routing

I conducted routing of the scaffold strand in the wireframe structure under the following conditions:
・The scaffold strand passes through every edge.
・The scaffold strand passes through each edge only once.
・Ensure that the DNA strands connecting the edges of the mesh do not cross.
・In cases where the above conditions cannot be met, if necessary, the scaffold strand passes through one edge twice. A double-pass edge is referred to as a 'double edge.'
For routing, I utilized software employed in previous research [1].
https://github.com/mohamma1/bscor

Fig.1 The path of scaffold strands in the rhombic dodecahedron wireframe structure guided by routing

This figure was generated using the 4vHelix software, as mentioned later, rather than the previously mentioned bscor software. The white lines indicate the path of the scaffold strands.

Strengthening the Edges

The edges of the wireframe structure, which is formed by adding staple strands to the routed structure, are composed of one or two DNA double helices. In this state, it is conceivable that the edges may deform during structural transformations, preventing the desired deformation as per the design. Therefore, to make the wireframe structure more robust and able to withstand deformations, each edge was transformed into a 4 Helix Bundle. The edge reinforcement was carried out through the following steps:
Step 1. Adding a loop of the scaffold strand to all edges (adding the second and third helices).
Step 2. Adding short scaffold strands (miniscaffold) to the edges other than double edges (adding the fourth helix). Miniscaffold is not required for double edges, as they already have two passes of the scaffold strand. Edge reinforcement was accomplished using the software developed by the authors of Reference 2.
https://github.com/marlol4/4vHelix

Closing corners using strand displacement

To close the corners, the fastening-DNA extending from the edges must grow towards the neighboring edges. We verified the phase of DNA double helices on caDNAno and designed the fastening-DNA to extend from the appropriate positions. Multiple strands of fastening-DNA extend from a single edge. The sequence of fastening-DNA was determined to ensure that binding does not occur among the fastening-DNA extending from the same edge.

The number of base pairs required for the mobility of edges

The required length 'l' of the hinge necessary to close the corners of the structure was determined using the following equation.

Assuming a distance 'Δh' of 3 nm between the double helices and aiming to close the angle 'θ' up to 30°, we find that 'l' equals 2.8977... nm. The hinge is designed as single-stranded DNA (ssDNA). Considering a length of 0.7 nm per ssDNA nucleotide, the minimum number of nucleotides needed for the hinge is 5.

The designed file

The ultimate design file
VertexSwitcher_structure.json download
VertexSwithcer_sequence.xlsx download

Simulation using oxDNA

The confirmation of structural stability was performed using oxDNA, a software for coarse-grained molecular dynamics simulations. The simulation consists of four main steps. First, a Rigid-body simulation is used to roughly shape the structures designed in caDNAno. Subsequently, short-time calculations known as MC relaxation and MD relaxation are carried out to alleviate any structural strains. Finally, the MD simulation is employed to calculate the temporal evolution of the structure.

Fig.2 MD Simulation of the 10nt Hinge Intermediate

Intermediate MD Simulation Input File

Stability Assessment by RMSF

We calculated the RMSF (Root Mean Square of Fluctuation) values based on the data obtained from oxDNA simulations to assess stability. RMSF quantifies the fluctuations of particles derived from MD simulations, representing the deviation (standard deviation) of each particle from its average position. We developed a Python program that converts RMSF values into a color map, allowing for visual assessment based on the magnitude of RMSF.
python file download