Representations of 3D surfaces used in computer graphics have been adopted as templates in an efficient method for making nanoscale objects from DNA, lowering the barriers to applications of DNA nanotechnology. See Letter p.441
The self-assembly of DNA molecules has established itself as a method of choice for the fabrication of nanometre-scale objects, but new approaches are needed to simplify the design and production of larger, structurally complex shapes. On page 441 of this issue, Benson et al.1 report just such a technique. Their method unites a centuries-old mathematical problem with a design principle that exploits the rendering of 3D objects by computer graphics.
The centre of the historic city of Königsberg (today's Kaliningrad) is built on and around an island in the mouth of the Pregel River, between two of the river's branches. Seven bridges connect the island and the three surrounding parts of the city. In the early eighteenth century, a mathematical question arose that became famously known as 'the Seven bridges of Königsberg': is it possible to devise a loop walk that visits all four parts of the city, and in which all bridges are crossed only once?
Leonhard Euler approached this problem by constructing an abstract representation of the city composed of vertices (the city parts) connected by edges (the bridges). In this way, he rigorously proved that no solution existed. He also came up with a simple rule that generally describes loop walks such as the one sought for Königsberg, which are now known as Eulerian circuits: they exist only if the degree of each vertex (the number of edges touching it) in a system is even2. In this seminal work, Euler laid the foundation not only for topology research, but also for the field of graph theory, which is fundamental to modern computer science.
When Benson and colleagues set out to assemble arbitrary 3D surfaces from DNA, they faced a special Eulerian-circuit problem. Their idea was to find a way to route a single strand of DNA (roughly 8,000 bases in length) along all the edges of the polygon meshes that constitute the surfaces of 3D computer graphics. This would provide a scaffold for the construction of any object from the DNA strand, as long as a polygon mesh could be made to describe the object's shape.
The authors selected seven polyhedral shapes of varying complexity to test their approach, ranging from a simple sphere to the rather complicated 'Stanford bunny'3 — a widely used test model for computer graphics that is based on the 3D scan of a ceramic rabbit figurine (Fig. 1). With the help of an algorithm, they searched the polygon meshes of each shape for Eulerian circuits known as A-trails, which visit all the edges of a mesh without crossing themselves. If no such A-trail could be found, the algorithm introduced a minimal number of 'helper' edges to satisfy Euler's conditions of having only even-degree vertices in the network. The software then populated the completed paths with the sequence of the DNA strand.
The final task was to define many oligonucleotides (short DNA molecules) whose sequence of bases was complementary to those of stretches of the long scaffold sequence, to ensure that the single strand folds into the desired shapes through DNA-duplex formation. These oligonucleotides also complete all vertices by connecting their adjacent edges, if they are not already connected by the scaffold itself. In principle, this approach allows the design and fabrication of essentially any shape that can be approximated by a polygon mesh.
The good news is that most computer-aided design tools provide exactly such polygon meshes, usually consisting of triangles. This is helpful because triangular frameworks are theoretically rigid when built from rigid elements. Double-stranded DNA can be considered to be stiff at the nanoscale, and the authors observed that the designed DNA systems are indeed sturdy enough to adopt the desired shapes through self-assembly. The shapes are clearly recognizable in electron micrographs (see Fig. 2 of the paper1).
Because the polygon structures approximate only the surfaces of the targeted shapes, the objects produced by Benson et al. are hollow. There is therefore room to improve the structural stability of the objects, for example by introducing 'stabilizer' duplexes that span surfaces inside each object. However, the authors' approach yields larger objects than those obtained by DNA origami — a widely used technique in which parallel DNA helices fill out a 2D or 3D shape4,5 — but uses the same amount of DNA.
Another advantage of Benson and co-workers' polygon structures is that they are stable in physiological conditions. This allows their immediate application in in vitro biology experiments — for example, DNA nanostructures have been investigated6 as agents that interact with living cells and as potential drug-delivery vehicles. To prevent them from degrading in future in vivo experiments, the structures could benefit from biocompatible coatings, such as lipid bilayers7.
This is not the first study to present polygon meshes constructed from DNA — decades of research have produced dozens of methods for building DNA-based polyhedra and wireframe structures8,9,10,11,12,13. But the current work arguably presents the most versatile and streamlined design method. With the help of the vHelix software, which was also developed in the Högberg laboratory and has been released at the same time as this paper (www.vhelix.net), in principle anyone could create any desirable shape, adjust the polygon-mesh size to the available length of the scaffold strand and obtain a list of oligonucleotide sequences that can be ordered from a DNA-synthesizing facility.
Research fields can thrive when the barrier is low enough for newcomers to enter them and to use new tools and methods. Because DNA nanotechnology has historically been interwoven with computer science, an excellent pool of software is already available to help researchers design and test DNA structures for such diverse applications as chemical-reaction networks, photonic devices and drug delivery, to name just a few. The vHelix software will enrich that pool, and inspire research by bringing the dream of nanoscale 3D printing closer to reality.Footnote 1
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