# The Free-Energy Landscape of a Mechanically Bistable DNA Origami
## 4 Discussion  
In this paper, we used the oxDNA coarse-grained model to compute the free-energy landscape of a jointed multi-block DNA origami that was designed to have two stable states. Somewhat surprisingly, the oxDNA landscape shows a single minimum corresponding to the open configuration. These results present a substantially different picture of the landscape to that inferred from experiment for which a significant population of origami in the closed state was observed. The bending of the compliant block associated with intermediate configurations, leads to a bistable landscape associated with joint 1, as intended in the origami design. However, the other three joints do not behave like completely free hinges in oxDNA and this leads to the destabilization of the closed state with the small opening angles at joint 3 and the inward bending of joint 4 being particularly unfavourable. The increase in the free energy of the hinge joints as their joint angles move away from their preferred values is due both to direct steric repulsions and the constraints increasingly placed on the configuration of the helices and linkers near the joint. We note that these effects are consistent with previous oxDNA results on jointed DNA nanostructures [22; 23] that have also found narrower distributions for the flexible components than observed in electron microscopy images; i.e., joints in oxDNA seem to be less flexible than inferred from experiment. So, what are the possible causes of the seeming disagreement between the simulations and experiment? One possibility is simply that the oxDNA model is deficient in its description of these structures. However, the behaviour of the joints must be a reflection of the structural and mechanical properties of the helices and single-stranded DNA at the joints, which are all things that oxDNA describes well. Moreover, these are not small effects; oxDNA is predicting that the closed state of the origami is 20 \(k_{B}T\) higher in energy than the open state. Another possible source is the heterogeneity in the ensemble of assembled origami in experiment. Whereas the simulations model a defect-free origami, there are likely to be a range of assembly and other defects in the experimental origami. These assembly defects probably not only include missing staples but also defects in the routing of the strands. The latter may be particularly relevant to multi-block origami, such as those studied here, which possess many scaffold links between the blocks. For example, if the blocks nucleate and assemble independently [42], then if the assembly of one block happens to lead to the topological entanglement of the external scaffold loops, such a defect is likely to be locked in. Furthermore, the assembly of further blocks might push these defects to the joints, potentially substantially changing the properties of the joint. Although there has been some quantification of missing staples [43; 44; 45], there is little information about other possible defects. Thus, it is conceivable that the population of closed configuration corresponds to origami that are locked into this structure due to assembly defects or that have more flexible joints due to missing staples. There is some evidence of this heterogeneity in the experimental results. For example, it is not clear why there was a small sub-population of U states even though such structures were designed to be at a maximum on the free-energy landscape. Again, it is possible that they might be locked in to these configurations by defects. Furthermore, that a fraction of the open configurations do not close on the addition of actuating strands that lead to binding between the frame and crank blocks, and the coupler and compliant blocks again suggests the presence of certain defects preventing the closing. One possible way to help address these issues and to quantify the heterogeneity in such ensembles of flexible origamis might be to use single-molecule techniques that can follow the large-scale dynamical motion of individual origami.