The DNA construct contains three parts: a 699-bp double strand DNA handle with biotin modification, a single strand telomeric DNA sequence 5’-GGG(TTAGGG)₇ (wtTel45) and a 2271-bp double strand DNA handle with digoxigenin modification. The contour length of the DNA construct is ∼ 1 μm. Two handles were prepared by PCR amplification of PBR322 with primers. The PCR products were purified by a QIAquick PCR Purification Kit (QIAGEN, Germany), and then digested by XbaI and KpnI (Ipswich, MA) respectively. The digested products were further purified using the QIAquick PCR Purification Kit, and the concentrations of handle products were determined with a UV spectrophotometer. To ligate single strand DNAs with handles, the ssDNA that can form one or two telomeric G-quadruplexes (blue) was annealed with flank 1 and flank 2 in 1:1:1 ratio by slowly cooling down from 95 °C to 25 °C, then ligated with two dsDNA handles in 1:1:1 ratio by T4 ligase at 16 °C overnight. Finally, Agarose gels were performed to check the final product, and the DNA constructs were stored at −20 °C.

Our single molecule manipulation experiments were performed by magnetic tweezers. As shown in Fig. 1(a), the two ends of the DNA construct are tethered via digoxigenin and anti-digoxigenin ligation to a glass coverslip and via biotin-streptavidin ligation to a 1-μm diameter Dynabeads (Invitrogen Norway). Two small NdFeB magnets on the DNA constructs are controlled to pull on the Dynabeads and thus stretch the DNA molecule. The real time position of the bead is monitored by a JAI Giga-Ethernet CCD camera at 60 Hz through an inverted microscope objective (Olympus 100 × 1.2, oil immersion). The extension (end to end distance) of the DNA construct is determined at nanometer resolution by analyzing the diffraction pattern of Dynabeads.^[25] The 1-μm diameter polystyrene reference beads are stuck on the coverslip using nitrocellulose and tracked simultaneously to eliminate the shift of the device. To ensure that only one DNA construct was tethered to a bead, we rotated magnet pairs for ∼ 50 turns at ∼ 5 pN and checked whether the bead is rotation-constrained, namely, more than one DNA being tethered to the bead. Our magnetic tweezers were controlled by a home-built LabVIEW program. In the force ramp experiment, magnet pairs were moved at nonlinear step size to keep a constant loading rate. The step size can be calculated according to the force-magnet position relationship fitted with exponential function.^[26,27] (see Appendix A “Force calibration”)

Fig. 1.

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	Fig. 1. (color online) (a) Schematic setup of magnetic tweezers (not to scale). The 45 nt wtTel45 sequence is tethered between a coverslip and a superparamagnetic bead with two 699 bp and 2271 bp dsDNA handles. (b) Typical trajectory with two distinct ruptures indicate two stable G-quadruplexes formed in wtTel45 sequence.

To bound the reference beads, the inner surface of coverslips was coated with ∼ 0.2% w/v nitrocellulose (Sigma-Aldrich) and 0.03% w/v polystyrene beads (ACMEmicrospheres) in alcohol and then heated at 150 °C for 5 min,^[28] allowing the nitrocellulose solvent to evaporate and the polystyrene beads to melt onto the surface as reference beads. Afterwards, 10-mg/ml anti-digoxigenin was used to modify the surface overnight at 37 °C and then dealt with passivation buffer (10-mg/ml BSA, 1-mM EDTA, 10-mM pH 7.4 phosphate buffers, 10 mg/ml Pluronic F127 surfactant (Sigma-Aldrich), 3-mM NaN₃) at room temperature for 4 h to avoid non-specific ligation between magnetic beads and the surface. In our experiments, the DNA constructs were diluted to 40 pM and blended with 10 × diluted Dynabeads MyOne in 1:1 volume ratio for 30 min. The DNA-bead mixture was injected into the flow cell and incubated for 30 min, then rinsing away the unconnected beads with TE buffer.

As shown in Fig. 1(a), the wildtype human telomeric G-quadruplex sequence (wtTel45) 5’-GGG(TTAGGG)₇ with a lower 699-bp dsDNA handle and an upper 2271-bp dsDNA handle is tethered specifically between an antidigoxigenin coated coverslip and a streptavidin-coated paramagnetic bead (MyOne Invitrogen). Force exerted on the paramagnetic bead is tuned by adjusting the magnets vertically and the extension is traced at a nanometer resolution based on the diffraction image of the bead.^[25] To demonstrate that our sample can form two contiguous G-quadruplexes, force jump experiments were performed. Figure 1(b) shows the force-jump experiments between 0.1 pN and 7 pN and two extension steps around 9 nm reveal two G-quadruplex ruptures at the high tension. According to other single molecule experiments on double strand DNA (dsDNA), conformation change cannot occur when the force is less than 60 pN.^[29–34] Repeated measurements and similar results reveal that two stable G-quadruplexes are formed in the wtTel45 sequence, which is consistent with the results previously reported by AFM and NMR.^[35,36]

To further quantify the two G-quadruplex ruptures formed in wtTel45 sequence, we perform the force-ramp experiments from 0.7 pN to 8.3 pN at the loading rate r = 0.16 pN/s. As shown in Fig. 2(a), two sequential extension jumps in each trajectory correspond to the unfolding of two G-quadruplexes, which is consistent with the result of previous force-jump experiment (Fig. 1(b)). For clarity, the trajectories are shifted in extension. The first rupture event, which happens with co-existence of the other G-quadruplex, is a key target for the investigation of the interaction between the G-quadruplexes. We repeat the force-ramp measurement and derive the unfolding force distribution p for the first G-quadruplex rupture as shown in the upper panel of Fig. 2(b).

Fig. 2.

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Fig. 2. (color online) Force ramp experiments of dimeric G-quadruplexes and mono G-quadruplex. (a) Typical force responses of dual G-quadruplexes in a stretching cycle (upper panel) with a loading rate of 16 pN/s (lower panel). (b) Unfolding force distribution of the first G-quadruplex in the dimeric G-quadruplexes fitted with Evans model (upper panel, N = 200) and monomeric G-quadruplex (lower panel, N = 198).

To compare the tension response of G-quadruplex in the presence and in the absence of another G-quadruplex, the same force-ramp measurements are performed on the monomeric G-quadruplex formed in wtTel21 sequence 5’-GGG(TTAGGG)₃ (see Appendix A in Fig. S3). The corresponding unfolding force distribution p of monomeric G-quadruplex is shown in the lower panel in Fig. 2(b). Compared with the monomeric G-quadruplex, the first ruptured G-quadruplex in the wtTel45 sequence prefers to unfold at lower forces. The experiment shows that the mechanical stability of G-quadruplex is attenuated by the existence of another G-quadruplex, which suggests the existence of interaction between G-quadruplexes. Our results agree well with the reported results that dimeric G-quadruplexes melt before monomeric G-quadruplex in previous CD thermal analysis.^[22,37]

In our force-ramp measurement, the force distribution in the force spectroscopy measurements of single molecules can be described by Evans’ model^[38] as follows: 1 where r is the loading rate, F is the external tension, k_B is the Boltzmann constant, and T is the absolute temperature. The corresponding to the unfolding rate at F = 0 pN and Δx_u corresponding to the distance between the folded state and the reaction energy barrier in the reaction coordinate, are treated as the fitting parameters. The best fitting parameters of the first unfolding G-quadruplex are s⁻¹, Δx_u = 2.1 ± 0.7 nm (mean ± SD), and the best fitting parameters of monomeric G-quadruplex are s⁻¹, Δx_u1 = 2.5 ± 0.8 nm. The first G-quadruplex in the wtTel45 sequence presents higher unfolding rate (at F = 0 pN) and lower unfolding force (Fig. 2(b)) than the monomeric G-quadruplex, which also indicates that the G-quadruplex in the wtTel45 sequence is less stable in the presence of another G-quadruplex due to the interaction between the G-quadruplexes. It should be noted that the reaction distance Δx determined in the force ramp experiment is a little larger than results in Refs. [39] and [40]. A possible explanation is that Bell’s model is no longer valid at low transition forces at such a slow loading rate, because it ignores the entropic elastic contribution in transition kinetics that is often significant at low forces.^[41]

To reveal the interaction between the two G-quadruplexes and to understand the consequence effect on the G-quadruplex, the force clamp measurement is performed by tracing the folding and unfolding kinetics of the dimeric G-quadruplexes at different forces. As shown in Fig. 3(a), the length of the samples are traced from 1.7 pN to 8 pN. At each tension, the measurement is sustained for fifteen min, which provides an adequate time to reveal the folding and unfolding kinetics of the G-quadruplex at a given tension. Two different unfolding processes are distinguished (the green and yellow regions for the first and second unfolding process respectively in Fig. 3(a)), which correspond to the sequential ruptures of the two formed G-quadruplexes in the wtTel45 sequence. The folding and unfolding transition of G-quadruplex are controlled by the external tension that tilts the equilibrium of G-quadruplex from folded state to unfolded state.

Fig. 3.

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Fig. 3. (color online) Folding and unfolding kinetics of two G-quadruplexes in wtTel45 sequence. (a) Trajectory (upper panel) under different constant forces (lower panel) showing two ruptures of G-quadruplex. (b) Relationships between reaction rate ku, kf, and tension F. The equilibrium tension Feq can be read from the point where ku = kf. The error bars reflect a ∼ 10% error in force determination. (c) Different folding and unfolding kinetics of two G-quadruplex near Feq. For the first G-quadruplex, τ0 = 20.5 s (left panel) and for the second G-quadruplex, τ0 = 4.0 s (right panel).

The reversible hopping behavior provides a framework for unraveling the different kinetics of two G-quadruplexes formed in the wtTel45 sequence. At a constant tension near the unfolding tension, G-quadruplex hops between folded and unfolded state. The unfolding rate k_u from folded to unfolded state can be described as an Arrhenius-like expression^[31,32] 2 where F is the external tension, k_B is the Boltzmann constant, and T is the absolute temperature. A similar relationship for the folding rate k_f can be calculated accordingly. The unfolded rate k_u increases and the folded rate k_f decreases with the increase of tension as shown in Fig. 3(b). At the equilibrium force F_eq, G-quadruplex hops between the folded and unfolded states with the same rate k_u = k_f and the average dwelling time τ₀ of the folded state is equal to that of the unfolded state. In Fig. 3(b), the equilibrium force F_eq can be read from the point where the folded rate k_f (red line) equals the unfolded rate k_u (blue line). Near F_eq, the folding and unfolding kinetics of the first and second G-quadruplexes are shown in Fig. 3(c), corresponding to the region marked with a black rectangle in Fig. 3(a). The values of average dwelling time τ₀ are 20.5 s and 4.0 s for the first and second G-quadruplex, respectively (Fig. 3(c)). The average dwelling time of the first G-quadruplex, much larger than that of the second G-quadruplex at F_eq, indicates the slower folding and unfolding kinetics at the equilibrium tension in the presence of another G-quadruplex. We perform the same measurement for the monomeric G-quadruplex, and the average dwelling time τ₀ = 2.7 s at F_eq is revealed, which is similar to that of the second G-quadruplex in the wtTel45 sequence (see Appendix A, Fig. S4 online). Unlike the monomeric G-quadruplex and the second unfolding G-quadruplex, the first unfolding G-quadruplex shows slower folding and unfolding kinetics, suggesting the existence of the interaction between G-quadruplexes.

By analyzing the different kinetics of the two G-quadruplexes formed in the wtTel45 sequence, we derive the free energy ΔG₀, an important quantity describing the stability of G-quadruplex. The relationship between the equilibrium rate constant k_eq = k_u/k_f and external tension F can be described as 3 where is the equilibrium rate constant at F = 0 pN, ΔG(F) = FΔx + Δ Φ (F) is the free energy cost for unfolding the G-quadruplex, and accounts for the force-dependent entropic free energy change.^[18] To calculate Δ Φ (F) the ssDNA force-extension curve x_ssDNA(F) can be described by a phenomenological model^[42] as follows: 4 where the empirical parameters h = 0.34 nm, a₁ = 0.21, a₂ = 0.34, f₁ = 0.0037 pN, f₂ = 2.9 pN, and f₃ = 8000 pN. The salt dependent parameter a₃ = 2.1 ln ([K⁺]/0.0025)/ln(0.15/0.0025), where [K⁺] is the salt concentration. The project length along the force direction of folded G-quadruplex is given by where l ∼ 1.7 nm.^[18] At F_eq such that k_eq = k_u/k_f = 1, we can derive free energy difference ΔG₀ by calculating the value of Δ Φ(F_eq). From the equation above, the values of free energy ΔG₀ for the first and second G-quadruplex in the wtTel45 sequence are obtained to be 2.9 k_BT and 5.0 k_BT respectively. For the monomeric G-quadruplex, the free energy ΔG₀ is 3.6 k_BT. The lower free energy of the first G-quadruplex reveals that the interaction between G-quadruplexes weakens the stability of G-quadruplex.

In the wtTel45 sequence, the two G-quadruplexes are connected via a TTA linker, which is suggested to play an important role in the interaction between two contiguous G-quadruplexes.^[22] We construct the mutant Tel45 sequence by replacing the TTA linker with an AAA linker and perform the measurements as shown in Fig. 4. In a representative trajectory, two sequential reversible unfolding processes are observed, corresponding to the two G-quadruplexes formed in (Fig. 4(a)). By plotting the folding and unfolding rate constant versus force, we obtain the equilibrium forces 1.6 pN and 4.1 pN for the first and second unfolding G-quadruplex in the mutant Tel45 sequence respectively (Fig. 4(b)). Compared with G-quadruplexes formed in the wtTel45 sequence, the two G-quadruplexes in the mutant Tel45 sequence show a relatively small equilibrium force, implying two less stable G-quadruplexes in the mutant Tel45 sequence. Near F_eq, the two G-quadruplexes hop between folded and unfolded state with a similar rate. The values of average dwelling time τ for the first and second G-quadruplex are 4.2 s and 3.6 s respectively (Fig. 4(c)), which are similar to that of the monomeric G-quadruplex, indicating similar folding and unfolding kinetics of the G-quadruplex in the mutant Tel45 sequence to those of the monomeric G-quadruplex. Our results demonstrate that the TTA linker plays a crucial role in the interaction between G-quadruplexes, which is consistent with previous simulation.^[22]

Fig. 4.

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Fig. 4. (color online) Folding and unfolding kinetics of two G-quadruplexes in mutant Tel45 sequence. (a) Trajectories (upper panel) under different constant tensions (lower panel) show two ruptures of G-quadruplex. (b) Relationships between rate constant ku, kf, and tension F. (c) Near Feq, similar folding and unfolding kinetics of G-quadruplex. For the first G-quadruplex, τ0 = 4.2 s (left panel), and for the second G-quadruplex, τ0 = 3.6 s (right panel).