Detailed Study of DNA Hairpin Dynamics Using ... - ACS Publications

A Bipedal DNA Motor that Travels Back and Forth between Two DNA Origami Tiles. Miran Liber , Toma E. Tomov , Roman Tsukanov , Yaron Berger , Eyal Nir...
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Detailed Study of DNA Hairpin Dynamics Using Single-Molecule Fluorescence Assisted by DNA Origami Roman Tsukanov, Toma E. Tomov, Rula Masoud, Hagai Drory, Noa Plavner, 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 ABSTRACT: The dynamics of two DNA hairpins (5′-TCGCCT-A31AGGCGA-3′ and 5′-TCGCCG-A31-CGGCGA-3′) were studied using immobilization-based and diffusion-based single-molecule fluorescence techniques. The techniques enabled separated and detailed investigation of the states and of the transition reactions. Only two states, open and closed, were identified from analysis of the FRET histograms; metastable states with lifetimes longer than the technique resolution (0.3 ms) were not observed. The opening and closing reaction rates were determined directly from the FRET time trajectories, and the Gibbs free energies of these states and of the transition state were calculated using the Kramer theory. The rates, which are undoubtedly of transitions between the fully closed and the fully open states and ranged from 2 to 90 s−1, were lower (∼10-fold) than the rates previously determined from fluorescence correlation spectroscopy. The heights of the barriers for closing were almost identical for the two hairpins. The barrier for opening the hairpin with the stronger stem was higher (4.3 kJ/mol) than that for the hairpin with the weaker stem, in very good agreement with the difference in stability calculated by the nearestneighbor method. The barrier for closing the hairpin decreased (∼8 kJ/mol) and the barrier for opening increased (∼4 kJ/mol) with increasing NaCl concentration (10−100 mM), indicating that higher ionic strength stabilizes the folded state with respect to the transition state and stabilizes the transition state relative to the unfolded state. The very good agreements in the dynamics measured for free hairpins, for hairpins anchored to origami, and for hairpins anchored to the coverslip and the very good agreement between the two single-molecule techniques demonstrate that neither the origami nor the coverslip influence the hairpin dynamics, supporting a previous demonstration that origami can serve as a platform for biophysical investigations. slowed by attachment to polystyrene beads,26 and stoppedflow (ion-jump) measurements32 led to questioning of this interpretation; these data suggest that the fast relaxation (80%) and an additional minor fast component. As explained later, we continue by analyzing only the slow component. On the basis of the agreement between the open-state fractions and between the dwell-time histograms, we concluded that (i) the origami does not influence the hairpin dynamics, (ii) immobilization on the coverslip glass does not influence the hairpin dynamics, and (iii) the diffusion-based and immobilization-based techniques are in very good agreement. 2.6. DNA Hairpin Dynamics. 2.6.1. Transition-State Free Energy Calculated Using Kramer Theory. Figure 6A summarizes the opening and closing rates of hairpin-only A31TA and A31-GC. To understand the influence of the stem sequence and of the NaCl concentration on the hairpin dynamics, the heights of the Gibbs free energy barriers for opening and closing the hairpins were calculated using standard transition-state Kramer theory:39 ⧧ kop,cl = k 0 exp[−ΔGop,cl /kBT ]

Figure 5. Very good agreement between the closed- and open-state dwell time histograms measured for immobilized hairpin-only and hairpin-origami and closing and opening rates measured at different NaCl concentrations for (left) A31-AT and (right) A31-GC; hairpinonly is indicated by blue symbols and hairpin-origami by red symbols. (A1, A2) Open-state dwell time histograms. (B1, B2) Closed-state dwell time histograms. The solid lines in A1, A2, and B1 are fits to a single-exponential function, and the solid lines in B2 are fits to a double-exponential function. (C1, C2) Calculated closing (solid symbols) and opening (open symbols) rates. For the opening of A31-GC, only the dominant slow (exponential) component is presented. Solid lines are to guide the eye.

Figure 6. Summary of the opening rates (open symbols) and closing rates (solid symbols) and of the transition free energies. (A) Opening and closing rates for A31-TA (red) and A31-AT (black) hairpin-only. (B) Heights of the opening and closing barriers for A31-TA (red) and A31-GC (black) calculated from the obtained rates using Kramer theory and free energies for melting of dsDNA duplexes with sequences identical to the stems of A31-TA (purple) and A31-GC (green) calculated using nearest-neighbor method.

states, respectively, and the pre-exponential factor k0 reflects the transition rate in the absence of a free energy barrier. The exact value of this factor is unknown. Woodside et al.17 found that data from optical trapping pulling experiments of DNA hairpins were best fitted using k0 = 3 × 106 s−1, and we used this value

(1)

where kop and kcl are the observed opening and closing rates, respectively, ΔG⧧op and ΔG⧧cl are the heights of the free energy barriers with respect to the free energies of the closed and open 11935

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here (Figure 6B; see the further justification in the Experimental Section). 2.6.2. Analysis of the Transition State. The heights of the barriers for closing are almost identical for the two hairpins at every NaCl concentration measured (differences of 1.0 ± 0.5 kJ/mol), indicating that the height of the barrier with respect to the open state is only weakly dependent on the stem sequence. This provides support for the hypothesis that the closing reaction depends mainly on the properties of the loop.14,22 The free energy barriers for opening the hairpins were 4.3 ± 0.2 kJ/ mol higher for A31-GC than for A31-TA at all NaCl concentrations. The stems of A31-GC and A31-TA differ by a single base pair positioned adjacent to the hairpin loop (a GC pair vs a TA pair, respectively; see Figure 1A). To understand the origin of the difference in barrier heights, we calculated the free energies required for melting 6 bp dsDNA duplexes with sequences identical to those of the A31-GC and A31-TA stems using the nearest-neighbor method40 (MFOLD; see the Experimental Section). The calculated free energies are summarized and compared to the Kramer free energies in Figure 6B. The differences between the free energies calculated using nearest-neighbor method for the two sequences are 4.4 ± 0.2 kJ/mol (with some dependence on the NaCl concentration), in very good agreement with the differences calculated by the Kramer theory for opening the two hairpins. This agreement supports the conclusion that the differences in the opening rates observed for the two hairpins are mainly a result of differences in the hybridization free energies of the two stems and not due to differences in the transition-state free energy itself; that is, the closed state of A31-GC is more stable than that of A31-TA. 2.6.3. Quasi-Two-State Hairpin. Large biomolecules like the DNA hairpins studied here may adopt many different conformational states (substates). In principle, single-molecule techniques can distinguish between different molecular states; however, the ability to do so depends on the temporal and spatial resolution of the technique. Short-lived states are more difficult to detect than those with longer lifetimes, and states with similar conformations (donor−acceptor distances in our case) are less distinguishable. The temporal resolution of the diffusion-based experiments is determined by the burst duration (1−8 ms for the hairpin-only and 8−40 ms for the hairpinorigami; data not shown). States that are visited for periods that are longer than a fraction of this duration (in our case, approximately >0.3 ms based on a rough estimation from numeric simulations;15,16 data not shown), could be recognized as an individual state, depending on the donor−acceptor distance. Only two predominant peaks were observed in the diffusionbased E histograms of A31-GC hairpin-only (Figure 7A). The minor intermediate E values observed in these histograms (called bridges) and the larger bridges observed for hairpinorigami (data not shown) and for A31-TA (Figure 2B1,B2) are most likely a result of interconversion between the two states during the transit in the confocal spot, and not of additional states. These results therefore suggest that only one quasi-open state and one closed state with lifetimes longer than approximately 0.3 ms exist. More specifically, no intermediate metastable state (>0.3 ms) in which the donor−acceptor distance was detectably smaller (smaller by 1 nm or more, as estimated from comparison to FRET measurements of dsDNA with different donor−acceptor distances; data not shown) than that of the average open state was observed. It is unlikely, for

Figure 7. Only two metastable states are observed, and the stabilities of the two hairpins differ. (A) Diffusion-based E histograms of A31-GC hairpin-only measured at various NaCl concentrations. (B) Open-state fractions of the two hairpins (hairpin-only) measured at NaCl concentrations from 1 to 500 mM.

example, that one of the stem regions forms a stable non-native interaction with the loop (e.g., with bases in the middle of the loop). Accordingly, conformations that yield only minor changes in the E value, including local small loop formation observed previously in studies of poly(dA),41 cannot be excluded. The average E value of the open states (0.20 ± 0.01) is at the edge of the method sensitivity (the E values are not equal to zero because of uncorrected leakage of donor photons into the acceptor channel; see the Experimental Section), and as a result, the donor−acceptor distance could not be determined accurately. Nonetheless, comparison to FRET measurements of dsDNA indicated that the average donor−acceptor distance was larger than 10.5 nm. In addition, only a minor increase in the average E value of the open state was observed upon increasing the NaCl concentration (0.3 ms) conformations with intermediate or high E values were observed. Long-lived conformations (e.g., those stabilized by non-native base-pairing interactions) are thus excluded. Most likely the open state does consist of an ensemble of metastable states (including those with high and intermediate E values); however, the low E values of the open state and the fact that only a slight shift toward higher values is observed at higher NaCl concentrations indicate that such metastable states constitute less than 5% (estimate) of the open state ensemble. The energy barrier for closing the hairpins decreased with increasing NaCl concentration and only slightly depended on the stem sequence. The closing reactions had singleexponential kinetics in all cases, supporting the conclusion that the interconversions between the substates that constitute the open state are fast in comparison with the open state lifetime. The dwell time histograms of the opening reaction of A31-TA fitted well to a single-exponential function, and those of A31-GC exhibited double-exponential kinetics. We propose that A31-GC may reopen before complete zipping in a detectable reaction, whereas reopening of A31-TA is too fast to be detected. However, further study is required in order to confirm this. Comparisons of the opening free energy barriers calculated using the Kramer theory and the free energies calculated using the nearest-neighbor method indicate that the free energy barrier for opening the hairpins depends directly on the stem hybridization free energy. For a direct comparison of experimental and theoretical transition-state energies, however, a theoretical method for calculation of the energy of the transition state is required.42 2.7. DNA Origami. Comparison of the fraction of open state (Figure 4) and of the shapes of the dwell time histograms of the open and closed states (and the calculated rates; Figure 5) of hairpin-origami and hairpin-only indicate that the origami had no detectable influence on the hairpin dynamics. The Coulombic repulsion of the considerably negatively charged origami was not felt by the hairpin, which was located 35 bp away from the origami. A previous study showed that origami had no influence on the dynamics of a DNA Holliday junction.37 Our study indicates that this conclusion is valid at low ionic strengths (10 mM NaCl) as well, and also for flexible single-stranded DNA. However, further study is required in order to characterize the influence of origami on hairpins that are anchored closer to the origami surface. Anchoring various molecular species to DNA origami carries many benefits.37,43−45 In diffusion-based single-molecule experiments, the large size of the origami slows the diffusion, yielding longer observation periods and increasing the number of photons acquired. Under our conditions, the burst durations were between 1 and 8 ms for the hairpin-only and between 8 and 40 ms for the hairpin-origami, and the average numbers of photons in a burst were 300 and 3000, respectively. These 11937

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The hairpin bottom strand was prepared containing a sequence identical to that of one of the origami staples (r-1t16f), allowing it to be incorporated into the origami in the annealing process and to branch out of the origami plane (Figure 1C), and the original r-1t16f staple was not introduced. To achieve specific binding of the origami to the coverslip surface, four staple strands, located ∼2 nm from the origami corners toward the center, were replaced by biotinylated staple strands. Each biotinylated staple strand was elongated by four T bases to increase the likelihood of binding to the coverslip surface. The staples were designed in such a way that they branched out of the origami on the side opposite the DNA hairpin. 4.3. Annealing Procedures. Hairpin-only: The top and bottom strands (1.5 μM in 10 μL TE-NaCl buffer (10 mM Tris, pH 8.0, 1 mM EDTA, and 100 mM NaCl) were annealed at 94 °C and then gradually cooled (30 min) to room temperature (using PCR). Hairpin-origami: The annealing mixture consisted of 2 nM scaffolds, a 10-fold excess of staples, and 20-fold excesses of the top and bottom strands in 50 μL of 1× TAE buffer (40 mM Tris, 1 mM EDTA, 40 mM acetic acid) and 12 mM MgAc. The origami was prepared as follows: incubated at 95 °C for 5 min, cooled to 60 °C at 0.5 °C/min, and cooled to room temperature at 0.2 °C/min (using PCR). After annealing, the origami was filtered through a 100 kDa filter (Amicon Ultra, Millipore, Billerica, MA, USA) by centrifuging five times at ∼14000g for 5 min in 50× TAE buffer (2000 mM Tris, 50 mM EDTA, and 2000 mM acetic acid) and 12 mM MgAc buffer (50× TAE buffer improved the origami yield during the filtration relative to 1× TAE buffer) and then once at ∼14000g for 10 min in 1× TAE buffer (to remove Mg2+ and the excess of TAE). The final spin was reversed at 1000g for 5 min. The product DNA origami structure was validated using atomic force microscopy (data not shown). 4.4. Diffusion-Based Experiments. 4.4.1. Optical Setup. The sm-FRET-ALEX experiments were carried out on an inhouse-built optical setup.10,16 In brief, a green CW laser beam (532 nm, CL532-025-L, Crystal Laser, Reno, NV, USA) was aligned/misaligned into a single-mode fiber using an acoustooptic modulator (AOM) (R23080-2-LTD, Neos Technologies, Melbourne, FL, USA), alternating with a red diode laser (640 nm, 1069417, Coherent, Auburn, CA, USA) that was electronically switched on and off. The AOM and the red laser were computer-controlled with a 12.4 μs on-time, a 12.6 μs off-time, and a phase shift of 12.5 μs. The intensity rise and fall times were less than 50 ns, and there was no time overlap between the lasers. The laser beams were combined using a dichroic mirror (Z532RDC, Chroma, Bellows Falls, VT, USA) and coupled into a single-mode fiber (P1-460A-FC-2, Thorlabs, Newton, NJ, USA). The laser intensities were tuned in such a way that the doubly labeled species would yield S ≈ 0.5 (70 μW for the green laser and 90 μW for the red laser, measured after the fiber while alternating). After collimation (objective PLCN10×/0.25, Olympus America, Melville, NY, USA), the combined green and red beams were introduced into a commercial inverted microscope (IX71, Olympus America) and focused about 70 μm inside the sample solution with a water-immersion objective [numerical aperture (NA) 1.2, 60×, Olympus America]. The emitted fluorescence was separated from the excitation light using a dichroic mirror (ZT532/ 638RPC, Chroma), focused into a 100 μm pinhole (P100S, Thorlabs), recollimated, split by a second dichroic mirror (FF650-Di01, Semrock, Lake Forest, IL, USA), passed through

features of the origami provide several benefits. The large number of photons increases the resolution and the accuracy of the measurement. Longer bursts increase the probability that structural fluctuations during the transition in the confocal spot will be observed and allows slower dynamics to be resolved. Controlling the diffusion time enables separation of the diffusion components from the kinetic components in FCS measurements,26,46 increasing the ability of the method to resolve the dynamics. In immobilization-based experiments, the origami ensures surface immobilization37 and provides control of the quality of the coverslip immobilization, as demonstrated here. Without the origami control experiment, the doubleexponential dwell time histograms observed for the opening of A31-GC (Figure 5B2) could have been mistakenly interpreted as being a result of unwanted interactions with the coverslip. The very good agreement between the hairpin-only and hairpin-origami dwell time histograms negated such an interpretation.

3. CONCLUSIONS Utilizing single-molecule fluorescence techniques, which enable separate investigations of hairpin open and closed states and of hairpin opening and closing reactions, we were able to study the hairpin dynamics in detail not possible with other methods. The characteristics of the open and closed states and of the transition states and their dependences on the buffer ionic strength and the stem sequence were examined. No third metastable state was identified, and the transition rates were found to be lower than previously reported based on FCS. From the very good agreements between the dynamics measured for hairpin-only and hairpin-origami and between the dynamics measured using the diffusion-based and immobilization-based techniques, we concluded that neither the origami nor the coverslip surface influenced the hairpin dynamics, supporting the idea37 that origami can serve as a platform on which biophysical investigations may be carried out. The various aspects of hairpin structural dynamics that were investigated in this work, the quality of the data and its spatial and temporal resolutions, the agreement between the two techniques, and the usefulness of the origami suggests that future systematic studies of DNA and RNA hairpins along the lines introduced here may significantly enhance our understanding of these interesting physical models and biologically important systems. 4. EXPERIMENTAL SECTION 4.1. Single-Stranded DNA Labeling. HPLC-purified bottom and top strands of DNA were purchased with a C6 dT internal amino modifier (iAmMC6T, IDT, Coralville, LA, USA) at position 10 from the 3′ end and at position 1 from the 5′ end. These positions were labeled with ATTO-550 and ATTO-647N (ATTO-TECH GmbH, Siegen, Germany), respectively, and purified by HPLC (reversed-phase C18, Amersham Bioscience, Uppsala, Sweden). Typical labeling yields and purities were ∼70% and >99%, respectively, as determined by HPLC. To prevent degeneration of the adenine base, the solutions were stored a basic environment (pH > 8). Biotinylated strands (IDT) were purchased HPLC-purified. 4.2. Origami Design. A DNA origami rectangle was prepared following Rothemund’s design.47 M13mp18 singlestranded DNA (New England BioLabs, Ipswich, MA, USA) was used as the scaffold, and the staples were obtained unpurified. 11938

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filters [an FF01-580/60 bandpass filter (Semrock) for the donor channel and a BLP01-635R long-pass filter (Semrock) for the acceptor channel], and focused into two single-photon avalanche photodiodes (SPADs (SPCM-AQRH-13, PerkinElmer Optoelectronics, Fremont, CA, USA). The TTL signals of the two SPADs were recorded as a function of time using a 12.5 ns resolution counting board (PCI-6602, National Instruments, Austin, TX, USA) and in-house-prepared Labview acquisition software (National Instruments 7.1). 4.4.2. Measurement Solution and Conditions. Measurements were carried out on diluted samples (30 μL of 3 pM solution) that were placed on a coverslip and sealed with silicone and an upper coverslip. The bottom coverslip was treated with KOH to prevent sticking to the surface, sonicated for 15 min in 1 M KOH solution, thoroughly washed with distilled water, and dried in an air flow. The measurement buffer comprised 10 mM Tris (pH 8.0), 1 mM EDTA, 10 μg/ mL bovine serum albumin (BSA, Sigma-Aldrich) to reduce sample sticking, 1−2 mM Trolox (Sigma-Aldrich) to reduce photobleaching and photoblinking of the dyes, and the indicated NaCl concentration. Data were collected over 15− 60 min, and the temperature was maintained at 22.5 °C. 4.4.3. Data Analysis and Presentation. Data analysis was performed with the in-house-written Labview software as described before.10,16 The beginnings and endings of bursts were determined by an all-photons burst search (APBS) using the following parameters: L = 200, M = 10, and T = 500 μs for hairpin-only and L = 2000, M = 100, and T = 2500 μs for hairpin-origami. For each burst, E and S were calculated according to eqs 2 and eq 3, respectively (see section 4.4.4), binned (bin size = 0.01), and plotted on one-dimensional E and S histograms and on a two-dimensional E/S histogram. The E histograms were smoothed with a running average for visualization purposes. 4.4.4. Calculation of E and S Values. Because in ALEX experiments two lasers alternately excite the donor and acceptor dyes, the calculation of E is somewhat different from that in a conventional single-laser experiment. E values were calculated using eq 2: E=

factor).48 This is evident from the fact that a low-E population (open hairpins) exhibited a higher S value than a high-E population (closed hairpins) when no correction was applied (data not shown). This phenomenon leads to a higher probability to detect open hairpin events than closed hairpin events, and numerical simulations showed that this problem cannot simply be solved by multiplying by a γ-dependent factor (data not shown). Therefore, to correct for this bias, 23% of the donor photons were stochastically deleted from the data files before the APBS, making the S values of the low- and high-E populations identical (Figure 2B1,B2). Numerical simulations showed that such photon deletion corrects for the γ-factor bias (data not shown). 4.4.6. Generation of E Histograms and Calculation of the Fraction of Open State. E histograms were generated from events having the correct S values (0.37 < S < 0.63 for hairpinonly and 0.25 < S < 0.40 for hairpin-origami). For the calculation of the fraction of open state, events with 0.1 < E < 0.35 were considered as open states, and events with 0.7 < E < 0.95 were considered as closed states. The fraction of open state was calculated by dividing the number of open-state events by the sum of the numbers of open- and closed-state events (areas under the corresponding E histograms peaks). Intermediate E values, corresponding to transitions between the states, were ignored. 4.5. Immobilization-Based Experiments. 4.5.1. Optical Setup. The sm-FRET-TIRF experiments were carried out on an in-house-built optical setup. In brief, a green CW laser beam (532 nm, MLL-FN-532, Changchun New Industries Optoelectronics Technology, Changchun, China) was aligned into a single-mode fiber. After the fiber, the beam was collimated, expanded, and then focused on the side of the back focal plane of a high-NA oil objective (NA 1.45, 60×, Olympus America) mounted on a commercial inverted microscope (IX71, Olympus America). The excitation intensity was tuned to meet two conflicting requirements. It needed to be strong enough to produce a signal that enabled identification of individual states and weak enough to allow time trajectories that lasted long enough to contain several transitions. We found that 30−100 mW, depending on the hairpin rates, allowed identification of several transitions before photobleaching (time trajectories of 4−12 s, camera frame of 5−15 ms). The emitted fluorescence was separated from the excitation light by a dichroic mirror (ZT532/638RPC, Chroma), split on the basis of wavelength (donor and acceptor) by a second dichroic mirror (FF650-Di01, Semrock), passed through a filter [an FF01-580/60 bandpass filter (Semrock) for the donor channel and a BLP01-635R long-pass filter (Semrock) for the acceptor channel], and focused into a fast EMCCD camera (IXON DU897E, Andor, Belfast, UK). 4.5.2. Measurement Solutions and Conditions. To ensure a reliable comparison of the diffusion-based and immobilizationbased results, the same solutions were used for the two measurements. 4.5.3. Procedure for Sample Immobilization. To control the immobilization process, good control over the solution volumes, incubation periods, and solution flow rates had to be achieved. This was done using a flow channel (sticky-Slide VI, Ibidi, Martinsried, Germany). The lower coverslip (which faces the objective) was pretreated with HF (1 min) and then washed thoroughly with distilled water. The immobilization process included several steps: (i) introduction of 60 μL (1 mg/mL) of biotin-coated BSA (BSA-biotin A8549, Sigma-

AD(EX) DD(EX) + AD(EX)

(2)

where DD(EX) and AD(EX) are the numbers of photons recorded in the donor and acceptor channels, respectively, during times in which the donor laser is on (the “donor laser on-time”), as commonly defined in ALEX experiments.10,15,16 No correction was made for donor photons leaking into the acceptor channel (donor leakage). The stoichiometry, S, was calculated by dividing the sum of the numbers of photons recorded in the donor and acceptor channels during the donor laser on-time by the sum of the numbers of photons recorded in both channels during the donor laser and acceptor laser on-times (eq 3): S=

DEX DEX + AEX

(3)

where DEX and AEX are the sums of the numbers of photons recorded in the donor and acceptor channels during donor laser on-time and the acceptor laser on-time, respectively. 4.4.5. Correction of γ-Factor Bias Problem. In our setup with ATTO-550 and ATTO-647N, the product of the detection efficiency and the quantum yield for the donor is larger than that for the acceptor (the ratio is known as the γ11939

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size of the open-state peak by the sum of the sizes of the closedand open-state peaks. 4.5.9. Generation of Dwell Time Histograms and Calculation of Rates. For each E versus time trajectory, periods with E < 0.5 were considered as open states and periods with E > 0.5 were considered as closed states. Open- and closed-state dwell time histograms were generated from more than 100 E versus time trajectories (accumulated from several movies). These histograms were fitted to single- or doubleexponential functions, from which opening and closing rates were calculated. To prevent bias caused by photobleaching, the last time segment in each trajectory (open or closed states) was rejected. 4.6. Estimation of the Difference in Heights of the Free Energy Barriers for the Two Hairpins Using the Nearest-Neighbor Model. Transition-state energies cannot be directly calculated using the nearest-neighbor model and the MFOLD program.40 Instead, we used MFOLD to calculate the free energies of formation (melting) of 6 bp duplexes with sequences identical to those of the A31-GC and A31-TA stems (5′-CGGCGA-3′ and 5′-AGGCGA-3′ from their complementary strands) at 22.5 °C and different Na+ concentrations (Figure 6B). If it is assumed that in melting of two strands the transition state is the unzipping of the last base pair, the difference between the transition-state and melted-state free energies is expected to come primarily from the translational entropy (because of the many microstates the unbound strands can occupy in the volume). Because the translational entropies of these two pairs of single-stranded DNA are expected to be almost identical, we can assume that the difference in the heights of the barriers for opening of our two hairpins is similar to the difference in stabilities calculated using the nearestneighbor approach. 4.7. The Pre-Exponential Factor k0. Adjusting the preexponential factor to obtain the best fit of the Kramer energies to the MFOLD energies yielded k0 = 2.3 × 106 s−1 (data not shown). With this value, all of the free energies decreased by around 0.5−0.7 kJ/mol with respect to the free energies calculated using k0 = 3 × 106 s−1. Nonetheless, these small changes have no influence on the qualitative conclusions regarding the hairpin dynamics. Because it is too early to claim that we determined k0 on the basis of measurements of only two hairpins, the value k0 = 3 × 106 s−1 taken from optical trapping experiments17 was used in this work.

Aldrich) into the channel, incubation for 10 min, and thorough washing with 0.5 mL of T50 (10 mM Tris, pH 8.0, 50 mM NaCl); (ii) introduction of 60 μL (0.2 mg/mL) of NeutrAvidin (ImmunoPure NeutrAvidin Protein, Pierce, Rockford, USA) followed by thorough washing with 0.5 mL of T50; (iii) gentle and slow injection of 60 μL of biotinylated hairpin-only or hairpin-origami (concentration ∼6 pM in 10 mM Tris, pH 8.0, 1 mM EDTA, 2−3 mM Trolox, and the indicated concentration of NaCl) followed by incubation for several minutes; and finally (vi) thorough washing with the measurement solution (0.5 mL) to remove the unbound samples from the channel. 4.5.4. Data Analysis. After the movies were acquired, data processing was performed with in-house-built MATLAB software (The MathWorks, Natick, MA, USA). 4.5.5. Overlapping Donor and Acceptor Images. For each movie, spots for several donors and the corresponding acceptors were manually selected. To each spot, a twodimensional Gaussian was automatically fitted, yielding the X and Y positions of the donor and acceptor spots. On the basis of these sets of positions, a nonlinear polynomial transformation was applied to overlap the donor and acceptor images, compensating for optical aberrations and imperfect alignment of the optical setup. 4.5.6. Generation of Donor and Acceptor Intensity versus Time Trajectories. For each movie, 15−50 of the brightest pixels in the acceptor or donor channel were manually selected, followed by automatic selection of the corresponding spots in the donor or acceptor channel. The intensity of each of the selected pixels was summed with the intensities of the eight surrounding pixels (altogether a 3 × 3 box centered on the brightest pixel). The per-pixel average background was estimated by averaging the intensity of the 16 pixels surrounding the 3 × 3 box. The background was subtracted from the intensity (after multiplication by 9 to reflect the contribution of the 3 × 3 pixel box to the signal). This operation was performed for the donor and the acceptor channels, for all of the selected spots, and for all of the movie frames, generating 15−50 background-corrected donor and acceptor intensity trajectories for each movie. E versus time trajectories were calculated by dividing the intensity in the acceptor trajectory by the sum of the intensities in the acceptor and donor time trajectories (as in a conventional calculation of E). 4.5.7. Selection of the Best Trajectories. First, the end time of each trajectory was determined as the time at which the sum of the donor and acceptor intensities (for any given frame) fell under a certain threshold (well above the background noise). If the intensity in every frame was above the threshold, the trajectory’s duration was the same as that of the movie. Second, the average intensity per frame (the sum of the donor and acceptor channels in each frame) was calculated. Finally, to ensure data quality, only time trajectories with average intensities and durations above certain thresholds were considered further. The data were then analyzed as described in the next two sections. 4.5.8. Generation of E Histograms and Calculation of the Fraction of Open State. E versus time trajectories from more than 100 individual molecules (several movies) were projected and accumulated to generate each E histogram (bin size = 0.01). Two prominent histogram peaks were observed: the open-state peak with E < 0.35 and the closed-state peak with E > 0.7. The fraction of open state was calculated by dividing the

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AUTHOR INFORMATION

Corresponding Author

*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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