## 2 DNA-DNA Interactions: Strand Displacement, Base Stacking and Transient Binding  
Here, dynamic DNA origami systems based on DNA-DNA interactions are introduced. This section covers devices whose movements rely on base-pairing (strand-displacement) systems that exhibit dynamic behavior based on DNA base-stacking interactions and tight-fitting DNA components. As early as 2009, [PERSON] et al. [15] fabricated a hollow DNA origami \"cuboid\" from six 2D origami sheets. The 3D box contained a controllable lid functionalized with a \"lock-key system\" comprised of dsDNA with sticky-end extensions. Fluorescent dyes, Cy3 and Cy5, embedded in the opposite faces of the box, facilitated the detection of irreversible lid-opening through a strand-displacement reaction using Forster resonance energy transfer (FRET). Three years later, [PERSON] et al. [60] demonstrated reversible opening and closing of a lid in a hollow 3D DNA origami box as a response to supplied opening and closing ssDNA keys. In 2017, [PERSON] et al. [61] constructed a DNA nanovault with a similar reversible opening/closing mechanism (Figure 1a). They were able to encapsulate a single enzyme inside the vault and demonstrate that closing the nanovault resulted in a notable reduction in enzyme activity. Another type of a dynamic DNA origami device was introduced by [PERSON] et al. [62], who created a DNA origami comprised of a \"rotor\" and a \"base\" component, connected with a short scaffold segment. They demonstrated a step-wise rotation of a rotor on top of the base through sequential strand-displacement reactions. Recently, [PERSON] et al. [63] applied a toehold-mediated strand-displacement-based lock-key system in a dynamic DNA origami beacon designed for high-sensitivity biosensing. By functionalizing the device with high numbers of fluorophores interacting via FRET in a closed-state device, they could demonstrate that opening the devices with target DNA keys caused a detectable decrease in FRET efficiency, even at DNA concentrations as low as 100 pM. To build dynamic devices, it is essential to understand the mechanical behavior of DNA origami and their responses under external physical forces. Numerous studies exploited these aspects of DNA nanostructures [64]; for example, [PERSON] et al. [65] designed and characterized a tunable DNA origami structure with a compliant part able to bend into different angles under the tension caused by ssDNA with various lengths. Later, they also studied a four-bar bistable mechanical system with a designed energy landscape, and showed that the conformational dynamics of the device could be controlled via strand displacement [66]. In 2015, [PERSON] et al. [67] demonstrated mechanical designs of DNA origami inspired by macroscopic devices, including a hinge (rotational motion), a slider joint (translational motion), and a complex crank-slider mechanism integrated from the former two (see Figure 1b). In addition, a Bennett linkage which could be actuated via strand displacement was also characterized. As another class of DNA-DNA interaction, a number of non-autonomous, autonomous, and directed DNA walkers were introduced and analyzed both experimentally and theoretically [58; 59; 68]. By taking advantage of the DNA origami addressability and programmability, the environment where the walker or robot is moving can be defined and precisely tuned. One example of such a system was presented by [PERSON] et al. [69], where \"molecular spiders\" made of a streptavidin body equipped with three catalytic deoxyribozyme legs were set to autonomously move along the predefined path on top of a DNA origami template. A very recent and sophisticated example of DNA-assembled robotics on a DNA origami platform was created by [PERSON] et al. [42]. They developed an algorithm for sorting two types of cargo and their destinations on a DNA origami platform (Figure 1c). The DNA robot constructed from three functional domains was able to pick up the cargo and release it at the desired location.