, 2 and 3, respectively). The PDA was validated (i) by comparing the opening and closing rates of hairpin-origami1 with that of immobilized hairpin-origami-1 measured using TIRF16 and (ii) by comparing the opening and closing rates of hairpin-only-2 with those of the more slowly diffusing hairpinorigami-2. To demonstrate that the PDA can resolve even faster dynamics and to enable studies at higher NaCl concentrations, rates of opening and closing of less thermodynamically stable hairpin-only-3 were measured. Finally, we compare the opening and closing rates of these three hairpins and that of a hairpin analyzed previously using TIRF16 (hairpin-0, 5 G·C pairs, Figure 1).
2. RESULTS AND DISCUSSION 2.1. Obtaining E-Histograms. Figure 2 show selected Ehistograms of hairpin-only-1, hairpin-origami-1, hairpin-only-2, hairpin-origami-2, and hairpin-only-3 (pink histograms) acquired using the diffusion-based sm-FRET and alternating laser excitation (ALEX)8,10,16,17 techniques and measured in different NaCl concentration. For typical two-dimensional E/Shistograms, see Figure S2 in the Supporting Information and ref B
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Figure 2. E-histograms (pink histograms) of all the hairpin-only and hairpin-origami constructs studied in this work and PDA best fits (black dots). Results of only selected NaCl concentrations are presented. Hairpin-only-1 histograms were not fitted using PDA, see text. The E-histograms and the PDA fittings were slightly smoothed with a running average algorithm to enable easier visual comparison. Nonsmoothed experimental histograms and PDA fittings of hairpin-only-3 are presented (right most column) for comparison.
diffusion in solution by 3−4 times. In the case of hairpin-only-1, without the origami, the bridges were very small (Figure 2). Because of the small bridge sizes, repeated analyses of hairpinonly-1 histograms yielded a broad distribution of rates; the PDA could not converge to the correct values. For example, for the intermediate NaCl concentration (40 mM) the PDA returned rates that (depending on the initial seeded rates) differed by more than 70% (slower or faster) than the correct hairpin-origami-1 rates (data not shown). For analyses of hairpin-origami data, repeated fittings initiated with different sets of initial parameters (rates and E values), resulted in less than 2% differences in the calculated rates and E values. This demonstrates that the origami extended the time window available for PDA to rates that are up to 4 times slower than those without the origami (∼10 s−1). An additional advantage of the origami is that the origami ensured that the hairpin environments were identical in solution and when immobilized to the coverslip surface.16,18 2.5. Recovering the Dynamics Independently of the Molecule Diffusion Time. The second validation of the PDA method is presented in Figure 4. By comparing the opening and closing rates obtained for hairpin-only-2 with those of the more slowly diffusing hairpin-origami-2, we tested whether the PDA was able to recover dynamics without being influenced by the time spent by the molecule in the confocal spot. As can be seen in Figure 4A, within experimental noise, the rates obtained for the two constructs were essentially identical at every NaCl concentration evaluated. As expected, because of its slower diffusion, the hairpin-origami produced larger bridges than the
Figure 3. Agreement between rates obtained using the diffusion-based PDA method and the immobilization-based TIRF. Data are for hairpin-origami-1. (A1) Typical dwell-time histogram obtained in the TIRF measurement. (A2) Typical E-histogram (red bars) obtained in the diffusion-based measurement and the PDA fit (black dots). (B) Opening (open symbols) and closing (closed symbols) rates obtained using PDA (red) in very good agreement with rates obtained using immobilization-based TIRF (blue).
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Figure 5. Summary and comparison of the experimental opening (open symbols) and closing (closed symbols) rates for the four hairpins and of theoretical opening rates calculated using nearestneighbor method (MFOLD) and transition state theory (solid lines). Hairpin-0 (black),16 harirpin-1 (red), hairpin-2 (blue), and hairpin-3 (pink).
Figure 4. Agreement between rates obtained using PDA for free hairpin and for hairpin attached to origami. (A) Opening (open symbols) and closing (closed symbols) rates of hairpin-only-2 (blue) and hairpin-origami-2 (red) in very good agreement. (B1−2) Ehistograms of hairpin-only-2 (blue bars) and hairpin-origami-2 (red bars) measured at 100 mM NaCl and corresponding PDA fits (black dots).
As evidenced by the decrease in opening rates with increased NaCl concentration, increased counterion concentration stabilizes the geometrically compact closed state more than it stabilizes the less compact transition state. Our results indicate that this salt dependence is well captured by MFOLD.
hairpin-only constructs (E-histograms in Figure 2 and in Figure 4B1−2); however, as the agreement between the rates of the two constructs indicates, the PDA correctly considered the diffusion, further validating PDA. In addition, the agreement between the dynamics of free hairpin and of hairpin attached to origami further indicates that the origami has no influence on the hairpin dynamics, supporting previous observations.16,18 2.6. Hairpin Dynamics. Figure 5 shows a comparison of the opening and closing rates of hairpins-1, 2, and 3 analyzed in this work and that of hairpin-0 analyzed previously.16 These hairpins differ only in stem sequence (Figure 1). The closing rates were essentially identical for the four hairpins at each NaCl concentration evaluated, indicating that closing rates depend on NaCl concentration and not on the thermodynamic stability of the stem. This means that the difference in Gibbs free energy between the open state and the transition state (ΔG‡closing) is not significantly influenced by the stem sequence but is influenced by the counterion concentration, in agreement with temperature-jump experiments of DNA and RNA hairpins.19 Increased counterion concentration reduces the intramolecular Coulomb repulsion caused by the negative charge on the DNA backbone to a greater extent in the geometrically more compact transition state than in the expended open state, accelerating the closing reaction at higher salt concentration. Furthermore, for each of the four hairpins and at every NaCl concentration evaluated, the experimentally determined opening rates are in good agreement with rates calculated using transition state theory based on stem hybridization energies estimated by the nearest-neighbor method20 (MFOLD, melting of a DNA duplex with sequence identical to that of the stem, see the Supporting Information). This means that the free energy for opening (ΔG‡opening) resembles that of melting energy of the corresponding duplex.
3. CONCLUSIONS We provide two independent experiential validations of the PDA method and demonstrate its reliability. We showed that the PDA is in very good agreement with the more established TIRF experiment and that the PDA successfully separates the dynamics from the diffusion component, resulting in correct rates. The extended temporal resolution provided by PDA enabled us to obtain rates that spanned over 2 orders of magnitudes; more than an order of magnitude faster than we were able to study using camera-based TIRF. The DNA origami slows the diffusion, extending the time window available for the PDA analysis to slower dynamics. The agreement between the rates measured for free hairpin and hairpin attached to origami demonstrates that the origami has no influence on the hairpin dynamics, further supporting its use as a platform for various biophysical investigations of guest molecules.16,18,21 In comparison to TIRF, the use of PDA and origami enabled investigation of hairpins with significantly different stem sequences and thermodynamic stabilities and enabled investigation at 6-fold higher NaCl concentration than before. On the basis of these extended data, we conclude that hairpin unfolding reaction resembles that of melting of duplex with sequence identical to that of the stem and that the folding reaction depends on counterion concentration and not on stem sequence. Thus, the hairpin loop influences the folding reaction and the stem influences the unfolding reaction. Single-molecule FRET analysis of freely diffusing molecules avoids limitations associated with immobilization-based methods, considerably simplifying the experiment and making it more biologically relevant. The excellent agreement we observe between the PDA fits and the resultant E-histograms suggest D
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(12) Torella, J. P.; Holden, S. J.; Santoso, Y.; Hohlbein, J.; Kapanidis, A. N. Identifying Molecular Dynamics in Single-Molecule FRET Experiments with Burst Variance Analysis. Biophys. J. 2011, 100, 1568. (13) Gopich, I. V.; Szabo, A. Decoding the Pattern of Photon Colors in Single-Molecule FRET. J. Phys. Chem. B 2009, 113, 10965. (14) Majumdar, D. S.; Smirnova, I.; Kasho, V.; Nir, E.; Kong, X.; Weiss, S.; Kaback, H. R. Single-Molecule FRET Reveals Sugar-Induced Conformational Dynamics in Lacy. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 12640. (15) Hohlbein, J.; Aigrain, L.; Craggs, T. D.; Bermek, O.; Potapova, O.; Shoolizadeh, P.; Grindley, N. D.; Joyce, C. M.; Kapanidis, A. N. Conformational Landscapes of DNA Polymerase I and Mutator Derivatives Establish Fidelity Checkpoints for Nucleotide Insertion. Nat. Commun. 2013, 4, 2131. (16) Tsukanov, R.; Tomov, T. E.; Masoud, R.; Drory, H.; Plavner, N.; Liber, M.; Nir, E. Detailed Study of DNA Hairpin Dynamics Using Single-Molecule Fluorescence Assisted by DNA Origami. J. Phys. Chem. B 2013, 117, 11932. (17) Tomov, T. E.; Tsukanov, R.; Masoud, R.; Liber, M.; Plavner, N.; Nir, E. Disentangling Subpopulations in Single-Molecule FRET and ALEX Experiments with Photon Distribution Analysis. Biophys. J. 2012, 102, 1163. (18) Gietl, A.; Holzmeister, P.; Grohmann, D.; Tinnefeld, P. DNA Origami as Biocompatible Surface to Match Single-Molecule and Ensemble Experiments. Nucleic Acids Res. 2012, 40, e110. (19) Kuznetsov, S. V.; Ren, C. C.; Woodson, S. A.; Ansari, A. Loop Dependence of the Stability and Dynamics of Nucleic Acid Hairpins. Nucleic Acids Res. 2008, 36, 1098. (20) SantaLucia, J. A Unified View of Polymer, Dumbbell, and Oligonucleotide DNA Nearest-Neighbor Thermodynamics. Proc. Natl. Acad. Sci. U. S.A. 1998, 95, 1460. (21) Pinheiro, A. V.; Han, D. R.; Shih, W. M.; Yan, H. Challenges and Opportunities for Structural DNA Nanotechnology. Nat. Nanotechnol. 2011, 6, 763.
that the PDA method should be able to resolve dynamics of molecular systems with even faster dynamics and smaller conformational changes than were studied here. The study extends our understanding of hairpin dynamics and demonstrates how PDA can be used to study freely diffusing biomolecules, such as DNA, RNA, and proteins, with millisecond resolution.
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ASSOCIATED CONTENT
S Supporting Information *
Principle influence of the dynamics on the E-histogram, the PDA method, the E/S histogram, experimental methods, and graph of burst duration and burst size distribution. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E. Nir: e-mail,
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS E.N. was supported by the Alon Fellowship, T.E.T. by the Negev Fellowship, and M.L. by the Darom Fellowship. REFERENCES
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