A DNA Cube

Those strands would have corresponded to the hexagonal projections down the threefold symmetric body diagonals. 

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Chen, J., Seeman, N.C. (1991b) The electrophoretic properties of a DNA cube and its sub-structure catenanes. Electrophoresis 12, 607-611 (1991). 

Figure 17 Synthesis of a DNA cube. Ten chemically synthesized strands, two 80-mers and eight 40-mers, are hybridized to form two quadrilaterals in the first step. (Adapted from N.C. Seeman. Acc. Chem. Res. 30 357-363,1997. With permission.)...

Figure 5. A DNA molecule whose helix axes have the connectivity of a cube. The molecule shown consists of six cyclic strands that have been catenated together in this particular arrangement. They are labeled by the first letters of their positional designations, Up, Down, Front, Back, Left, and Right. Each edge contains 20 nucleotide pairs of DNA, so we expect that their lengths will be approximately 68 A. All of the twisting has been shown in the middle of the edges for clarity, but the DNA is base-paired from vertex to vertex. From model building, the axis-to-axis distance across a square face seems to be approximately 100 A, with a volume (in a cubic configuration) of approximately 1760 nm3 when the cube is folded as shown.

Fig. 4 Ligated linked products from flexible DNA components. (a) A stick cube and (b) a stick truncated octahedron. Each edge of the cube and the truncated octahedron contains two turns of double-helical DNA. The twisting is confined to the central portion of each edge for clarity, but it actually extends from vertex to vertex, (c) Bonomean rings. Scission of any of the three rings shown results in the unlinking of the other two rings. (View this art in color at www.dekker.com.)...

Pelesko, John A. Self Assembly The Science of Things That Put Themselves Together. Boca Raton, Ela. Chapman and Hall/CRG, 2007. Discusses natural self-assembling systems such as crystals and soap films and goes on to discuss viruses and self-assembly of DNA cubes and electronic circuits. Excellent introduction to a field of growing importance. 

The truncated octahedron and the rhombic dodecahedron provide periodic cells that are approximately spherical and so may be more appropriate for simulations of spherical molecules. The distance between adjacent cells in the truncated octahedron or the rhombic df)decahedron is larger than the conventional cube for a system with a given number of particles and so a simulation using one of the spherical cells will require fewer particles than a comparable simulation using a cubic cell. Of the two approximately spherical cells, the truncated octahedron is often preferred as it is somewhat easier to program. The hexagonal prism can be used to simulate molecules with a cylindrical shape such as DNA. 

Czader A, Bittner ER (2008) Calculations of the exciton coupling elements between DNA bases using the transition density cube method. J Chem Phys 128 035101... 

Fig. 9.12 Octahedral hosts, (a) Murakami s cyclophane-based cube, (b) X-ray crystal structure of the [(V06)(RP03)g]+ (R = tBu, OSiMe3) ion, (c) Seeman s DNA-based cube (printed with permission by Professor Nadrian Seeman, for further details see http Wseemanlab4.chem.nyu.edu).

The fourth is a cube synthesized by Chen and Seeman, the components of which are based upon DNA (Fig. 9.12c). [35] The directionality and ability of the double helix to form branched junctions are exploited for the edges and vertices, respectively. Interestingly, each face of this molecule forms a cyclic strand which is catenated with strands of adjacent faces. Molecular modeling experiments indicate the length of each edge to be approximately 6.8 nm. 

Careful design was used by Seeman to prepare complementary DNA strands that self assemble into a cube with 20 nucleotide pairs along each edge. Other derivatives include nylon DNA , through the synthesis of peptide nucleic acids (PNA), and polyethylene glycol derivatized DNA. Figure 8.1 illustrates the DNA knots that can be prepared using these techniques. 

The Holliday junctions formed during recombination are mobile, but synthetic immobile Holliday junctions can be synthesized by using nonhomolo-gous base sequences or by locking the jrmctions. This has permitted careful physical study of these and other more elaborate synthetic junchons. With suitable choices of base sequences for the oligonucleotides from which they are made, such junctions will assemble spontaneously. Double-stranded DNA with immobile junctions is a very suitable construction material on a "nanochemical" scale. It has been assembled into knots, rings, cubes, and more complex polyhedra. ... 

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