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Using the vHelix plugin for Autodesk Maya, we designed a barrel‐like structure containing an internal block connected using ssDNA (Figure 2.5). These ssDNA segments act as an entropic spring, tensioning the internal block. The internal block, in the inactive state of the structure, also presents three dsDNA that connects its bottom to the rest of the structure, anchoring the internal block in its initial position (Figure 2.5c). The length of the ssDNA springs is designed to exert a total tension of around 17 pN on the internal block (see Materials and Methods). In the presence of a stimulus, the internal block would be disconnected from the stopping strands and the tension on it by the ssDNA springs would pull it toward the top part of the structure.

We aimed to study the feasibility of a structure of this kind using an in silico approach, in particular using the simulation software oxDNA. Because of computational restraint in modeling the dynamic changes in big molecular structures like DNA origami (composed of tens of thousands of nucleotides), we decided to simulate the structure before and after the activation, thus leaving the analysis of the activation itself for future studies. This also because although various possibility for the actuation of nanostructures have been proposed [69], the fast and reliable actuation in physiological media has not been extensively studied yet. We designed two states for the structures, representing before and after the actuation: the only difference between the two is the presence, in the inactive form, of the blocking strands.

Using oxDNA, we simulated both the structures to analyze the stability in solution and the activity of the ssDNA springs on the internal block. Both versions of the structure present a good stability in solution, without clear signs of stress apart from the designed, prestressed ssDNA. From a qualitative analysis of the structure, there is a clear difference in the behavior of the internal block between the two states. In the inactive structure, the blocking strands are successful in keeping the internal block in position, after an initial movement from the design position, due to the prestressed ssDNA strands. On the opposite, in the active structure the internal block stays away from the designed position for most of the simulation, confirming the spring action of the tensed ssDNA.

Figure 2.5 DNA origami barrel‐like structure. (a) Perspective view. (b) Front and bottom view. In the front view, the internal block can be seen. (c) Schematics for the activation of structure: the internal block is kept in position by strands interactions. After a stimulus, the strands are displaced, and the internal block is pulled up. In (a) and (b) the the dark grey strand is scaffold strand; the lighter grey strands are the staple strands.

In order to quantify the force created by the ssDNA springs, we used the force package included in oxDNA to simulate the action of a force opposite to the tension applied by the ssDNA springs (the details are explained in the Materials and Methods). In this case, the force applied goes from 0 to 20 pN, increasing linearly during the simulation. We applied this force to the active version of the structure, in order to infer if the design rules we followed were successful. The force has been applied on one of the nucleotides on the bottom of the internal block, to mimic the position of a possible conjugated protein or aptamer, that could be pulling on a bound target. From a qualitative analysis of the simulation, we can see that the internal block moves closer to the design position with the increase of the force applied.

Trying to improve on this analysis, we aimed to quantify the differences we could see in the simulation trajectories (Figure 2.6). In order to do so, we designed a Python script to analyze the simulations, following the movements of the center of mass of the internal block (Figure 2.6a) (see Materials and Methods for additional details). From this analysis, it is clear how, in the inactive structure, the internal block is stabilized by the blocking strands in a specific position that is close to the initial position (but different from the designed one) (Figure 2.6b, c). In contrast, the internal block in the active structure stabilizes to a higher position during the simulation, thanks to the spring action of ssDNA, after an initial fast equilibration phase (Figure 2.6b).

When a growing force is applied to the internal block, the trajectory is less uniform (Figure 2.5c). In the beginning, the curve resembles the curve in the active form, but once the force starts increasing, the internal block comes closer and closer to the equilibrium position in the inactive version. Interestingly, it appears that during the simulation with the forces, the internal block starts arriving at the inactive level around 10 pN, stabilizing at that level after 14 pN, which is a force smaller than the one we were trying to achieve. This is probably because the approximation used during the design only took into consideration the ssDNA springs and completely ignored the loss of energy that can happen in the strands of the internal block.

Figure 2.6 Quantification of the movement of the internal block during the simulation. (a) The movement of the internal block from the starting position (dashed lines) in every recorded step of the simulation (solid lines) is calculated following the movement of the center of mass of the internal block (dot). (b and c) Graph of the movement of the internal block from the position at the beginning of the simulation vs the simulation points and the force applied. In light grey is the movement of the constrained structure, in dark grey the movement of the unconstrained structure (b) Movement of the internal block when no force is applied. (c) Movement of the internal block when a growing force is applied.