the calculated force. We showed that oxDNA, in combination with vHelix, is a powerful and versatile tool that can be used for in silico screening of DNA nanostructure with different mechanical attributes and to test these design, like already demonstrated by studies on rigidity refinement of DNA nanostructures [57, 58].
2.6.1 Materials and Methods
The wireframe meshes for the structure were designed in Autodesk Maya, then exported in STL format and converted to PLY format using the software Meshlab. If necessary, unwanted edges and vertices can be manually deleted from the PLY file before the next steps. The software package BSCOR (available at www.vhelix.net) was used to automatically find the scaffold routing through the mesh and construct a DNA nanostructure. The resulting RPOLY file has been loaded in vHelix (available at www.vhelix.net), a plugin for Autodesk Maya that allows the user to manipulate DNA structures in 3D.
To obtain the ssDNA segments, the staple strands have been manually deleted by the structure, leaving only the scaffold. The length of the ssDNA segments has been adjusted by removing four bases in each segment to allow for the right tension and the length of the spring.
The length of the ssDNA springs has been designed modeling the ssDNA using a modified FJC (mFJC) model for polymers [68, 70]. Given the force that we wanted to achieve, using the model we set a length of 69 nucleotides for the ssDNA segments. Using this mFJC model, one can express the force F on each end of a long (R >> l k) polymer as:
where R is the average end‐to‐end distance (in this structure, around 36 nm), N k is the number of Kuhn segments (in this structure, 69 nucleotides), and l k is twice the persistence length (1.5 nm).Knowing the force F we wanted to apply (around at least 12 pN in total on the internal block), it is possible to calculate the length and the number of nucleotide necessary to achieve it. Considering the dimensions of the structure, we designed each of the six ssDNA spring to have a tension of around 2.8 pN, for a total tension of around 17.2 pN on the internal block.
The vHelix designs were save in the Maya ASCII format and converted to the oxDNA format using the web platform tacoxDNA [71]. Since these files could contain nonphysical geometry, which could potentially lead to extreme artificial forces on the backbone and the failure of the simulation, we first perform two minimization and relaxation steps. After these steps, the structures were simulated for 108 time‐steps, which roughly corresponds to 1.5 μs of simulation time. Snapshots of simulation trajectories were saved every 20 000 time‐steps, resulting in 5000 data points per simulation.
The simulations were performed using the oxDNA2 model, with an Anderson‐like thermostat at 30 °C and a salt concentration of 0.15 M, similar to physiological buffers like PBS. All the structures have been simulated “blocked” in place by five harmonic traps of high stiffness placed on five nucleotides on the bottom of the structures. This was to avoid the rotation and diffusion of the structure during the simulation and to simulate the possible attachment to a biological membrane.
On one of the activated structures, a force has been applied on one of the nucleotides on the bottom of the internal block. This force grows linearly with time, going from zero to around 20 pN, with a rate of 20 pN every 108 time‐steps, and is directed vertically toward the bottom of the structure.
The simulations have been visualized using the software VMD. The analysis of the trajectory has been carried out using a custom Python script (Figure 2.6a). In each structure, the nucleotide numbers of the helices to examine (the ones forming the internal block) are used as the input for the script. This step is facilitated by the use of the web tool oxView [72]. The coordinates of the nucleotides are used to define the center of mass of the internal block, averaging the coordinates of the nucleotides on the entire simulation. The coordinates of the center of mass during the simulation are then subtracted from the coordinates of the center of mass at the beginning of the simulation, and this distance is then plotted.
References
1 1 Rothemund, P.W.K. (2006). Folding DNA to create nanoscale shapes and patterns. Nature 440 (7082): 297–302.
2 2 Douglas, S.M., Dietz, H., Liedl, T. et al. (2009). Self‐assembly of DNA into nanoscale three‐dimensional shapes. Nature 459 (7245): 414–418.
3 3 Wagenbauer, K.F., Sigl, C., and Dietz, H. (2017). Gigadalton‐scale shape‐programmable DNA assemblies. Nature 552 (7683): 78–83.
4 4 Douglas, S.M., Marblestone, A.H., Teerapittayanon, S. et al. (2009). Rapid prototyping of 3D DNA‐origami shapes with caDNAno. Nucleic Acids Research 37 (15): 5001–5006.
5 5 Ke, Y., Douglas, S.M., Liu, M. et al. (2009). Multilayer DNA origami packed on a square lattice. Journal of the American Chemical Society 131 (43): 15903–15908.
6 6 Ke, Y., Voigt, N.V., Gothelf, K.V., and Shih, W.M. (2012). Multilayer DNA origami packed on hexagonal and hybrid lattices. Journal of the American Chemical Society 134 (3): 1770–1774.
7 7 Dietz, H., Douglas, S.M., and Shih, W.M. (2009). Folding DNA into twisted and curved nanoscale shapes. Science 325 (5941): 725–730.
8 8 Han, D., Pal, S., Nangreave, J. et al. (2011). DNA origami with complex curvatures in three‐dimensional space. Science 332 (6027): 342–346.
9 9 Schnitzbauer, J., Strauss, M.T., Schlichthaerle, T. et al. (2017). Super‐resolution microscopy with DNA‐PAINT. Nature Protocols 12 (6): 1198–1228.
10 10 Douglas, S.M., Bachelet, I., and Church, G.M. (2012). A logic‐gated nanorobot for targeted transport of molecular payloads. Science 335 (6070): 831–834.
11 11 Shaw, A., Lundin, V., Petrova, E. et al. (2014). Spatial control of membrane receptor function using ligand nanocalipers. Nature Methods 11 (8): 841–846.
12 12 Kuzyk, A., Schreiber, R., Fan, Z. et al. (2012). DNA‐based self‐assembly of chiral plasmonic nanostructures with tailored optical response. Nature 483 (7389): 311–314.
13 13 Gopinath, A., Miyazono, E., Faraon, A., and Rothemund, P.W.K. (2016). Engineering and mapping nanocavity emission via precision placement of DNA origami. Nature 535 (7612): 401–405.
14 14 Bathe, M. and Rothemund, P.W.K. (2017). DNA nanotechnology: a foundation for programmable nanoscale materials. MRS Bulletin 42 (12): 882–888.
15 15 Xiong, Y., Yang, S., Tian, Y. et al. (2020). Three‐dimensional patterning of nanoparticles by molecular stamping. ACS Nano 14 (6): 6823–6833.
16 16 Helmi, S., Ziegler, C., Kauert, D.J., and Seidel, R. (2014). Shape‐controlled synthesis of gold nanostructures using DNA origami molds. Nano Letters 14 (11): 6693–6698.
17 17 Castro, C.E., Kilchherr, F., Kim, D.‐N. et al. (2011). A primer to scaffolded DNA origami. Nature Methods 8 (3): 221–229.
18 18 Šulc, P., Romano, F., Ouldridge, T.E. et al. (2012). Sequence‐dependent thermodynamics of a coarse‐grained DNA model. The Journal of Chemical Physics 137 (13): 135101.
19 19 Snodin, B.E.K., Randisi, F., Mosayebi, M. et al. (2015). Introducing improved structural properties and salt dependence into a coarse‐grained model of DNA. The Journal of Chemical Physics 142 (23): 234901.
20 20 Snodin, B.E.K., Schreck, J.S., Romano, F. et al. (2019). Coarse‐grained modelling of the structural properties of DNA origami. Nucleic Acids Research 47 (3): 1585–1597.
21 21 Maffeo, C. and Aksimentiev, A. (2020). MrDNA: a multi‐resolution model for predicting the structure and dynamics of DNA systems. Nucleic Acids Research 48 (9): 5135–5146.
22 22 Anastassacos, F.M., Zhao, Z., Zeng, Y., and Shih, W.M. (2020). Glutaraldehyde cross‐linking of oligolysines coating DNA origami greatly reduces susceptibility to nuclease degradation. Journal of the American Chemical Society 142 (7): 3311–3315.
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