Conclusion and Future Directions

II. Design and Implementation of Stacking Bonds

II.3. Conclusion and Future Directions

Our goal was to develop new systems in which we could create large sets of orthogonal and isoenergetic bonds. Starting from relatively large sequence spaces, we achieved the creation of relatively small sets of bonds: the flexibility of DNA helices forced us to pick bond types that were both simple and rigid, and thus less numerous. Can one do better? To solve this problem in the

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binary code system, inactive patches could be implemented by more rigid non-stacking “steric blockers” (which would prevent neighboring active patches from bending) or replaced by “weakly active patches” (with ‘AT’ on their blunt ends). Stacking polarity has revealed itself to be a strong symmetry breaker. This suggests that inactive patches could also be replaced by active patches with an opposite stacking polarity, creating a stacking polarity-based binary code. For both binary and shape coding systems, the flexibility of active patches could be directly addressed by increasing the density of crossovers near the edge, or using multi-layer 3D origami^16,68, rather than single-layer origami (for such different architectures, strand polarity might have to be redefined). Hybrid codes⁵⁹,which simultaneously use binary coding and shape coding, offer another possible route to greater bond diversity without directly addressing flexibility. Above all, it will be important to have better energy models so we can maximize the difference between correct and incorrect bonds.

More immediately, stacking bonds offer a couple of practical advantages over DNA hybridization for the hierarchical assembly of origami into larger, more complex structures. When origami are joined by DNA strands such as “sticky-ends”, each new origami-origami interaction requires the design and synthesis of unique sequences. Our binary-coding approach allows bond type to be reprogrammed easily and cheaply, post-synthesis, merely by pipetting a different subset of the edge staples. Further, neither of our approaches requires the purification usually needed for sticky-end-based approaches: the binary coding approach requires quenchers, but the shape coding approach allows the direct coupling of origami without additional steps. One disadvantage of stacking bonds is that the total binding energy is limited by the size of the origami: a greater range of binding energies might be achieved in a sticky-end-based approach by changing sticky-end lengths.

So far, we have concentrated on replicating the combinatorial nature of DNA hybridization, and ignored its other useful properties. In particular we have ignored strand displacement^30,31, the dynamic mechanism by which a partially-complementary duplex and a third, free strand of DNA can rearrange (without initial dissociation of the duplex) to form a duplex with greater complementarity, thus freeing one of the two originally duplexed strands (Figure II-18a). This mechanism is the foundation for a large number of DNA nanomachines and circuits, both providing a fuel source to drive non-equilibrium reactions and enabling the order in which reactions occur to be programmed. An analogous displacement mechanism for stacking bonds might allow programming of large-scale rearrangements of origami, in the context of much larger DNA nanomachines (Figure II-18b).

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Figure II-18. Dynamic displacement mechanisms. (a) For DNA strands, a strand with a longer binding region (red) can displace a strand with a shorter binding region (indicated by a blue arrow, where partial self- binding occurs within the black strand). Figure adapted from ref. 1. (b) For origami nanostructures connected by stacking bonds, a similar displacement mechanism could be achieved based on competition between a structure with a longer binding region (orange) and an initial bond with a shorter binding region (indicated by a blue arrow), which might allow programming of large-scale rearrangements of DNA nanostructures.

Looking ahead, we believe that stacking bonds will offer important new mechanisms for force-induced bond rearrangement that are difficult or impossible to implement with DNA hybridization. In order for DNA structures linked by DNA hybridization to rearrange, DNA helices must unwind and then rewind; this could involve a high activation energy, depending on the number and strength of the links involved. Stacking bonds, on the other hand, may exhibit low activation energies for sliding under shear forces. If so, we hope to use stacking bonds between mechanical parts that must both self-assemble initially, and then slide past each other (while maintaining contact) under the shear forces applied by molecular motors—many biological nanomachines meet this challenge^36,74 and such a capability is fundamental if we are to build truly complex nanomachines.

Finally, we return to the question, “What causes two complementary DNA strands to bind?”

One answer is that base stacking is the dominant stabilizing force and the specificity derives from base pairing. But base pairing has a couple of components: in addition to the interaction between hydrogen bond donors and acceptors, there is the geometric complementarity of the base pairs.

These factors are difficult to disentangle since, without geometric fit, hydrogen bonds could not form. However, in certain contexts it appears that geometry alone underlies specificity:

geometrically complementary base analogs can be incorporated into DNA by a polymerase in the +

+

a b

d c

Supplementary Figure S61:Opening of scaffold secondary structure by strand displacement.aFive bases of undesired secondary structure in the scaffold occur in the middle of the binding site for the red staple.bThe red staple strand can still bind by 10 bases adjacent to the hairpin stem and gain a ‘toehold’.cA random walk at the junction between the staple and hairpin allows the staple strand to gain three more basepairs.dEventually the random walk results in the hairpin opening, which allows the rest of the staple to bind.

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(a) (b)

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absence of hydrogen bonding⁷⁵. Hence perhaps the role of base pairing is mostly to provide a geometric framework—aligning the two bases in a plane—that encourages and allows stacking if and only if the bases are complementary, and the molecular recognition of DNA hybridization may be thought of as mostly “stacking interactions given specificity by geometric complementarity”.

Here we have used DNA origami as a geometric framework to align complementary sequences of blunt-end stacking interactions. Thus, in a sense, DNA hybridization and our systems work on a very similar principle—the geometric relationships between stacking interactions in our systems just operate at a ten-times larger scale.