J. Phys. Chem. B 2008, 112, 127-133
127
Probing the Complete Folding Trajectory of a DNA Hairpin Using Dual Beam Fluorescence Fluctuation Spectroscopy Jaemyeong Jung,† Rachelle Ihly, Eric Scott, Ming Yu, and Alan Van Orden* Department of Chemistry, Colorado State UniVersity, Fort Collins, Colorado 80523 ReceiVed: August 3, 2007; In Final Form: October 17, 2007
The conformational fluctuations of dye-quencher labeled DNA hairpin molecules in aqueous solution were investigated using dual probe beam fluorescence fluctuation spectroscopy. The measurements revealed the flow and diffusion times of the DNA molecules through two spatially offset optical probe regions, the absolute and relative concentrations of each conformational substate of the DNA, and the kinetics of the DNA hairpin folding and unfolding reactions in the 1 µs to 10 ms time range. A DNA hairpin containing a 21-nucleotide polythymine loop and a 4-base pair stem exhibited double exponential relaxation kinetics, with time constants of 84 and 393 µs. This confirms that folding and melting of the DNA hairpin structure is not a two state process but proceeds by way of metastable intermediate states. The fast time constant corresponds to formation and unfolding of an intermediate, and the slow time constant is due to formation and disruption of the fully base-paired stem. This is consistent with a previous study of a similar DNA hairpin with a 5-base pair stem, in which the fast reaction was attributed to the fluctuations of an intermediate DNA conformation [J. Am. Chem. Soc. 2006, 128, 1240-1249]. In that case, reactions involving the native conformation could not be observed directly due to the limited observation time range of the fluorescence correlation spectroscopy experiment. The intermediate states of the DNA hairpins are suggested to be due to a collapsed ensemble of folded hairpins containing various partially folded or misfolded conformations.
Introduction Fluorescence correlation spectroscopy (FCS) has been widely used to study the conformational fluctuations of biological molecules in free solution on the submicrosecond to hundreds of microseconds time scale.1-17 For example, in the study of DNA hairpin folding, the DNA can be labeled with a dyequencher pair, such that folding of the hairpin causes quenching of the fluorescent dye, and unfolding causes the fluorescence to be recovered. Dynamic equilibrium between folded and unfolded conformations gives rise to local fluorescence intensity fluctuations that can be analyzed by FCS.1-4,8,12,13,15 FCS can reveal the relaxation time of the reaction and the equilibrium distribution of folded and unfolded conformational states. From these parameters, the kinetic rate constants for folding and unfolding of the hairpin structure can be derived. There are several drawbacks to conventional FCS that hinder its more widespread application in the study of biomolecule conformational fluctuations. For example, if the reaction being studied occurs on a similar time scale to the transit time of the molecules through the optical probe region, the reaction correlation decay becomes entangled with the diffusion decay. Under these circumstances, the time dependent parameters governing reaction and diffusion cannot be independently determined on the basis of FCS alone. Also, information about the equilibrium distribution of the reaction is often inaccessible because the amplitude terms on which this information depends also depend on the fluorescence intensities of the reactants in their different conformational states. Prior knowledge of the * To whom correspondence should be addressed: E-mail: vanorden@ lamar.colostate.edu. † Present Address: California Institute for Quantitative Biomedical Research, University of California, Berkeley, CA 94720.
fluorescence intensities is required before the equilibrium constant can be determined. Finally, chemical reactions can only be studied by FCS if the reaction occurs on a faster time scale than the transit time of the molecule through the optical probe region. Slower reactions give correlation decays that are truncated by diffusion. DNA hairpins and other small biological molecules have diffusion correlation times ranging from ∼100 to ∼300 µs,1-4,8,12,13,15 severely restricting the range of reaction times that can be studied. Each of the problems mentioned have sometimes led to erroneous interpretations of FCS data in the study of biomolecule conformational fluctuations. We are developing new FCS analysis techniques that can address some of the difficulties described above.12,13 Our strategy combines single-beam fluorescence autocorrelation spectroscopy (FACS),1-16 dual-beam fluorescence cross-correlation spectroscopy (FCCS),12,13,18-24 and photon counting histogram (PCH)25-33 analysis to study the chemical relaxation properties of biomolecules in continuously flowing aqueous solutions. The FCCS analysis reveals the flow and diffusion properties of the molecules, independent of chemical reactions. The chemical relaxation properties are derived from the FACS analysis, with the flow and diffusion properties constrained to the values determined by FCCS. Finally, the equilibrium distribution and fluorescence intensities of the reactants are obtained from the PCH. In a previous study, we used this combined technique to characterize the conformational fluctuations of DNA hairpin molecules containing a 21 nucleotide polythymine loop connected by a 5-base pair (bp) stem.13 Our analysis revealed that the conformational fluctuations observed by FCS represented only a small part of a much broader folding landscape. The reaction probed by FCS was attributed to a dynamic equilibrium
10.1021/jp076248t CCC: $40.75 © 2008 American Chemical Society Published on Web 12/13/2007
128 J. Phys. Chem. B, Vol. 112, No. 1, 2008 between the unfolded state of the hairpin and a meta-stable reaction intermediate. Reactions involving the fully folded hairpin occurred on a much longer time scale than the molecular transit time through the FCS probe volume, such that the folded conformation appeared static on the FCS time scale. This suggests a much longer reaction time for the overall hairpin folding reaction than is accessible by conventional FCS. Indeed, single-molecule studies of DNA hairpin folding have observed reaction times for similar sized hairpins occurring on the time scale of milliseconds to hundreds of milliseconds, many times longer than the FCS time scale.34-39 However, single-molecule experiments cannot observe the microsecond fluctuations probed by FCS because of their limited time resolution. Hence, there is a need to “fill the gap” in time resolution between FCS and single-molecule experiments. Here, we describe a method to expand the FCS time scale so that both fast and slow reactions can be observed in the same FCS experiment. In dual beam FCCS, the transit time of the molecules between spatially offset probe beams can be controlled by adjusting the flow velocity of the analyte solution. Chemical reactions that occur during the transit time between probe beams modulate the cross-correlation function. By monitoring the changes in the cross-correlation function versus flow velocity, we can observe reaction correlation decays on the ∼100 µs to ∼10 ms time scale. Combining this information with single beam autocorrelation analysis can reveal the full reaction correlation decay over a broad range of time scales, from tens of nanoseconds to tens of milliseconds. Our goal in developing this expanded FCS time scale was to observe the complete folding trajectory of a DNA hairpin, from the extended state, through the intermediate state, and finally to the fully folded native state. The present report describes our accomplishment of that goal in the case of a DNA hairpin molecule containing a 21-nucleotide polythymine loop and a 4-bp stem. Importantly, the full reaction correlation function observed for this DNA hairpin suggested the same three-state folding mechanism proposed previously in our study of 5-bp hairpin DNA.13 The correlation decay for the folding reaction was double exponential with reaction time constants of 84 and 393 µs. This confirms two general characteristics of DNA hairpin folding kinetics that were missing from the original studies.1,40 (1) The formation of the fully base-paired native DNA hairpin structure does not generally occur directly but rather can proceed by way of metastable intermediates, and (2) formation of the native hairpin structure is much slower than revealed in earlier folding kinetics studies on DNA hairpins of similar size and composition.1,41 These conclusions are supported by several recent experimental and theoretical reports on DNA and RNA hairpin folding, in which complicated reaction kinetics were observed even for hairpins with stem sizes as small as one or two base-pairs.13,15,42-50 Experimental Section The DNA hairpins investigated in this study had sequences 5′-AACC(T)21GGTT-3′ and 5′-AACCC(T)21GGGTT-3′. These sequences are denoted 4-bp and 5-bp hpDNA, respectively. The hairpins were labeled at the 5′ end with rhodamine 6G (R6G) and at the 3′ end with dabcyl quencher, such that folding of the hairpin induced quenching of the R6G fluorescence. The analyte solutions consisted of an aqueous buffer containing 10 nM DNA, 2.5 mM Tris-HCl, 250 µM EDTA, and 100 mM NaCl. All experiments were performed at an ambient temperature of 20 °C. Melting curve analysis revealed that both hpDNA constructs were stable in their natively folded conformations
Jung et al.
Figure 1. Normalized melting profiles for 4-bp (blue) and 5-bp (red) hpDNA samples from fluorescence intensity measurements at temperatures varying from 5 °C to 85 °C. Melting profiles were observed using a steady-state flourometer.
under these conditions (Figure 1). The native fractions of 4and 5-bp hpDNA were estimated to be ∼75 and ∼96%, respectively. A control sample containing unstructured DNA of sequence R6G-T21-dabcyl was analyzed under the same conditions for comparison. Labeled, HPLC purified DNA samples were obtained from Qiagen (Alameda, CA). The dual beam fluorescence fluctuation spectroscopy experiment used to analyze the samples has been described in detail previously.12,13 Briefly, two spatially offset laser beams from a 514.5 nm Ar-ion laser were focused inside a flow chamber using a high numerical aperture microscope objective. Focusing of the laser beams formed two confocal excitation and detection volumes positioned ∼2 µm apart along the flow axis. The laser power was adjusted to ∼40 µW per beam to minimize triplet blinking and photobleaching of the fluorescent probe molecules and cross-talk between the two detection channels. Fluorescence from each focal region was collected by the microscope objective as the analyte molecules flowed sequentially through the two optical probe regions. The fluorescence was monitored using two single photon counting avalanche photodiode detectors, and the detected photons were accumulated into successive 1 µs counting intervals using a multichannel scalar card. The accumulated photocounts were subjected to simultaneous dual beam cross-correlation, single-beam autocorrelation, and photon counting histogram analysis. Results and Discussion Fluorescence Cross-Correlation Spectroscopy. Dual beam fluorescence cross-correlation spectroscopy was accomplished by flowing the analyte solution through the two spatially offset FCS probe regions.12,13,18-24 Fluorescence fluctuations detected from each probe region were cross-correlated to determine the diffusion and flow properties of the molecules as they flowed through each probe region sequentially. The cross-correlation function of the control DNA sample is given by the equation:18
GC0(τ) - 1 )
(
)(
1 1 1 Ntot 1 + τ/τD 1 + κ2τ/τ 0 D
) [ 1/2
]
r2(1 - τ/τF)2 exp (1) 1 + τ/τD
where Ntot is the average occupancy of DNA molecules inside the optical probe region, τD is the average diffusion time of a DNA molecule through a single optical probe region, τF is the
Folding Trajectory of a DNA Hairpin
J. Phys. Chem. B, Vol. 112, No. 1, 2008 129 only depend on the parameters Ntot, r, τF, and τD and are independent of the conformational fluctuations. Given the parameters Ntot, r, and τD obtained from cross-correlation analysis of the samples at slow flow velocities, together with the measured flow times, a hypothetical pure diffusion and flow cross-correlation function, G0C(τF) - 1, for the hpDNA samples could be predicted for each curve. Reaction correlation functions, gR(τF), were then extracted from the cross-correlation curves using
gR(τF) ) [GrC(τF) - 1][G0C(τF) - 1]-1
Figure 2. Cross-correlation functions measured for 4-bp hpDNA (red) and poly(dT)30 unstructured DNA (black) samples at various analyte flow velocities. The intensities were normalized to show convergence of the cross-correlation functions at slow flow velocity. The inset shows the reaction correlation functions, gR(τF), derived for each sample using eq 3. The red circles denote 4-bp hpDNA, and the black circles denote unstructured DNA.
average transit time between two probe regions, and r is the ratio R/ω0, where R is the distance between probe regions and ω0 is the confocal radius in the radial dimension. κ0 is the ratio ω0/z0, and z0 is the confocal radius in the axial dimension. κ0 was constrained to the value 0.104 ( 0.002, determined previously for our optical setup.12,13 For the hairpin DNA samples, the cross-correlation function included an additional contribution arising from the conformational fluctuations of the hairpin:
GrC(τ) - 1 ) gR(τ)[G0C(τ) - 1]
(2)
where gR(τ) is the reaction correlation function characteristic of DNA hairpin folding and unfolding. The cross-correlation function is a pseudo-Gaussian shaped curve that rises to a peak near τ ≈ τF. The peak amplitude and dispersion are modulated by the reaction and diffusion properties of the species being probed. Figure 2 (black curves) shows a series of cross-correlation functions obtained for the control DNA sample at various flow velocities of the analyte solution. The peak amplitudes decrease, and the widths broaden with decreasing flow velocity because of increased diffusion of molecules away from the flow axis during the transit time between probe beams. For each crosscorrelation function measured, the parameters Ntot, r, τD, and τF can be determined by fitting to eq 1. The cross-correlation functions colored in red (Figure 2) were obtained from the 4-bp hpDNA sample. These curves show excess amplitude relative to the control samples because of conformational fluctuations of the hpDNA. In the limit of slow flow velocity, it is found that GrC(τ) - 1 (eq 2) converges to G0C(τ) - 1 (eq 1). As the flow velocity slows, the correlation of the DNA hairpin conformational fluctuations during the transit time of the molecules between probe regions is lost, such that cross-correlation functions measured at slower flow velocities
(3)
Figure 2 (inset) plots gR(τF) versus τF for the 4-bp hpDNA sample. Points obtained by applying the same analysis to the control DNA sample are also shown for comparison. The former plot shows the reaction correlation function of 4-bp hpDNA in the time range of 100 µs to 10 ms. In the case of 5-bp hpDNA, a similar analysis showed a slight correlation decay that was too gradual to be characterized adequately. This suggests minimal conformational fluctuations of the 5-bp hpDNA occur in this time range. Fluorescence Autocorrelation Spectroscopy. Single-beam autocorrelation analysis of the fluorescence fluctuations detected in the individual probe regions was carried out simultaneously with the cross-correlation analyses. The autocorrelation functions provided information about conformational fluctuations occurring at faster times, down to 1 µs. Figure 3 shows autocorrelation functions and corresponding cross-correlation functions (inset) for 4- and 5-bp hpDNA samples flowing at slow velocity. The autocorrelation function characteristic of the hpDNA samples undergoing diffusion, flow, and conformational fluctuations is given by51
GrA(τ) - 1 )
(
)(
1 1 1 g (τ) Ntot R 1 + τ/τD 1 + κ2τ/τ 0 D
)
1/2
(1 + Te-τ/τT) ×
[
]
(rτ/τF)2 exp (4) 1 + τ/τD Ntot, r, τD, and τF could be constrained to the values determined from cross-correlation. T and τT are parameters relating to rapid fluctuations observed for all samples, including unstructured DNA with and without dabcyl quencher. These fluctuations may be attributed to triplet blinking of the R6G52 or interactions between R6G and DNA. In any case, they did not interfere with our analysis of the slower conformational fluctuations of the DNA hairpins. Figure 3 compares the experimental autocorrelation functions measured for the 4- and 5-bp hpDNA samples to the predicted autocorrelation functions assuming pure diffusion and flow (blue curves) and diffusion, flow, and fast blinking (green curves). The pure diffusion and flow autocorrelation functions were predicted using the values of Ntot, r, τD, and τF determined from the cross-correlation functions shown in the Figure 3 insets. The fast blinking parameters, T and τT, were obtained by fitting the experimental autocorrelation functions to eq 4 after constraining the parameters Ntot, r, τD, and τF and assuming a singleexponential decay model for the reaction correlation function. This only affects the autocorrelation function at lagtimes below ∼10 µs. The diffusion, flow, and fast blinking autocorrelation functions (green curves) are denoted G0A(τ) - 1. The excess amplitudes of the experimental autocorrelation functions relative to G0A(τ) - 1 are due to DNA hairpin conformational fluctua-
130 J. Phys. Chem. B, Vol. 112, No. 1, 2008
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Figure 3. Experimental and theoretical autocorrelation and cross-correlation (inset) functions obtained for (A) 4-bp hpDNA and (B) 5-bp hpDNA samples at a selected flow velocity. The selected flow velocity was slow enough so that the reaction contribution did not affect the cross-correlation function. The black dots denote the experimental auto- and cross-correlation data. The blue curves are predicted pure diffusion and flow autocorrelation functions that would be observed in the absence of conformational fluctuations and fast blinking. These curves were derived from the cross-correlation analysis parameters. The green curves show the contribution of fast blinking. The excess correlation observed in the experimental data is attributed to DNA hairpin conformational fluctuations, as seen in the residuals plots, which show the deviation of the experimental autocorrelation functions (blue markers) relative to the diffusion, flow, and fast blinking autocorrelation functions (red markers).
tions. The reaction correlation functions in the 1 to ∼300 µs time range were extracted from the observed autocorrelation functions using
gR(τ) )
[GrA(τ)
-
1][G0A(τ)
-1
- 1]
(5)
For the 4-bp hpDNA, the reaction correlation decay was truncated by the flow and diffusion correlation decay. The reaction correlation decay depended on the analyte flow velocity, becoming broader as the flow velocity slowed, a clear sign that the average conformational fluctuations are slower than the molecular transit time through the optical probe region. Hence, the full reaction correlation function could not be determined from single-beam autocorrelation analysis alone. For the 5-bp hpDNA, the reaction correlation decay was independent of the sample flow velocity, indicating the conformational fluctuations observed in our FCS experiment always occurred much faster than the flow and diffusion times for this hairpin. Full Reaction Correlation Function. Figure 4 shows the full reaction correlation function of 4-bp hpDNA from 1 µs to 10 ms. This data was assembled by combining the reaction correlation functions determined by auto- (eq 5, filled circles) and cross- (eq 3, open circles) correlation analysis. Data points from the autocorrelation analysis corresponding to lagtimes longer than 200 µs were discarded because they were truncated by the flow and diffusion correlation decay. Figure 4 also shows the part of the reaction correlation function of 5-bp hpDNA determined by autocorrelation analysis for comparison (open diamonds). Importantly, the full reaction correlation function of 4-bp hpDNA does not exhibit single-exponential relaxation kinetics, as would be expected for a predominantly two-state reaction. Rather, the decay exhibited double exponential relaxation, which
was analyzed using the following equation for the full reaction correlation function:
gR,4-bp(τ) ) 1 + B1 e-τ/τR1 + B2 e-τ/τR2
(6)
Table 1 shows the parameters obtained by fitting to this equation. The double exponential behavior of the 4-bp hpDNA reaction is consistent with a three-state reaction mechanism involving open, intermediate, and native DNA hairpin structures: k1
k2
-1
-2
}N h 2 {\ }N h3 N h 1 {\ k k
(7)
Here, N1, N2, and N3 are the average occupancies of the unfolded, intermediate, and native states of the DNA hairpins, respectively. The parameters τR1 and τR2 in eq 6 are related to the forward and reverse rate constants according to the equations (see ref 13, Supporting Information):
1 1 ≈ k1 + k-1 and ≈ k2 + k-2 τR1 τR2
(8)
To resolve the four rate constants, the equilibrium constants
K1 )
k1 N2 k2 N3 ) and K2 ) ) k-1 N1 k-2 N2
(9)
must also be known. PCH Analysis. We used PCH analysis to determine the equilibrium constants for the 4-bp hpDNA folding reactions shown in eq 7.25-33 The PCH is a probability distribution for the number of detected photons observed during a specified counting interval. In the present experiment, we used a counting interval of 9 µs. The PCH depends on the occupancy of the
Folding Trajectory of a DNA Hairpin
J. Phys. Chem. B, Vol. 112, No. 1, 2008 131
Figure 4. Reaction correlation functions for 4-bp hpDNA (black dots and open circles) and 5-bp hpDNA (open diamonds). For the 4-bp hpDNA, the reaction correlation function was derived from a combined cross- (open circles) and auto- (black dots) correlation analysis, using eqs 3 and 5, respectively. This data was fit to single (red dashed line) and double (blue dotted line) exponential decay models. The residuals plot shown for the 4-bp hpDNA sample shows that the double exponential decay model (blue dots) best describes the data. The data for the 5-bp hpDNA sample were derived from the autocorrelation analysis (eq 5) only. This data was fit to a single-exponential decay. Significant conformational fluctuations were not observed in the crosscorrelation measurements of the 5-bp hpDNA sample.
optical probe region and the average photodection rate from each fluorophore. On the basis of our previous study, we assumed the open and intermediate states of the hairpin exhibited appreciable fluorescence intensity that contributed to the PCH, whereas the closed state made a negligible contribution to the PCH because of efficient quenching of the R6G fluorophore.13 Hence, a two-state PCH model, dependent on the parameters N1, 1, N2, and 2, was used, where 1 and 2 are the average photodetection rates for an individual hpDNA molecule in its open and intermediate states, respectively. The latter parameters are referred to as the molecular brightness. In experiments using one-photon fluorescence excitation, the PCH also depends on a parameter, F, which corrects for nonideality of the confocal volume.30-32 Our PCH analysis of 4-bp hpDNA is shown in Figure 5, and the fitting parameters are presented in Table 1. Comparing the residuals plots for single state and two-state PCH analysis confirmed that the two-state model was most representative of our data. Given the occupancies N1 and N2 determined using the two-state PCH model and given Ntot determined by cross-correlation analysis, N3 was obtained using N3 ) Ntot -(N1 + N2). From thence, the equilibrium constants, K1 and K2, and all four rate constants were calculated (see Table 1). Melting curves, such as the ones shown in Figure 1, can be analyzed to estimate the equilibrium constant of a two-state reaction at a given temperature using the equation
Kmelt )
Imax - I I - Imin
(10)
Figure 5. Photon counting histogram obtained for the 4-bp hpDNA sample, after rebinning the detected photocounts into 9 µs counting intervals. The experimental data (black dots) were analyzed by fitting to one- (blue dotted line) and two- (red dotted line) component models. The normalized residuals plot shows that the two-component model best describes the data.
TABLE 1: FCS, PCH, and Kinetic Parameters for 4-bp hPDNA Foldinga FCS analysis cross-correlation τF (ms) 2.53(5) r 12.7(9) τD (µs) 207(14) 3.97(52) Ntot autocorrelation τT (ms) 4.03(67) T 0.178(13) reaction correlation B1 0.888(74) B2 0.575(74) τR1 (µs) 84.2(6.8) τR2 (µs) 393(48)
PCH analysis N1 1 (kHz) N2 2 (kHz) F
0.86(47) 0.671(69) 0.92(63) 0.19(12) 0.55(19)
equilibrium and kinetic parameters N3 K1 K2 K3S Kmelt k1 (103 s-1) k-1 (103 s-1) k2 (103 s-1) k-2 (103 s-1)
2.2(1.6) 1.07(93) 2.4(2.4) 2.7(8) 3.09(28)b 6.1(2.8) 5.7(5.6) 1.8(2.2) 0.75(54)
a
b
Values in parentheses are standard deviations in the last digits. Value determined from melting curve analysis.
where I is the fluorescence intensity at the temperature of interest, and Imax and Imin are the fluorescence intensities at the maximum and minimum temperatures, respectively. It is assumed that Imax and Imin are proportional to the concentrations of fully open and fully closed hpDNA. For the 4-bp hpDNA sample at 20 °C, the melting curve analysis predicts Kmelt ≈ 3.1. By comparison, we can predict Kmelt at our laboratory temperature of 20 °C using the FCS and PCH parameters measured for the 4-bp hpDNA sample. This predicted value is referred to as K3S and is given by
132 J. Phys. Chem. B, Vol. 112, No. 1, 2008
Ntot1 K3S )
Jung et al.
∑i Nii
∑i Nii - Ntot3
(11)
K3S can be determined if 3, the molecular brightness of the fully closed hairpin, is known. We have estimated this parameter by assuming that all of the fluorescence observed from a sample of 5-bp hpDNA in 500 mM NaCl at 5 °C was coming from the fully closed hairpin. According to melting curve analysis, the fraction of fully folded hairpin structures is >98% under these conditions.13 Given the average fluorescence count rate measured from this sample and the value of Ntot determined by FCS, we obtained 3 ≈ 0.036 kHz. It is assumed that this same value also applies to the closed state of 4-bp hpDNA at room temperature. In fact, this is probably an upper limit because of the small contribution to the fluorescence coming from the open and intermediate states in the 5-bp hpDNA sample. On the basis of our evaluation of 3 and the other parameters in Table 1, we obtained K3S ) 2.7 ( 0.8 for the 4-bp hpDNA. This value agrees with Kmelt within experimental error, suggesting our PCH and FCS analyses and proposed three-state mechanism can explain the melting curve obtained for 4-bp hpDNA. We can also compare Kmelt and K3S to the overall equilibrium constant K ) K1K2 ≈ 2.6 obtained for the 4-bp hpDNA sample. Within experimental error, there is good agreement among all three parameters. This suggests the folding kinetics probed using our FCS experiment was sensitive to fluctuations involving all of the reactants present in the sample. There was no evidence for hidden dark states that were static on the time scale of our experiment. By contrast, the single-exponential decay shown for the 5-bp hpDNA (Figure 4, open diamonds) represented only a small fraction of the reactants present, as reported in our previous study.13 The bulk of the DNA existed in a fully folded state that was essentially static on the time scale of our experiment. Hence, the reaction correlation function for the 5-bp hairpin shown in Figure 4 was caused by dynamic equilibrium between states N1 and N2 only. At this time, we can place a lower limit on the overall reaction time of 5-bp hpDNA folding of ∼10 ms. Discussion. The observations presented above suggest both DNA hairpins in our study react according to a similar threestate mechanism involving a reaction intermediate that is stable on the time scale of ∼50 to ∼100 µs. On the basis of previous suggestions from both experiment and theory, this intermediate state is attributed to a collapsed ensemble of structures containing a closed hairpin loop and various partially folded or misfolded stem structures.13,42-50 Further investigation of these intermediate states could potentially reveal general information about the primary mechanism of DNA duplex formation and disruption. Such reactions are among the most fundamental processes in biology. It has been noted previously that DNA hairpin folding rates measured using single-molecule techniques34-39 do not agree well with those determined using FCS1-4,8,12,13,15 or laserinduced temperature jump (T-jump) spectroscopy41,48,50,53-55 for similar sized hairpins. In particular, reaction rates measured using single-molecule experiments are often many times slower than those reported by FCS or T-jump. We suggest these discrepancies are caused by the different measurement times probed by the different experiments. FCS and T-jump experiments mainly focus on the submicrosecond to hundreds of microseconds time scale, while single-molecule techniques are generally restricted to the millisecond time scale and above.
Our research has shown that important processes occur in the DNA hairpin folding reaction over a broad range of time scales. Rapid fluctuations involving intermediate states occur on a time scale where FCS and T-jump are most sensitive, whereas slower reactions involving formation and disruption of the native structure are more accessible to single-molecule experiments. Hence, the discrepancies between previous FCS, T-jump, and single-molecule experiments may be due to the different types of reactions being probed. A second issue has to do with the trapping forces applied to the DNA in single-molecule optical trapping experiments. Such experiments observe predominantly two-state folding behavior over a range of DNA sizes and sequences, which seems to contradict the observations presented here.37,38 However, the intermediate states of the DNA are likely to be much less stable than the native states. The trapping forces being applied to the molecule may destabilize the intermediate states, so that only direct folding of the native structure can occur when the DNA is positioned inside an optical trap. Here, we have sought to “bridge the gap” between the different time regimes probed in FCS and single-molecule experiments, and thereby observe the complete folding trajectory of a DNA hairpin in the same FCS experiment. We have accomplished this objective for the first time in the case of 4-bp hpDNA. We can attempt a comparison between the rate constants we determined for this hairpin and those that would be expected if the same sized hairpin were to be studied in a single-molecule optical trapping experiment. Woodside et al. measured folding and unfolding rates of DNA hairpins with stem structures containing 6 to 30 bp.38 By measuring the reaction rates over a range of applied trapping forces and extrapolating to zero force, they determined the “unloaded” reaction rates for each hairpin. This unloaded rate is thought to be equivalent to the intrinsic rate constant of the unperturbed reaction. A systematic increase in the hairpin unfolding rate was observed with decreasing stem size for stem sequences containing 50% G-C content. Extrapolating to a stem size of 4 bp reveals a predicted unfolding rate of ∼500 s-1 for our 4-bp hpDNA. By using kunfold ≈ (1/k-1 + 1/k-2)-1, our experiment reveals an unfolding rate of ∼650 s-1 for the 4-bp hairpin, in excellent agreement with the predicted value. Hence, the overall rate of hairpin unfolding is predicted to be the same for both FCS and optical trapping experiments. The difference is that in FCS, the reaction proceeds by way of stable intermediates, and in optical trapping, the folding would occur directly. Conclusions We have used a combination of dual-beam FCCS, singlebeam FACS, and single-beam PCH to study the folding and unfolding kinetics of 4- and 5-bp hpDNA. In the case of 4-bp hpDNA, we observed both fast and slow fluctuations of the hairpin structure, consistent with a three-state reaction involving extended, intermediate, and native hairpin conformations. The fast fluctuations were attributed to folding and unfolding of an intermediate, and the slow fluctuations were attributed to formation and disruption of the native stem structure. In the case of 5-bp hpDNA, only fast fluctuations, attributed to the intermediate reaction, were observed. The higher stability of the 5-bp hairpin structure gave rise to much slower folding and unfolding of the native conformation, which could not be observed on the time scale of our FCS experiment. This caused the native structure of the 5-bp hairpin to appear static on the FCS time scale. These results shed additional light on the mechanism of intramolecular DNA duplex formation by pointing
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