Kinetics of Toehold-Mediated DNA Strand Displacement Depend on FeII4L4 Tetrahedron Concentration

The toehold-mediated strand displacement reaction (SDR) is a powerful enzyme-free tool for molecular manipulation, DNA computing, signal amplification, etc. However, precise modulation of SDR kinetics without changing the original design remains a significant challenge. We introduce a new means of modulating SDR kinetics using an external stimulus: a water-soluble FeII4L4 tetrahedral cage. Our results show that the presence of a flexible phosphate group and a minimum toehold segment length are essential for FeII4L4 binding to DNA. SDRs mediated by toehold ends in different lengths (3–5) were investigated as a function of cage concentration. Their reaction rates all first increased and then decreased as cage concentration increased. We infer that cage binding on the toehold end slows SDR, whereas the stabilization of intermediates that contain two overhangs accelerates SDR. The tetrahedral cage thus serves as a versatile tool for modulation of SDR kinetics.

D NA nanotechnology relies on the toehold-mediated strand displacement reaction (SDR). This reaction between two DNA structures initiates at the single-stranded (sticky) end, called a toehold, where the shorter strand in the duplex exchanges with a longer complementary invader strand, requiring no enzymatic mediation. 1 After having been introduced by Yurke et al. in 2000, 2 SDR has been used to transfer information in DNA computing, 3−5 to amplify signals in catalytic biosensors, 6−8 to power the movement of DNA motors and robots, 9−11 construct reprogrammable DNA nanostructures, devices, soft materials, and systems, 12−18 and even applied in living cells. 19 The reaction rates of SDR increase exponentially with toehold length, making it an easy way to tune kinetics. 20 To provide flexible control, alternative strand displacement mechanisms, such as remote toehold 21 and allosteric toehold, 22 have been developed to regulate the reaction rate, but these methods require additional spacer domains or invader strands. The presence of these additional sequences complicates the design, and precise tuning of SDR kinetics following DNA strand design is not possible using current methods. Thus, a means to precisely adjust the kinetics of toehold mediated SDR without changing the original design, DNA sequence, and structure would be of value to the community.
Over the last decades, various metal−organic cages with different three-dimensional structures have been synthesized. 23−26 Their tunable sizes and properties have enabled these cages to be used in numerous applications including catalysis, 27 separations, 28 molecule sensing, 29 and the stabilization of reactive species. 30 Recent biomedical applications of cages have attracted attention, 31 for instance in drug delivery, 32−34 cancer therapy, 35,36 and biosensing. 37 To exploit their properties relevant to these applications, cages must interact specifically with biomacromolecules. Our previous work has shown that water-soluble tetrahedral cage Fe II 4 L 4 (cage 1 in Figure 1b) binds to nonpaired bases in DNA structures. 38 Ferrous ions occupy the four vertices of this cage, and tris(4-aminophenyl)methanol residues define the four faces of the tetrahedron. 39 Cage assembly using ferrous sulfate enables preparation in aqueous buffer solution. Since free nucleotides on toehold ends and intermediates are present during SDR, we inferred that cage 1 may bind to these domains and alter the kinetics of SDR. Studies undertaken herein provided strong support for this hypothesis, indicating that the cage can regulate the kinetics of SDR in a concentration-specific manner.
We first employed the fluorescence-quenching property of the cage, as demonstrated in previous work, 38 to study the interaction between cage 1 and different DNA structures with fluorescent labels (Figure 1a). As shown in Figure 1c, the fluorescent tag fluorescein (6-FAM) on DNA duplex D1 without free nucleotides is minimally quenched in the presence of cage 1, with a quenching efficiency (QE, Supporting Information S1.5) of only 0.19. Once free nucleotides are present to form an overhang in DNA D2, the QE increased to 0.77. This is the expected outcome because the cage binds preferentially to unpaired DNA nucleotides, as reported previously. 38 The QE for nicked DNA molecule D3 is still as high as 0.59, even though the overhang is fully hybridized with the complementary strand. This result implies that the cage bound selectively to the DNA nick. We infer that the loose base pairs and enhanced local flexibility around the DNA nick site thus provide a good site for cage binding, leading to high QE. 40 These results thus indicated that cage 1 binds selectively to unpaired nucleotides and loose base pairs.
To further understand the underlying mechanism of cage 1 binding to DNA overhangs, a series of DNA duplex molecules were prepared and treated with 1 ( Figure 2a). First, we found that the length of overhang affects the quenching. This inference is supported by the data shown in Figures 2a and S1a. By comparing DT2, DT3, and DT5, which contain two, three, and five dT nucleotides, respectively, we observed greater cage quenching of fluorescence for strands having longer overhangs. Second, overhangs containing different pentanucleotides (DT5, DC5, and DA5, Figure 2a) showed similar quenching behavior. We infer thus that cage 1 binds more strongly to thymines than to adenines and cytosines, but the differences are small. Guanine was not investigated here because of its quenching effect on FAM. 41 Third, we compared the binding of cage 1 to DNA duplex molecules with different chemical structures at the extended domain (DT2, DS3, DS6, and DS9 in Figure 2b). As shown in Figures 2a and S1b, the fluorescence intensities of DS6 and DS9 are close to those observed in the case of intact duplex D1, which indicates that the contribution of the additional carbon chain to cage binding is limited. However, the presence of the flexible phosphate group (highlighted in green in Figure 2b) in the overhang of DS3 promotes the cage-based quenching and makes it approach the magnitude observed in DT2. We infer the phosphate group to enhance binding through electrostatic interactions with the positively charged cage. Although the phosphate groups also distribute along the side chains of D1, they are immobilized in the stiff double helix structure rather than in the flexible overhang. To further verify the role of the phosphate groups in cage binding, we phosphorylated the 3′ end of the nick site in D3, next to the 5′-FAM label (D3p, Figure 2c). The additional phosphate group enhanced the cage-based quenching ( Figure S2) and improved the binding affinity ( Figure S1c). We replaced the negatively charged  phosphate group by a neutral methylphosphate group (D3m, Figure 2c) and received a similar quenching result for D3 and D3m ( Figure S1, S2) at similar K d (Figure 2d). However, the K d was a factor of 2 larger than for the D3p, which demonstrates the importance of the negative side-chain charge for cage binding. The dissociation constants for all our tested DNA structures are listed in a table in Figure 2d. We also investigated the effect of temperature on cage binding. As an example, we chose DT5 and measured cage interaction at elevated temperature of up to 70°C. The results are presented in Figure S3, where the low fluorescence intensity (FI) between 15 and 30°C indicates that cage 1 binds tightly to DNA. During the gradual increase of the temperature beyond 30°C, the FI increases gradually until leveling off at around 60°C . The main reason for the FI increase is due to the thermal instability of the cage, as we have shown elsewhere. 38 Since the essential DNA structure for toehold-mediated DNA strand displacement is a DNA duplex with an overhang (Figure 3a), that is similar to the structures of DX5 (X = T, C, A) investigated in Figure 2, we hypothesized that cage 1 might bind to the unpaired overhang segment in the same way as the binding of cage 1 to DX5 and ssDNA 38 and thus influence the course of the strand displacement reaction. We first examined a DNA duplex containing a toehold end with five nucleotides (toehold-5) to study the effect of cage 1 on the SDR. As shown in Figure 3a and 3b, fluorescence of the substrate strand F (containing the fluorescent label and toehold end) is initially suppressed by the quencher appended to complementary strand Q. Following addition of invader strand I, fluorescence should thus increase. We used a buffer with a lower concentration of Mg 2+ (5 mM) in the case of toehold-5 to capture more detailed information because strand exchange initially occurred too rapidly for this strand in 10 mM Mg 2+ buffer. As shown in Figure 3b and Table S3, in the presence of cage 1, the reaction rate slowed as the concentration of the cage increased, with all reactions having reached completion within 700 min. This result demonstrates that cage 1 influences the kinetics of SDR but it does not change the extent of reaction. In addition, if the base mismatch happened in the toehold domain, the speed of the SDR was very slow (dash lines, Figure S4). Since the cage can bind to the DNA bulge caused by base mismatch, 38 it stabilized the mismatched bases and accelerated the SDR (solid lines, Figure S4).
We next investigated the impact of cage 1 upon SDR mediated by a shorter toehold, toehold-3, containing only three nucleotides. Strand displacement is slow for toehold-3 (Figure 3c), as expected given the positive correlation between toehold length and SDR rate. However, the presence of cage 1 was observed to accelerate the rate of SDR, with a maximum rate enhancement observed with 250 nM of cage 1. This result Beyond 250 nM, cage 1 was observed to slow the rate of SDR (Figure 3e), as was observed in the case of toehold-5. As shown in Figure 3d and Table S4, the rate of toehold-3 mediated SDR, gauged by the reciprocal of half completion time, as a function of cage concentration initially rising and then falling.
To explain the concentration-dependent effect of cage 1 on the kinetics of toehold-mediated strand displacement, each step of the reaction must be considered separately. The process of toehold mediated SDR is shown schematically in Figure 4a, and its possible energy landscapes are presented in Figure S5. 42 As Ix and Q remain the same in all reactions, the only relevant difference between experiments is the number of unpaired nucleotides of the toehold on Fx. During SDR, when the cage 1 bound to Ix is removed after the hybridization of Ix and F, the released strand Q will bind to the cage at the same time. Ix has the same sequence as Q except the toehold binding domain (3−5 bases). Two FAM-labeled ssDNA differing only by three bases (FT5 and FT2, Table S1) were compared for cage binding to mimic Ix and Q. As expected, similar K d values were obtained for them and the cage showed a slightly higher affinity to the longer one ( Figure S6). Therefore, cage 1 binding to Ix is tighter than to Q, and increasing the length of Ix leads to tighter binding, which explains why toehold-5 mediated SDR is inhibited at lower concentrations of cage 1 than toehold-3. For clarity in the following discussion, we will focus on the state having cage bound to the F•Q complex as cage bound to the single-stranded Ix and Q strands is the same for all systems. Figure 4b shows our postulated mechanism for how cage 1 inhibits SDR. The toehold end in step 1 is bound to cage 1 before being invaded by strand Ix. The presence of bound cage at this key domain would increase the energy barrier for the initial binding of Ix ( Figure S5a), thus slowing the reaction.
Longer unpaired overhang sequences lead to tighter cage binding (Figure 2a). Hence, the inhibitory effect is clearer in the case of toehold-5, and a higher concentration of cage is necessary to slow the reaction in cases involving the short toehold (Figure 3e).
We ascribe the acceleration of toehold-3 mediated SDR by the cage at concentrations below 250 nM (Figure 3c) to the stabilizing effect of cage 1 on the DNA intermediates M 0 and M 2 −M 15 (Figure 4a), which are stepped through as strand displacement proceeds. As shown in Figure 4c, at the low concentration of cage 1, although the short toehold end bound to the cage loosely, the intermediate M 0 with two overhangs at the toehold domain provided more free nucleotides to enhance the binding. At the same time, the unstable structure M 0 was stabilized and the initial energy barrier of SDR was reduced ( Figure S5b). In intermediates M 2 −M 15 , two overhangs are also present. As reported by Winfree and co-workers, 42 the second overhang on the DNA intermediate from step 2 will cause destabilization of the DNA complex, increasing the energy barrier to SDR. This destabilization effect of the second  Figure S7). The absorbance at 58°C is normalized to 1.

Nano Letters
pubs.acs.org/NanoLett Letter overhang is also verified here in Figure 4e by comparing the melting temperatures (T m ) of X 0 Y 0 and X 5 Y 3 . To mimic the condition of an F•Q•Ix DNA intermediate, the same sequence was used for the X i Y j complex except the poly-T loop and overhangs of X i Y j (Table S1), where "i" and "j" define the lengths of the overhangs on strands X and Y, respectively. The two short overhangs of X 5 Y 3 decreased the melting temperature (T m ) compared to X 0 Y 0 . Furthermore, when cage 1 was added to X 5 Y 3 , the T m increased (Figure 4f), implying that cage 1 enhanced the stability of the DNA intermediate. In the SDR, the second overhang was generated in step 2 (M2, Figure 4d), which increased the instability and incurred a free energy penalty for branch migration. The newly formed unpaired nucleotide provides an ideal binding site for the cage, however, leading 1 to bind and stabilize the DNA intermediate M 2 , lowering the energy barrier to SDR ( Figure S5b). A similar energy-lowering effect would be observed for the subsequent intermediates M 3 −M 15 . Since the inhibitory effect is weak for toehold-3 at low concentrations of cage, the accelerating effect plays a dominant role in this concentration range. Further addition of cage 1 would enhance inhibition, finally slowing the reaction. Thus, the toehold-3 mediated strand displacement rate rose first and then dropped as progressively more cage 1 was added ( Figure 3d). The effect of cage 1 on the stability of dsDNA with short overhang (Y 3 +cY 0 ) was also investigated ( Figure  S8), but its T m was not substantially changed.
In principle, the two enhancement factors should also apply to toehold-5 mediated SDR, but they are counteracted by tight toehold binding, ultimately causing inhibition. However, when the concentration of cage decreased to a low enough level to weaken the initial toehold blocking, the acceleration of toehold-5 mediated SDR in low Mg 2+ buffer was also observed ( Figure S9). This result supports our mechanism for the cage concentration based kinetic modulation of SDR.
To further verify the mechanism of kinetics change upon cage binding for more toehold lengths without considering sequence-dependence, we investigated the SDRs mediated by poly-T toeholds with 3−5 T nucleotides (FT3−5, Table S1) as shown in Figures 5 and S10. The reaction rates of these three kinds of toeholds all increased with 1 concentration up to a maximum value, subsequently slowing as 1 increased further. The cage concentration at the most rapid rate for each toehold increased as the toehold length decreased, which supports the conclusion that more cage is needed to slow the shortertoehold-mediated SDR. Figure 5 summarizes the effect of cage concentration on the SDR mediated by toehold ends of different lengths, which provides guidance on modulating SDR kinetics for future applications.
In conclusion, we first studied how tetrahedral Fe II 4 L 4 cage 1 binds to unpaired nucleotides in duplex DNA. The flexible phosphate groups of single-stranded DNA provided cage binding sites. The longer the overhang, the tighter the binding of the cage to DNA, with different DNA bases affecting binding only to a limited extent. On the basis of this information, we were able to use cage 1 to modulate the kinetics of toehold-mediated DNA SDR.
The SDRs mediated by toehold ends in different lengths (3−5) were all first accelerated and then inhibited with increasing concentration of cage 1. We infer the inhibitory effect to be caused by cage binding on the toehold end, and the acceleration to be due to stabilization of the intermediates involving the binding of the second overhang to the cage. This knowledge enables fine control over the kinetics of toeholdmediated SDR, from acceleration to deceleration, governed by tetrahedral cage 1, thus providing a new means to tune SDR using an external stimulus without changing the original design.
Compared with conventional SDR, there are several unique features for cage-tuned SDR. First, the exponential length dependence of the rate of the SDR allows only for a rather coarse change as the toehold length can only be changed one base at a time. Addition of cage 1 with the correct concentration enables fine-tuning of the kinetics by adjusting the cage concentration without changing the original design. Second, the cage-based modulation is controllable with additional external parameters. Our metal−organic cage is formed through self-assembly of metal ions and organic ligands with adjustable stability. For example, the cage can be disassembled by heat or chelating agents, thus enabling control over SDR. Third, targeted modulation of one specific SDR is possible by using the cage. As shown in Figure 2, the negative charge of the DNA side chain in the toehold domain is vital for the cage binding. By making the target toehold more negatively charged or by making other toeholds neutral, we can realize targeted modulation of the desired SDR in the future. Finally, the cage may also be used to tune SDR in different nanosystems, providing an external mechanism to precise control. Given the significance of toehold-mediated DNA SDR across numerous fields, including nanotechnology, molecular computing, and biosensing, this method and other new applications of metal−organic cages to mediate DNA interactions show great promise.  Figure 5. Dependence of the reciprocal of half completion time (1/ t 1/2 ) of toehold-T3, -T4, and -T5 mediated SDRs on the cage concentration; half completion times (t 1/2 ) were obtained from the kinetic data in Figure S10.