DNA rendering of polyhedral meshes at the nanoscale

Abstract

It was first suggested 1 more than 30 years ago that Watson-Crick base pairing might be used to rationally design nanoscale structures from nucleic acids. Since then, and especially since introduction of the origami technique 2 , DNA nanotechnology has seen astonishing developments and increasingly more complex structures are being produced [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . But even though general approaches for creating DNA origami polygonal meshes and design software are available 14,16,17,[19][20][21] , constraints arising from DNA geometry and sense/antisense pairing still impose important restrictions and necessitate a fair amount of manual adjustment during the design process. Here we present a general method for folding arbitrary polygonal digital meshes in DNA that readily produces structures that would have been very difficult to realize with previous approaches. This is achieved with a high level of automation of the design process, which uses a routing algorithm based on graph theory and a relaxation simulation to trace scaffold strands through the target structures. Moreover, unlike conventional origami designs built from closed-packed helices, our structures have a more open conformation with one helix per edge and are thus stable in salt conditions commonly used in biological assays.The starting point of the present method is a 3D mesh representing the geometry one wishes to realize at the nanoscale. Focusing only on polyhedral meshes, i.e. meshes which enclose a volume inflatable to a ball, and in contrast to several previous approaches 14,17,19 (see Extended Data Fig. 1) we aim to replace the edges of the mesh by single DNA double helices such that the scaffold strand traverses each of these edges once. This problem is closely related to the Chinese Postman Tour problem 22 in graph theory, which we use to find solutions as doing so by hand would be practically impossible for most meshes. The main principles underpinning our design paradigm are that the technique should allow meshes to be triangulated to optimize structural rigidity; that each edge should be represented by one double helix to enable construction of large structures using as little DNA as possible (though some meshes require two helices to render certain edges as discussed below); and that vertices should be nonBenson et. al, -DNA Rendering of Polyhedral Meshes at the Nanoscale Confidential 2 crossing (i.e. the scaffold should not cross itself in the vertices to ensure non-knotted paths with fewer topological-and kinetic traps during folding, and planar vertex junctions that avoid mesh protrusions due to stacking of crossing helices at each vertex).The overall design scheme is split into four discrete steps: i) Drawing of a 3D polygon mesh in a 3D software, Fig. 1a. ii) Generating an appropriate routing of the long scaffold strand through all the edges of the mesh, Fig. 1b-e. iii) Determining the least strained DNA helix arrangement realizing the 3D mesh, Fig. 1f-i. And iv), Optional fine tuning of the des...

Characterizing DNA Star-Tile-Based Nanostructures Using a Coarse-Grained Model

“…6−14 New software also makes designing large nanostructures with tailored properties easier than ever. 15,16 Some of these synthetic structures are static and include crystals, 17−19 polyhedra, 12,20−25 wire-frame designs, 11,26,27 and topological structures such as mobius strips, 28 while others are "active" systems that include walkers, 29,30 gears and hinges, 31 robots, 32,33 and crank-sliders. 34 However, having total control over the structural as well as time-dependent properties of selfassembled DNA nanostructures remains a significant design challenge.…”

Automated design of DNA origami

“…This conventional design strategy was turned on its head last year by the first topdown software for building wireframe DNA nanoarchitectures 7 . The software vHelix 7 is based on selecting a target shape that fits to the length of the available scaffold and subsequently creating a polyhedral meshwork of the object-an approach well known in computer graphics.…”

“…1a). The wireframe motif is based on two interconnected DNA double helices (i.e., doublecrossover (DX) molecules), allowing more structural robustness than the previously reported topdown objects with single duplex edges 7 . After designing the shape and obtaining the sequences, researchers fabricate the structures using standard annealing routines.…”

Supramolecular Wireframe DNA Polyhedra: Assembly and Applications

“…Almost at the same time, Högberg et al and Schmidt et al, independently, presented a general method to fold arbitrary 3D DNA structures with trigonal mesh elements, and most of the edges of the meshes were single duplexes (thus suitable for experiments in low ionic-strength environments). [49,50] More recently, Bathe et al demonstrated a generalizable top-down strategy towards an inverse sequence design of DNA origami based on a target shape ( Figure 4E). [51] This allows a fully automatic sequence generation by a computer program with significantly facilitated synthesis of nearly arbitrary wireframe DNA architectures.…”

“…This technique has offered DNA nanotechnologists unlimited imaginations to create nearly arbitrary shapes on the nanoscale towards various possible applications. [44][45][46][47][48][49][50][51] In addition, because the sequence of the scaffold M13 strand is known, intellectual burden during the design of a complex DNA structure is greatly reduced with the aid of a properly written computer program.…”