Evidence of a Three-State Mechanism in DNA Hairpin Folding

Abstract

DNA hairpins are a model system for biomolecule folding as well as key structures in biology and nanotechnology. However, limitations in traditional solution-phase spectroscopy shorten the window of observable kinetics and cannot account for static heterogeneity. Here, we show that the application of 2-Dimenstional Fluorescence Lifetime Correlation Spectroscopy (2DFLCS) to a solution-phase molecule trapped in an anti-Brownian Electrokinetic (ABEL) trap bypasses those limitations, enabling kinetic analysis of the dynamics of single solution-phase molecules on a broad range of timescales down to microseconds. The analysis unambiguously shows that DNA hairpin folding proceeds via a three-state system, where hairpins fold initially on the scale of 10s-100s of microseconds from a random coil to a partially closed intermediate, and then form a stable fully closed state.

Graphical Abstract

The folding and unfolding kinetics of DNA hairpins has been studied for decades as a model biomolecular system,^1-3 key biological structure,^4-6 and nanotechnological building block.^7-10 However, outstanding fundamental mechanistic questions remain due to experimental limitations. In particular, experiments must be performed in solution to avoid confounding surface interactions. Principally, Fluorescence Correlation Spectroscopy (FCS) has been used to demonstrate the existence of fast sub-millisecond steps in the folding process. However, FCS yields signals difficult to unambiguously assign to intramolecular or translational (diffusion) dynamics, is unable to capture dynamics slower than the diffusion time through the detection volume (a few ms),^{2, 11-14} and most importantly, cannot account for molecule-to-molecule (static) heterogeneity since signals are combined from the entire molecular ensemble. Studies have attempted to decouple the intramolecular folding component from the diffusional component via Förester Resonance Energy Transfer (FRET) ratios,^{15, 16} diffusion deceleration,¹⁷ or higher order correlation analysis,¹⁸ but the analysis still relies on ensemble-averaging. Often these studies model via stretched exponentials, which are phenomenological and cannot fully describe the underlying conformational landscape.^{15, 16, 19} Here, we apply an anti-Brownian electrokinetic trap^20-28 (Figure 1a) in combination with two-dimensional fluorescence lifetime correlation spectroscopy,^{11, 29} which we term ABEL-2DFLCS,³⁰ to present a unified picture of DNA hairpin dynamics and show the existence of a three-state model without the need for stretched exponential fitting.

Figure 1:

a) Cartoon of how the ABEL trap is used to trap molecules in solution. Briefly, a confocal beam scans a 4x4 raster scan pattern to localize our molecule of interest. Once located, a voltage is applied to the trap to push the molecule back towards the center. b) Fluorescence intensity trace of a single trapped DNA hairpin in 10ms bins, beginning at ~47.5 seconds and bleaching at ~49 seconds. Donor intensity (ATTO647N) is shown in blue, Acceptor intensity (Cy7) is shown in purple. c) Reaction correlation extracted from a single molecule. Inset shows a cartoon of DNA hairpin (ATTO647N red star, Cy7 gray star) folding with two distinct kinetic steps with a fast (pink) and slow (blue) correlation time. Double exponential (green), stretched exponential (red), and monoexponential (orange) fits are shown as solid lines, d) residuals as dotted lines.

One model for DNA hairpin dynamics is a two-state model, where the hairpin is described as either open – where the loop is randomly coiled and stem unhybridized- or closed – where the stem is completely formed, with no other stable conformations. When fluctuations between open and closed are measured by FCS, the change in the autocorrelation function due to the change in intramolecular distance can be analyzed to determine intramolecular dynamics. The kinetics can be described with a single exponential (eq 1), with a characteristic reaction time ${\tau }_{rxn}$, and stretch factor $\beta$ to describe the system’s ability to sample the energetic landscape.¹⁵

$$\mathrm{G}(\mathrm{t})=\alpha \text{exp}(-(\frac{\mathrm{t}}{{\tau }_{rxn}})\beta )$$ eq 1

There has been substantial discussion of the value of $\beta$. As the hairpin rapidly accesses a large fraction of its available energetic landscape over the course of the observation, $\beta$ approaches 1 and the molecule behaves ergodically; conversely, if each hairpin is allowed to explore a more limited fraction of the landscape (static heterogeneity) or if the time required to explore the entire parameter space is comparable to the measurement time (dynamic heterogeneity), the closer $\beta$ is to 0. While fitting a stretched exponential and extracting $\beta$ is typically a phenomenological analysis, it has been used to examine heterogeneous kinetics in catalysis and surface chemistry^31-33 and biomolecule folding.^{31, 34, 35} In hairpins^{15, 16, 19} it can be a consequence of dynamic heterogeneity (a molecule whose reaction rate changes over time), static heterogeneity (molecule-to-molecule differences), or instrumentation interferences (diffusion).³⁶

Alternatively a three-state model has been proposed with reactions on two different timescales.³⁷ In addition to the typical dynamics seen on the order of tens to hundreds of microseconds, this additional state, whether it is an extended open¹⁸ or partially folded closed form,³⁷ adds a kinetic step only observable on the millisecond timescale. As a result, autocorrelation decay is a double exponential with two weighted reaction times. These reaction times and their amplitudes are related to the underlying rate constants of both steps and are derived in SI S.2.

$$G(t)={\alpha }_1\text{exp}(-\frac{t}{{\tau }_{rxn1}})+{\alpha }_2\text{exp}(-\frac{t}{{\tau }_{rxn2}})$$ eq 2

With traditional FCS, it is difficult to determine which picture is accurate. The first issue concerns the observation window of a diffusing molecule, which limits the accessible timescale to the time it takes to diffuse through the confocal excitation volume. If there truly are millisecond and longer-lived additional states, they are effectively static on the FCS timescale. Second, dynamics on the same timescale of diffusion may be confused with intensity changes from diffusion, giving the appearance of spurious conformational dynamics. Finally, averaging over many molecules degrades the analysis: an observed stretched exponential implies a range of behaviors among single-molecule contributors, and thus can derive from a distribution of many monoexponential decays, multiexponential decays, or stretched exponential decays, with each indicative of very different underlying mechanisms.

ABEL-2DFLCS has the unique ability to bypass these issues.³⁰ By countering Brownian motion of trapped molecules, observation windows are extended to seconds removing the diffusion component of signal, all while performing a true single-molecule experiment, whereas traditional FCS acquires data at or near the single-molecule level and ensembles averages it to increase signal. Taken together, ABEL-2DFLCS grants the ability to simultaneously examine fast (10-100s of microseconds) and slow (>1ms) dynamics. By removing the key interferences of diffusion and molecule-to-molecule heterogeneity while enabling access to wide range of dynamics timescales, ABEL-2DFLCS allows us to definitively identify whether the underlying kinetics are a two-state or three-state mechanism.

FRET labeled (ATTO647N donor, Cy7 acceptor) DNA hairpins consisting of a 15-basepair non-dynamic spacing sequence to prevent complete quenching of the donor, and 5-basepair dynamic sequence stem, and either a 21-base poly-T (T21) or 30-base poly-A (A30) loop were trapped in a pH 8 0.25x Tris-EDTA buffer supplemented with 100mM NaCl and 10% glycerol by volume. Experiments were repeated with the addition of 10mM MgCl₂ to drive equilibrium towards the closed state. These conditions and sequences were selected to closely match those of previous efforts that identified conflicting mechanisms of folding. Previously, different investigations on these A30 hairpins^{15, 16, 19} and T21 hairpins^{18, 37, 38} demonstrated either stretched exponential kinetics or three-state kinetics, respectively, despite having highly similar stem composition and loop length. In our experiments, we use both sequences to make up the dynamic portion. To minimize interaction between the dynamic sequence and the static sequence, we include an abasic site to reduce cooperative base stacking between the two sequences (see SI for further discussion).³⁹ For 2DFLCS analysis,^{2, 11, 29, 40-45} lifetime components of the individual molecules were first extracted from the donor channel using 2-dimensional maximum entropy method (2D MEM) analysis, and the correlations analyzed using fluorescence lifetime correlation spectroscopy (FLCS).^{46, 47} See SI for full materials and methods.

The 2D MEM analysis returns two fluorescence lifetime components: a long lifetime consistent with a far end-to-end distance, and a short lifetime consistent with a closer end-to-end distance (Fig S6.1). This result is not proof positive of either a two-state or three-state mechanism, as a third state may have structural and photophysical properties too similar to either the open or closed state to be distinguished. Because only two lifetime components can be detected, the autocorrelations and cross correlations from FLCS can be expressed as:³⁰

$$G_{11}=G_D(1+K_{obs}{G}_r)$$ eq 3

$$G_{22}=G_D(1+\frac{1}{K_{obs}}{G}_r)$$ eq 4

$$G_{12}=G_{21}=G_D(1-G_r)$$ eq 5

These extracted correlations are then used to determine the diffusion portion of the correlation $G_D$, equilibrium constant $K_{\mathit{obs}}$, and the reaction correlation $G_r$, which holds the kinetic information of the hairpin dynamics. Here, $K_{\mathit{obs}}$ is the ratio of the quenched to unquenched populations, distinct from the three formal equilibrium constants $K_{\mathit{eq}}$ for each pair of states (SI S.2). While $G_D$ would show a decrease at the millisecond scale for free diffusion, the canceling of Brownian motion by the ABEL trap pushes that decrease to hundreds of milliseconds or seconds. This shift allows the analysis to focus uniquely on intramolecular dynamics: the reaction correlation $G_r$ is examined to be a single exponential, stretched exponential, or double exponential decay to mechanistically explore the underlying dynamics without contribution from diffusion (See SI S.1 for judging fits). As shown in Figure 1c,d, the decay is conspicuously well-described by a double exponential, indicative of a three-state mechanism. Importantly, this observation requires the single-molecule precision of ABEL-2DFLCS, as analyzing the reaction correlations averaged over all molecules often results in a stretched exponential decays (SI S.9), as seen in past investigations of hairpin dynamics.^{15, 16, 19}

Figure 2 shows reaction correlations extracted from individual hairpins in four scenarios: either the T21 (left) or A30 (right) hairpins in the presence (bottom) or absence (top) of MgCl₂. The three-state model is unambiguously supported for all conditions and hairpin sizes (N = 35, N = 33 for T21 without and with magnesium, and N = 34 and N = 35 for A30 without and with magnesium). These two decays consist of a fast reaction (pink) on the order of 10s-100s of microseconds, and a slow reaction (blue) on the order of milliseconds. In each scenario, the double exponential decay fit of the reaction correlation was the best fit for a majority of molecules (74%, 71%, 70%, and 86% for T21 and A30 without MgCl₂, and for T21 and A30 with MgCl₂, respectively), with the rest being either the non-stretched single-exponential decay (0%, 12%, 6%, and 3%) or the stretched-exponential decays (26%, 18%, 24%, and 11%). These percentages are consistent with the precision of our analysis given the limited acquired photon count (see SI S.3).

Figure 2:

Fit reaction correlations of individual DNA hairpins in each set of conditions. Reaction correlations (black) are obtained by FLCS and fit with a double exponential decay (green). The relaxation time of both slow and fast components are shown as vertical lines (blue and pink). Left Side: T21 hairpins, Right Side: A30 hairpins. Top Half: Buffer without MgCl₂, Bottom Half: Buffer with MgCl₂

Moreover, if hairpins behaved in a two-state manner, we should see certain identifiable signatures. In the regime where previously seen stretched exponentials were suggested to be due to molecular diffusion or averaging with static heterogeneity,³⁴ individual molecules would be expected to decay as simple monoexponentials, in stark contrast to our observations. On the other hand, the presence of dynamic heterogeneity would retain the stretched exponential shape observed with ensemble averaged FCS for each molecule, rather than display the multiple and distinct drops in reaction correlation we see in our data.

The reaction times observed here are consistent with three-state behavior demonstrated on the same T21 stem-loop sequence by Van Orden, measured separately in two different experiments, a variation on FCS^{18, 37} and stopped-flow⁴⁸ measurements. Our observed reaction times are slightly longer as expected due to our buffer containing 10% glycerol. A similar hairpin sequence consisting of the same loop composition but a one base-pair shorter stem showed similar double-exponential behavior when measured with diffusion-decelerated FCS.¹⁷ However, these previous experiments relied on ensemble averaging to generate their autocorrelations, which cannot account for molecule-to-molecule heterogeneity in kinetics. With our data, we show that the individual molecules go through both steps, supporting a three-state folding mechanism for these DNA hairpins. Values for the fast and slow reactions for all three-state hairpins are shown in Figure 3. Regardless of loop composition, reaction times are at comparable timescales, suggesting that the loop sequence does not qualitatively alter the folding mechanism, and each step has little heterogeneity from molecule-to-molecule.

Figure 3:

Histograms of fast (pink) and slow(blue) reaction times of three-state hairpins. Vertical lines designate the median reaction times of each component (dark pink and dark blue). T21 and A30 are separated as the left and right sides, while the absence vs presence of MgCl₂ is shown as top or bottom. Median values for each quadrant are as follows: T21-MgCl₂: 1.18e-04s and 1.87e-03s; T21+MgCl₂: 7.02e-05s and 7.33e-03s; A30-MgCl₂: 2.27e-04s and 3.72e-03s; A30+MgCl₂: 7.40e-05s and 2.11e-03s.

The only construct that seems to have heterogeneity in reaction times is the A30 hairpin without MgCl₂, where the fit reaction times for the fast component are highly variable, ranging from tens of microseconds to a millisecond. We believe this result is not due to major molecule-to-molecule heterogeneity, but an analytical limitation: for processes with similar reaction times or where one correlation component’s amplitude is much greater than the other, it is difficult to accurately fit both the slow and fast reaction components, resulting in an artificially large spread of correlation times. This phenomena is observed in simulated data when the slow and fast reaction times are within an order of magnitude of each other (SI Figure S3.6). We note that using FLCS to clearly identify both steps is dependent on the temporal separability of those steps. Our previous study examined hairpins that appeared to show two-state behavior, but differences in stem sequence and length,¹⁴ absence of abasic sites,³⁹ and viscosity¹⁶ can all affect timescales of dynamics, or potentially, the mechanism. Importantly, all of the direct literature comparisons discussed here use the same stem length and GC content.^{15, 16, 18, 19, 37, 38} Even as our kinetic data differs from some previous reports,¹⁹ the thermodynamic behavior is broadly consistent. The A30 hairpin studied by Klenerman et al. shows a $K\approx 1$ in 100mM NaCl, which increases by an order of magnitude upon the addition of magnesium,¹⁶ which stabilizes the duplex.⁴⁹ $K_{\mathit{obs}}$ extracted by ABEL 2DFLCS are highly similar, with a median value of 0.97 and 10.97, respectively(Fig. 4a, cyan and blue). The T21 hairpin as reported by Van Orden et al. has had different equilibrium constants reported based on the method used, but ranges from $K_{\mathit{overall}}=4.47-8.35$. ^{37, 48} In our experiment, the same hairpin shows a slightly lower $K_{\mathit{obs}}=3.09$ (Figure 4a, yellow). While there is no report on the same hairpin with magnesium, we do see an increase in $K_{\mathit{obs}}$, consistent with the stabilizing properties of magnesium on DNA duplexes.⁴⁹Though ABEL-2DFLCS shows that DNA hairpins can be accurately described as a three-state system, assignment of a structural identity, either an additional open state or closed state, or where that state appears in the folding mechanism, is impossible solely by looking at the correlations alone (SI Section S.3). Further, response to MgCl₂ cannot provide a simple identification, as magnesium can stabilize the duplexed form of DNA resulting in a long lived state, or it can increase the flexibility of single stranded DNA and slow the rate of accessing an extended open state.⁵⁰ Either way, both can cause the same observed millisecond scale decay.

Figure 4:

a) $K_{\mathit{obs}}$ extracted by ABEL 2D FLCS from individual hairpins, with median values plotted as vertical lines. b) and c) Forwards (x-axis) and backwards (y-axis) rate constants for the slow (blue) and fast (pink) reactions for individual T21 hairpins in the absence (b) and presence (c) of 10mM MgCl₂. Large markers are placed to show the center of mass of the rate constants in b and c. The center of mass for T21 in absence of 10mM MgCl₂ is shown as a faded marker.

Fortunately, the single-molecule intensity traces, free of the contribution from diffusion, in conjunction with 2DFLCS, offers a path forward. If there is a long-lived extended conformation, conspicuous jumps in intensity should be seen lasting for several milliseconds. Tellingly, we do not observe the repeated appearance of such long-lived bright states (SI Figures S4.1 and S4.2), leading us to identify the third state as a partially closed conformation. Such a state would be indistinguishable from the more long-lived low-FRET closed state. Thus, we conclude that DNA hairpin folding begins with a rapid transition from a random coil to a partially closed intermediate, followed by a slow process to form the fully closed complex (Figure 1c inset). The transition from a random coil to a partially closed intermediate is likely not as simple as end-to-end collision, which takes place on the scale of single digit microseconds in single-stranded DNA overhangs.^{51, 52} Rather, this transition is indicative of the formation of a more stable compact state like the one observed by Israels et al., which also takes place on the tens to hundreds of microseconds.⁵³ However, it is important to note that the end-to-end distance reported in the prior study is 46.5Å, while we believe the ends of our DNA HP are in contact with each other, given the inability to distinguish the two closed states.

Assuming this mechanism with a partially folded intermediate, we generated expressions for all four forward/backward rate constants from $K_{\mathit{obs}}$, the individual reaction times, ${\tau }_{rxn1}$, ${\tau }_{rxn2}$, and their relative amplitudes (SI S.2). The forwards and backwards rate constants of the fast and slow folding steps of the T21 hairpin are shown in Figure 4b and 4c, showing the impact of magnesium ions is greatest on the slow (blue) reaction, dramatically decreasing the forwards/backwards rates (± standard error of the mean) from 1,700±270s⁻¹/ 170±69s⁻¹ to 210±260s⁻¹/29s⁻¹±87s⁻¹ (values of all rate constants for each system in SI S.7). This change is likely due to the charge screening effect of magnesium ions, which promote the formation of the partially closed state by decreasing the repulsion of the two stems, and increasing the stability of both closed states, decreasing the rate of interconversion. A more subtle change in the fast reaction is also consistent with prior studies of hairpin folding that focus on the effect of counterions. These studies demonstrate that on the timescale of tens to hundreds of microseconds, the rate of folding increases with the concentration of counterions, while unfolding remains unchanged.^{18, 54} Similarly, we see that while the rate of folding for the fast reaction increases from 2,400s±450s⁻¹ to 7,900± 1,300s⁻¹ upon the addition of magnesium, the rate of unfolding changes very little from 4,900s⁻±1,600s⁻¹ to 5,400± 610s⁻¹.

While these results show clear evidence of three-state behavior, the generality of this scheme for all DNA hairpin constructs should be discussed. The DNA hairpins that we examine here were chosen because they have been studied extensively by previous efforts, where they were observed to exhibit dynamics that could not be explained by homogenous two-state behavior, but disagreements persisted in the precise nature of the mechanism.^{15, 16, 18, 19, 37, 38} However, the applicability of a three-state mechanism is also seen to vary with sequence or environment. For example, changes in stem and loop composition, and presence of magnesium ions, can both strongly impact the separability of the time components (A30 −MgCl2 is poorly separated, T21 + MgCl2 is strongly separated), making a three-state mechanism harder to distinguish from a two-state mechanism, or potentially changing the mechanism all together. Differences in sequence and environment likely explain the monoexponential behavior observed in previous ABEL-2DFLCS studies on different hairpins, which possessed a shorter stem and were studied at higher glycerol concentrations.³⁰ A larger survey of hairpins over a range of conditions is needed to comprehensively map the generality of the three-state mechanism beyond these well-studied constructs.

Here, ABEL-2DFLCS clearly demonstrates the three-state nature of DNA hairpin dynamics, and examining the single-molecule intensity traces further identifies the additional state as a partially closed intermediate likely between a random coil and fully hybridized stem. The single-molecule perspective and long observation window of the ABEL trap enable the unambiguous elucidation of the two distinct reaction steps upon folding, without influence of heterogeneity or diffusion. Understanding that nucleic acid hairpins possess these two reactions on disparate timescales may provide insight into regulation of gene expression, protein-DNA interactions,⁵⁵ RNA dynamics,^{56, 57} and protein-RNA interactions.⁵⁸ ABEL-2DFLCS is poised to derive future biophysical mechanistic insights by combining single-molecule observations with analysis over multiple timescales.

Supplementary Material

Contains more detailed materials and methodology, additional simulations, and fits to all analyzed molecules.