Force-induced unfolding of DNA and RNA hairpins observed by SMFSIn order to observe strand invasion into nucleic acid hairpins via SMFS, we generated molecular constructs that allowed us to connect the hairpins to 1 μm-diameter silica beads that could be trapped by the two infrared laser beams of a commercial optical trap setup (Fig. 1A, C-Trap® LUMICKS, see Methods for more details). Our toehold hairpins were folded from 124 nt long DNA or RNA sequences derived from a gene regulatory toehold switch15 and consisted of a 14 nt long single-stranded toehold and a 52 bp long stem connected by a 6 nt long loop region (see Supplementary Fig. 1). As schematically shown in Fig. 1A, in a so-called dumbbell assay, the 5’ and 3’ ends of the hairpins were hybridized to two 185 nm long double-stranded DNA handles connecting the hairpin to the silica beads via biotin/streptavidin and digoxigenin/anti-digoxigenin linkers. Since the DNA handles had their overhangs on the 5’ end, a single-stranded adapter (gray in Fig. 1A) was used to hybridize the 3’ end of the hairpin to the handle. Single-molecule experiments were performed using a microfluidic flow cell where a single molecule suspended between the two traps can be exposed to different solution conditions by moving the traps into different microfluidic streams (Fig. 1B). In a typical experiment, the two beads are trapped in the beads channel, the dumbbell is formed in the buffer channel and subsequent measurements can be performed in either a channel containing only buffer solution or in the trigger channel containing 100 nM trigger strand (for more details see Methods section “Measurement preparation”).To characterize the mechanics of the hairpin, we initially performed single-molecule unzipping experiments on both the DNA and the RNA hairpin in the absence of trigger molecules. Stretch/relax cycles obtained at a pulling velocity of 0.2 µm/s of the hairpin are shown in Fig. 2A, B. During stretching, rapid transitions marking increasing unfolding of the hairpin can be observed. Several intermediates (I1, I2, and I3) are populated on the way from the fully folded (Fol) to the fully unfolded (Unf) state. We estimated the number of nucleotides unfolding in the transition from each state to the next by fitting the traces with a worm-like chain (WLC) polymer model46,47 (colored lines in Fig. 2A, B and Supplementary Table 1). While unfolding forces are significantly higher for RNA as compared to DNA, the length changes from one intermediate to the next are identical in the DNA and RNA hairpins within the resolution of our experiment. Sequence details of the folded and unfolded portions of the partially unfolded intermediates based on our length measurements can be found in Supplementary Fig. 2. Upon relaxation, the molecule readily folds back to the fully folded state (light gray traces in Fig. 2A, B).Fig. 2: TMSD for DNA and RNA.A Representative force-extension curves (stretching: black, relaxation: gray) in the absence of trigger strands. The colored curves correspond to fits of a WLC model to the data for the different intermediate states. The inset shows unfolding transitions in more detail. B Analogous for RNA. C Passive mode trace of a DNA (upper trace with zoom) and RNA hairpin (lower trace) when moving from buffer to trigger channel. Binding of a trigger occurs after a lag time of ≈ 2 s, followed by toehold-mediated strand invasion, which is observed as the force drops. An exponential fit was used to determine the invasion time (black dashed line). In contrast, RNA invasion times are significantly longer (2 ms as obtained from the time between the two dotted lines), and an intermediate state is populated during the invasion process. An exponential fit to the part after the intermediate still gives longer invasion times compared to DNA (black dashed line). D Plots of invasion time vs. force. Gray crosses: system response time (see Methods for details, N = 20). To guide the eye, we used an exponential function to fit these data points (gray line). Blue circles: DNA hairpin with DNA trigger (N = 20). Dark green circles: RNA hairpin with RNA trigger (N = 3). Dark green triangles: RNA hairpin with an RNA trigger with two proximal mismatches (see Supplementary Fig. 1 for sequence details, N = 46). Dark green squares: RNA hairpin with RNA trigger without magnesium (N = 5). Invasion times via fitting the part after the intermediate. Light green circles: RNA hairpin with RNA trigger (N = 3). Light green triangles: RNA hairpin with an RNA trigger with two proximal mismatches (N = 46). Light green squares: RNA hairpin with RNA trigger without magnesium (N = 5). Data are presented as mean values ± standard deviation (s.d.). E Representative force-extension curves after TMSD. Colored curves correspond to WLC fits: toehold bound (TB), fully invaded (FI) and fully invaded as well as fully unfolded state (FU) state. Source data are provided as a Source Data file.To obtain a more detailed kinetic and energetic characterization of the unfolding-refolding equilibrium transitions, we also performed so-called passive mode experiments where we kept the distance between the laser foci constant while observing the fluctuations of the molecule through its intermediate states over tens of seconds (Supplementary Fig. 2C, D). For DNA, a zoom into the data shows 5 different populated levels corresponding to the intermediates mentioned above (Fig. 2A). Assignment and coloring of the states were done using hidden-Markov-modeling (HMM)48 (see Supplementary Methods “Analysis of SMFS data”). From passive mode data, we calculated the folding free energy of the hairpin from the ratio of the population probabilities of the folded and unfolded state, correcting for energetic contributions from stretching the linkers and spring energies from the beads deflected from the trap centers (see Supplementary Methods “Extracting free energies” for details). We find a folding free energy of − 92.8 kBT (− 54.9 kcal/mol), which is in reasonable agreement with the values predicted by nucleic acid thermodynamics software packages (NUPACK49 (DNA: − 118.88 kBT (− 70.50 kcal/mol), mFold50: − 118.93 kBT (− 70.53 kcal/mol)). The deviations can be explained by systematic errors in the force calibration of the tweezers (see Supporting Information paragraph after Supplementary Table 2 for more details). The kinetics of RNA folding/refolding is significantly slower as compared to DNA (Supplementary Fig. 2D and F). This slow kinetics precludes observation of RNA unfolding at equilibrium. While equilibrium transitions can be observed between intermediates Fol, I1, I2, and I3, the construct stays permanently unfolded as soon as the fully opened state is reached (see sample trace in Supplementary Fig. 2D). Supplementary Table 2 summarizes the free energy values obtained in our experiments compared to calculations using software packages.Single-molecule observation of toehold-mediated strand displacement (TMSD)Here and in the following, we use a nomenclature for the experiments, where the first letter indicates the nature of the invaded hairpin (R: RNA, D: DNA), the second letter denotes the invader (R/D), the third letter denotes the position of a mismatch (p: proximal, c: central), and the following number gives the number of mismatches.To perform single-molecule TMSD experiments with our setup, we took advantage of the microfluidic capabilities of the optical trap. A toehold hairpin was held at a constant force low enough that the hairpin would be in the folded state but high enough to produce a measurable signal upon strand invasion. When the molecule was transferred from the buffer channel to a channel containing 100 nM of trigger strand molecules (Fig. 1B), binding of a trigger strand to the toehold hairpin and the following invasion of the hairpin stem manifested itself in a sudden drop in trapping force due to the elongation of the invaded hairpin (Fig. 2C, upper trace). For the fully complementary trigger strand sequence, the binding of the trigger strand and completion of the invasion process occur almost simultaneously, and we cannot distinguish between the two events. When we utilize a system with two trigger mismatches (RRp2), however, it is possible to observe toehold binding and invasion processes independently (Supplementary Fig. 3C), as the mismatches prolong the time between initial binding and strand invasion to about 100 ms.We obtained the time for complete invasion from an exponential fit to the relaxation phase of the force drop (see Fig. 2C, middle trace). For DNA, we find that strand invasion transitions triggered by an invader occur very fast and cooperatively within typically ≈ 10−100 μs (mean: 42 ± 5 μs, N = 20, 20 molecules, standard error of the mean (s.e.m.), blue circles in Fig. 2D). The measured transition times for DNA were very close to the response time of our instrument (gray symbols and line) given by the relaxation of the beads in water, which we measured by autocorrelation analysis51. We conclude that at the forces applied in our experiment, the whole strand invasion process covering 36 base pairs occurs within less than or equal to 42 microseconds. Given that backward invasion steps are highly unlikely under the high forward biasing forces (see Supplementary Methods “Strand displacement and mean first passage time for a 1D random walk” for more details), our results suggest an upper limit of 1.2 μs (42 μs/36) for a single step of invasion at forces of ≈ 10 pN.For RNA, the total time of the invasion process is significantly longer owed to an intermediate with a millisecond lifetime (see Fig. 2C, bottom trace, and Supplementary Fig. 4). In a buffer containing 20 mM MgCl2, we find an average total invasion time of 1.39 ± 0.08 ms, (N = 49, 6 molecules, s.e.m.) (dark green circles and triangles in Fig. 2D). Note that the green triangle symbols were not measured with the fully complementary sequence but rather with a trigger strand carrying 2 proximal mismatches (RRp2). The reason for introducing these mismatches was to allow backward invasion at low loads to increase the number of data points that could be obtained with a single molecule. The duration of the invasion event will not be largely affected since it will still have to proceed through 34 of the 36 base pairs. In the absence of MgCl2, the intermediate is still populated, albeit with shorter lifetimes, and the average total invasion time drops to 630 ± 110 μs (N = 5, 5 molecules, s.e.m., dark green squares in Fig. 2D). We find that the invasion times are largely independent of force (Fig. 2D and Supplementary Fig. 5), indicating that the intermediate state pausing the invasion process may be due to secondary structure formation in the trigger strand, which is not subject to mechanical force.Since the total invasion time in RNA is dominated by the intermediate state where branch migration is halted, we tried to estimate the timescale on which branch migration proceeds by an exponential fit to the part of the relaxation trace following the intermediate (see Fig. 2C, bottom trace). In the presence of 20 mM MgCl2, we find an average invasion time of 213 ± 17 µs (N = 49, 6 molecules, s.e.m.) (light green circles and triangles in Fig. 2D). In the absence of MgCl2, the average invasion time drops to 99 ± 14 µs, (N = 5, 5 molecules, s.e.m.) (light green squares in Fig. 2D). As done above for DNA, we calculated the time for a single step of RNA invasion of 5.9 µs at forces of ≈ 14 pN in MgCl2, and 2.8 µs at forces of ≈ 10 pN in the absence of MgCl2.Direct observation of repeated forward and backward invasion under forceFor both DNA and RNA, the hairpin stayed permanently invaded after TMSD, and even a drastic reduction of force would not lead to a reversal of the invasion. Consequently, stretch/relax cycles in the buffer channel with the trigger-bound complex (Fig. 2E) show the molecule always in the fully invaded state (FI), indicating that backward invasion does not happen at non-zero force values. The additional unfolding transition we observe at ≈ 12 pN (DNA) and ≈ 17 pN (RNA) merely reflects the unfolding of the remaining hairpin from the FI to the fully unfolded state (FU).To allow observation of repeated forward/backward invasion steps close to thermodynamic equilibrium, we sought to disfavor forward invasion over backward invasion by introducing sequence mismatches into the center of the branch migration domain of the invader strand (red base in Fig. 3A)26,52. Such a mismatch will raise the free energy of the fully invaded (FI) state over the toehold-bound (TB) state because it possesses one complementary base pair less. Application of force will now introduce an additional intermediate state at the mismatch position (IM). The force can be chosen such that the IM state and the FI state have the same free energy, and continuous forward/backward invasion between IM and FI will be observed. In comparison to a fully complementary trigger strand (Figs. 2, 3, 1st trace), using a trigger sequence with a single G → T mismatch at position 19 of branch migration domain b’ (DDc1, for sequence details, see Supplementary Fig. 1), we now observe the expected rapid forward/backward invasion equilibrium at forces around 3-4 pN (Fig. 3B, 2nd trace, forward/backward invasion marked in blue). Analysis of the involved contour length changes confirms the structural interpretation of the various states (see Supplementary Tables 3 and 4). An additional mismatch on the trigger strand introduced adjacent to position 19 (DDc2, for sequence, see Supplementary Fig. 1) shifted the force fluctuations observed from ≈ 3-4 pN to ≈ 5 pN (Fig. 3B, 3rd, trace, purple).Fig. 3: Direct observation of repeated forward/backward invasion by introducing trigger mismatches in SMFS experiments.A Conformational states during invasion of a mismatched trigger strand into a toehold hairpin: Toehold-bound (TB); invaded until the mismatch position (IM); fully invaded (FI); fully unfolded (FU). The mismatch is highlighted in red (DNA) and orange (RNA). B Force-extension traces of a DNA toehold hairpin with a fully matched DNA trigger (DD, first trace), DNA trigger strands with one or two mismatches (DDc1, second trace, and DDc2, third trace, respectively), and an RNA toehold hairpin with an RNA trigger strand with one mismatch (RRc1, fourth trace). For better visualization, each trace is horizontally shifted with a constant offset. The insets show the mismatched positions and sequence details. C Force-versus-time traces recorded at Favg,1/2 for the mismatched trigger strands DDc1, DDc2, RRc1, showing several forward/backward invasion transitions between the IM and FI states due to strand displacement. D Force dependence of forward and backward invasion transition rates between the IM and FI states. The dotted lines represent extrapolations of the data based on a model described in the SI (“Model for transition rate-extrapolation”). Data points of one sample molecule are shown. Weighted averages of the fitted parameters of all molecules are summarized in Supplementary Table 5. Source data are provided as a Source Data file.We also investigated the effect of an analogous mismatch (G → U mismatch at position 19) in an RNA trigger strand invading an RNA toehold hairpin (RRc1, for sequence, see Supplementary Fig. 1). The force at which the invasion starts is shifted to even higher values (≈ 10 pN) and the kinetics of forward/backward invasion is slowed down so that multiple forward/backward invasion events were rarely observed at the timescale of our pulling experiments (Fig. 3B, 4th trace, pulling velocity 0.2 μm/s green). For this reason, pulling and relaxation traces for RRc1 displayed a strong hysteresis because the structure remained in the FI state until the force was reduced to values as low as 3 pN. Traces for an RNA construct (RRc2) analogous to DDc2 can be found in Supplementary Fig. 5. These traces exhibit an even larger hysteresis, and pulling forces as high as 14 pN are required to induce branch migration (Supplementary Fig. 5B).For a quantitative assessment of the kinetics of this repeated branch migration process, we performed passive mode measurements with all three systems at different forces. Figure 3C shows sample traces at forces where IM and FI states were populated to 50 % (termed Favg,1/2 forces in the following). The higher forces of DDc2 vs. DDc1, as well as the significantly slower kinetics in RRc1, are readily visible. Sample traces for other forces are shown in Supplementary Fig. 7.A plot of the forward and backward invasion rates measured at different forces allows extrapolation to zero force (Fig. 3D, dashed lines). Zero force rates show that the double mismatch slows down the invasion of DDc2 by an order of magnitude as compared to DDc1 (0.053 ± 0.015 s−1 (N = 17, 1 molecule (shown in Fig. 3D middle), s.d. of the fitting parameter) vs. 1.57 ± 0.12 s−1 (N = 21, 1 molecule (shown in Fig. 3D top), s.d. of the fitting parameter)). In contrast, backward invasion rates are affected less (1500 ± 400 s−1 (N = 17, 1 molecule (shown in Fig. 3D middle), s.d. of the fitting parameter) vs. 900 ± 60 s−1 (N = 21, 1 molecule (shown in Fig. 3D top, s.d. of the fitting parameter)). The pronounced effect on invasion rates can be readily understood given the much higher barrier the invading strand has to overcome when two base pairs need to be broken before an invasion can move forward compared to only one. The slightly lower extrapolated rates for backward invasion in the case of DDc1 may reflect that backward invasion for the double mismatch has essentially one base pair less to compete with the invader strand and hence occurs faster. A summary of all measured and extrapolated rates can be found in Supplementary Table 5.The extrapolated value we find for backward invasion at zero force can provide an estimate for an upper limit of the speed of branch migration per base pair. We find backward invasion rates of ≈ 1000/s (weighted mean: 780 ± 30 s−1 (DDc1, N = 102, 9 molecules, s.e.m., see Supplementary Table 5) and 1480 ± 220 s−1 (DDc2, N = 60, 6 molecules, s.e.m., see Supplementary Tab. 5)) for branch migration across 17 (DDc1) or 16 (DDc2) bases and, hence, an upper limit of \({\tau }_{0,D}\) <= 59 μs (0.5 x (1/(780 s−1 x 17) + 1/(1480 s−1 x 16)) = 58.8 μs). Note that for calculating the upper limit and since the process occurs under a strong biasing force, we assume linear scaling with the number of bases covered (see discussion in the Supplementary Methods “Strand displacement and mean first passage time for a 1D random walk”).Comparison between DDc1 and RRc1 (Fig. 3D top vs. bottom) shows that both values for forward invasion extrapolated to zero force (1.57 ± 0.12 s−1 vs. 0.009 ± 0.003 s−1), as well as backward invasion (900 ± 60 s−1 vs. 230 ± 90 s−1) are slower for the RNA construct. The lower value we find by extrapolating the backward invasion branch directly shows that branch migration in RNA is considerably slower than in DNA. The same estimate as that used in the previous paragraph yields a value for RNA branch migration that is slower by a factor of 4.4 (\({\tau }_{0,R}\) < = 260 μs). For RRc2, conformational transitions recorded in passive mode experiments were too slow to allow an accurate estimate of the corresponding kinetic rates (Supplementary Fig. 5C).Simulation of force−extension curves and energy landscapesTo aid the interpretation of our experimental results on force-induced TMSD and help understand the impact of mismatches in the invader sequence, we studied the TMSD process using oxDNA simulations. OxDNA44,45 is a coarse-grained DNA model that represents each nucleotide as a single rigid body with interactions parameterized to reproduce structural, thermodynamic, and mechanical properties of single-stranded and double-stranded DNA. The model has been extensively employed to simulate strand displacement processes and has been shown to be in good agreement with experiments26,53,54 and has also been shown to accurately capture the mechanical response of DNA to tension55,56. We also employed the RNA version of the model, oxRNA57, to study the RNA TMSD under force.We began by creating DNA constructs composed of DNA handles, adapters, DNA hairpins, and trigger strands using the oxView tool58. We then performed molecular dynamics (MD) simulations in the absence of trigger DNA, in which we applied tension to both ends of the DNA handle and pulled on the toehold hairpin with a constant velocity of 0.14 mm/s (Fig. 4A, left). The pulling velocity is larger than the experimental one, as the experimental pulling rates are hard to achieve in MD simulations. The calculated force-extension curve showed hairpin unfolding transitions around 22 pN. This value is higher than the forces observed in experimental results (Fig. 2A), likely due to the faster pulling rate in the simulation. Snapshots of the simulated DNA molecule visualize the state of the hairpin at different forces attained during the stretching process.Fig. 4: Simulation of force-extension traces of the toehold hairpin and free-energy landscape of TMSD with mismatched sequences using oxDNA.A Averaged force-extension curve was obtained from pulling the DNA construct at a constant speed of 0.14 mm/s, comparing the toehold hairpin (red) and with a fully complementary trigger strand (violet). The simulation has 7 replicas. The curves represent the mean values, and the outline of the curves represents ± 1 s.d. Snapshots of the DNA constructs are shown to depict the intermediate states observed during the unfolding process. B The most formed base pairs of RNA trigger strands during the SD are shown on both the predicted secondary structure and 3D structure (marked in green). C, D Free-energy landscapes for different trigger strands: fully complementary (C), one distal mismatch (D). C: N = 10, D: N = 10. Data are presented as mean values ± standard deviation (s.d.). The DNA constructs’ sequences are depicted below, with the mismatches highlighted in red. The coordinates represent the specific pairing interactions between the target sequence and the trigger sequences in each state of the system. The free-energy landscapes are shown for various force conditions, distinguished by different colors. An additional adenine was added to the 3’ end of the incumbent strand, where the force is directly applied to. Source data are provided as a Source Data file.When we start the pulling simulation with a fully complementary trigger strand (DD) bound to the toehold, strand invasion by the trigger promotes the unfolding process, and invasion is finished before reaching 10 pN (Fig. 4A, right). The short unfolding transition at around 20 pN corresponds to the force-induced unfolding of the remaining stem (see overlay in Supplementary Fig. 12A for comparison between DD and without trigger).Furthermore, during the branch migration process on both our DNA and RNA model, we observed the formation of secondary structures on the trigger strand (Fig. 4B and Supplementary Fig. 12B, C). The secondary structures we found for RNA triggers were much more stable than those for DNA. We hypothesized that they could explain the slower branch migration rate and intermediate state we observed experimentally during RNA/RNA as compared to DNA/DNA strand displacement (Fig. 3D and Supplementary Figs. 3, 4, and 5).We next performed molecular dynamics simulations of the full system where we applied constant force (ranging from 2 pN to 10 pN) on the DNA hairpin (see Supplementary Methods “Simulation protocols” for more details). Simulations with different trigger strand variants demonstrated that consistent with our experiments, increasing pulling forces generally accelerated the overall kinetics of the branch migration process and biased it toward full displacement (Supplementary Fig. 12D, E, and F). For example, when a pulling force over 5 pN was applied, the single and double central mismatches (DDc1 and DDc2) could be overcome more easily than at 2 pN. These findings offer further evidence that the impact of mismatches can be fine-tuned by varying the applied pulling force.The single-nucleotide resolution of the oxDNA simulation can further provide a better qualitative understanding of the free-energy landscape of the system when subjected to an externally applied force. The free-energy sampling simulations of the full system are, however, very compute-intensive, and we hence studied a simplified system where we reduced the length of both the toehold hairpin and trigger strand. We focused on a three-stranded system with a total of only 30 bp (Fig. 4C, D), and we applied constant forces ranging from 0 to 5 pN to the strands. We obtained the free-energy landscapes from simulations as a function of the number of base pairs formed by the target strand with the trigger and the incumbent for different force biases (Fig. 4C, D) using umbrella sampling53 (see Supplementary Methods “Simulation protocols” for more details).From the free-energy landscapes, we observe that as the force increases, the states with more base pairs formed between the invader and the substrate become more favorable. A 2D free-energy landscape as a function of the number of base pairs formed between invader and substrate and incumbent and substrate, respectively, is shown in Supplementary Fig. 11A, B, and C. The larger the applied force, the more favored the states with the trigger bound to the incumbent, as seen in the 2D projections of the free-energy landscapes. We further note that the free-energy landscape (Fig. 4C) shows a small local minimum at around 8 base pairs formed with the trigger strand that coincide with longer waiting times in the MD simulations. These likely originate from a sequence-dependent effect of poly-A stacked regions in the trigger strand. The position of the minima coincides with the increased state occupancy observed in the kinetic simulation (see Supplementary Fig. 12D and E). However, these local minima in the free-energy landscape are not expected to have a measurable effect in the experiment.We further investigated the effect of mismatches on the free-energy landscape for different applied forces. We then simulated a proximal mismatch, similar to the experimentally studied mismatch shown in Supplementary Figs. 3 and 6. The mismatch between the trigger and incumbent strand creates a barrier to the displacement (Supplementary Fig. 11D), and two mismatches (Supplementary Fig. 11E) further increase the barrier (≈ 5 kBT (1 mismatch) vs. ≈ 12 kBT (2 mismatches). In the case of one proximal mismatch and 2 pN force (Supplementary Fig. 11D, red trace), the non-invaded state (T10) and “fully” invaded state (13) have almost the same free energy. In the case of the distal mismatch (Fig. 4D), we observe a barrier of ≈ 5 kBT at the position of the mismatch, which is reduced by applying increasing pulling force.Force-induced TMSD in a DNA/RNA hybridCompared to B-form DNA duplexes, double-stranded RNA and RNA-DNA hybrids adopt an A-form helix conformation59. However, double-stranded RNA is significantly more stable than RNA-DNA hybrids (Fig. 5A middle vs. right), which makes invasion into an RNA stem by a DNA invader free-energetically unfavorable60,61,62. In the absence of force (black free-energy landscape Fig. 5B), the strand invasion process of DNA replacing RNA in an RNA duplex is free-energetically unfavorable and unlikely to happen spontaneously. We surmised that in SMFS experiments, tilting the free-energy landscape by an applied pulling force would allow us to equilibrate forward and backward invasion processes and thus enable observation of strand displacement by a DNA trigger (Fig. 5B gray free-energy landscape).Fig. 5: Force-induced DNA-RNA hybrid TMSD and free-energy landscapes at Favg,½ and zero load.A Average nearest neighbor free energy per base pair for DNA, RNA, and DNA-RNA hybrid. B Schematic of force-induced DNA invading RNA process. DNA trigger invasion to RNA hairpin is unfavorable due to the free-energy difference between RNA-RNA stem and DNA-RNA strand. The free-energy landscape (black) can be tilted by force, resulting in a flat free-energy landscape (gray) with equal forward/backward invasion rates. C Force versus time trace of DNA-RNA hybrid TMSD. Each intermediate state during the branch migration process is distinguished by color. TB: toehold bound (dark blue) DR1, 2, 3: intermediates 1 (yellow), 2 (light blue), 3 (green), FI: fully invaded (brown). D Extracted free-energy profiles: almost flat landscape at 10.6 pN and uphill landscape at zero load. Source data are provided as a Source Data file.Figure 5C shows a passive mode experiment where a fully complementary DNA trigger invades the RNA hairpin (RD) at an average force Favg,1/2 = 10.6 pN. In contrast to the DD and RR constructs measured in Fig. 2, we can observe repeated forward/backward invasion transitions occurring close to equilibrium. These transitions occur via pronounced intermediates TB, RD1, RD2, RD3 and FI. Similarly, pulling/relaxation cycles show the same intermediates populated close to equilibrium (Supplementary Fig. 8). It is important to note that all intermediates occur at significantly lower forces compared to the intermediates populated during unzipping of the RNA hairpin in the absence of a trigger (compare Fig. 2B). Moreover, those intermediates also occur at different positions with the possible exception of RD1 (8 vs. 9 bp invaded). Our finding of several intermediates for the RD construct strongly indicates that sequence effects play an essential role in invasion. We computed the relative free-energy differences between each pair of intermediate states by Boltzmann inversion of the population probabilities, which confirmed that for an applied average force of 10.6 pN, all states were roughly at the same free energy (Fig. 5D, gray). Including the measured transition rates between the various states allowed us to extract also transition state energies and construct a schematic free-energy landscape assuming an Arrhenius pre-factor of 3 × 106 s−1 63 and transition state positions in the middle between the states (gray free-energy landscape in Fig. 5D). Force dependent rates and extrapolations to zero load are shown in Supplementary Fig. 8. Transformation to zero load yields the black free-energy landscape in Fig. 5D. The difference in free energy between TB and FI in the black free-energy landscape of ≈ 40 kBT is consistent with the expected free energy required to fully break an RNA duplex until position 36 with subsequent formation of an RNA/DNA hybrid (cf. Supplementary Tables 2 and 7). Under a load of Favg,1/2, all lifetimes between transitions are on the order of milliseconds; however, when reducing the load, backward invasion rates will quickly win over forward invasion rates, and the equilibrium will strongly shift towards the TB state.
