Method and apparatus for controlling properties of nucleic acid nanostructures

#Molecular self-assembly with scaffolded deoxyribonucleic acid (DNA) origami enables arranging many thousand nucleotides with subnanometer precision at specified locations in space to yield custom-shaped objects with dimensions on the scale of 1 to 1000 nanometers (1 nanometer, nm, =10−9 meters). [See Rothemund, P W K. “Folding DNA to create nanoscale shapes and patterns.”, Nature, 440, 297-302, (2006); Lulu, Q., Ying, W., Zhao, Z., Jian, Z., Dun, P., Yi, Z., Qiang, L., Chunhai, F., Jun, H., Lin, H. “Analogic China map constructed by DNA”, Chinese Sci Bull, 51, 2973-2976, (2006); Douglas, S M., Chou, J J., Shih, W M. “DNA-nanotube-induced alignment of membrane proteins for NMR structure determination”, Proc Natl Acad Sci U.S.A., 104, 6644-6648, (2007); Andersen, E S., Dong, M., Nielsen, M M., Jahn, K., Lind-Thomsen, A., Mamdouh, W., Gothelf, K V., Besenbacher, F., Kjems, J. “DNA origami design of dolphin-shaped structures with flexible tails”, ACS Nano, 2, 1213-1218, (2008); Ke Y., Sharma, J., Liu, M., Jahn, K., Liu, Y., Yan, H. “Scaffolded DNA origami of a DNA tetrahedron molecular container”, Nano Lett, 9, 2445-2447, (2009); Andersen, E S., Dong, M., Nielsen, M M., Jahn, K. Subramani, R. Mamdouh, W., Golas, M M., Sander, B., Stark, H., Oliveira, C L P., Pedersen, J S., Birkedal, V., Besenbacher, F., Gothelf, K V., Kjems, J. “Self-assembly of a nanoscale DNA box with a controllable lid”, Nature, 459, 73-76, (2009); Douglas, S M., Dietz, H., Liedl, T., Högberg, B., Graf, F., Shih, W M. “Self-assembly of DNA into nanoscale three-dimensional shapes.”, Nature, 459, 414-418, (2009); Dietz, H., Douglas, S M., Shih, W M. “Folding DNA into twisted and curved nanoscale shapes.”, Science, 325, 725-730, (2009); Douglas, S M., Marblestone, A H., Teerapittayanon, S., Vazquez, A., Church, G M., Shih, W M. “Rapid prototyping of 3D DNA-origami shapes with caDNAno”, Nucleic Acids Res, 37, 5001-5006, (2009) Ke, Y., Douglas, S M., Liu, M., Sharma, J., Cheng, A., Leung, A., Liu, Y., Shih, W M., Yan, H. “Multi-layer DNA origami packed on a square lattice”, J Am Chem Soc, 131, 15903-15908, (2009); Pound, E., Ashton, J R., Becerril, H A., Woolley, A T. “Polymerase chain reaction based scaffold preparation for the production of thin, branched DNA origami nanostructures of arbitrary sizes.”, Nano Lett, 9, 4302-4305, (2009); Endo, M., Hidaka, K., Kato, T., Namba, K., Sugiyama, H. “DNA prism structures constructed by folding of multiple rectangular arms”, J Am Chem Soc, 131, 15570-15571, (2009); Kuzuya, A., Komiyama, M. “Design and construction of a box-shaped 3D-DNA origami.”, Chem Commun (Camb), 4182-4184, (2009); Liedl, T., Högberg, B., Tytell, J., Ingber, D E., Shih, W M. “Self-assembly of three-dimensional prestressed tensegrity structures from DNA”, Nat Nanotechnol, 5, 520-524, (2010); for which the entire contents of each are hereby incorporated as if fully set forth herein, except as the terminology is inconsistent with the terminology used elsewhere herein].

#DNA origami entails folding a single-stranded ‘scaffold’ DNA molecule up to several thousand bases long into custom-shaped single-layer or multi-layer bundles of B-form DNA double helices with the help of a set of short (<60 bases) single-stranded ‘staple’ oligonucleotides that are currently derived from chemical synthesis. DNA origami objects can be designed in a few hours with the help of software developed specifically for this purpose, and the manual labor required for setting up assembly reactions and purification is limited to handling a multi-channel pipette and running agarose gels. A rich diversity of shapes has been built so far with scaffolded DNA origami. A comprehensive review has recently been published in Shih, W M., Lin, C. “Knitting complex weaves with DNA origami”, Curr Opin Struct Biol, 20, 276-282, (2010) the entire contents of which are hereby incorporated as if fully set forth herein, except as the terminology is inconsistent with the terminology used elsewhere herein.

#Scaffolded DNA origami enables the programmable synthesis of complex nanoscale structures with a broad range of potential scientific and industrial applications. However, the rational design of DNA origami structures to target specifications is currently limited by a lack of quantitative tools for predicting the solution shape and mechanical integrity of designed structures, and using these predictive capabilities for unsupervised, automated design.

#The present invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which:

#FIGS. 1A and 1B are block diagrams that illustrate multiple example representations of a portion of a DNA molecule, according to an embodiment;

#FIG. 1C is a block diagram that illustrates multiple representations of linked cylinders formed from one or more DNA molecules, according to an embodiment;

#A method and apparatus are described for controlling derived properties, such as relaxed shape, internal strains, or elastic properties of nucleic acid nanostructures. In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid unnecessarily obscuring the present invention.

#Deoxyribonucleic acid (DNA) is a replicating, usually double-stranded long molecule that encodes other shorter molecules, such as proteins, used to build and control all living organisms. DNA is composed of repeating chemical units known as “nucleotides” or “bases.” There are four bases: adenine, thymine, cytosine, and guanine, represented by the letters A, T, C and G, respectively. Adenine on one strand of DNA always binds to thymine on the other strand of DNA; and guanine on one strand always binds to cytosine on the other strand and such bonds are called base pairs. Any order of A, T, C and G is allowed on one strand, and that order determines the complementary order on the other strand. The actual order may determine the effect of that portion of the DNA molecule. Information on a portion of one strand of DNA can be captured by ribonucleic acid (RNA) that also comprises a chain of nucleotides in which uracil (U) replaces thymine (T). Determining the order, or sequence, of bases on one strand of DNA or RNA is called sequencing. A portion of length k bases of a strand is called a k-mer; and specific short k-mers are called oligonucleotides or oligomers or “oligos” for short.

#Some embodiments of the invention are described below in the context of scaffolded DNA origami comprising double helix structures with one or more Holliday junctions modeled using a finite element numerical model. However, the invention is not limited to this context. In other embodiments the shape and other properties are determined for single helix DNA or ribonucleic acid (RNA) structures, with or without Holliday junctions using finite element or other numerical models, such as finite difference numerical models. The proposed computational modeling framework may be applied to DNA/RNA structures that are internally stabilized mechanically using secondary small molecules such as synthetic nucleic acids, amino acids, etc., which are modeled using distinct physical properties in the finite element model. The computational framework uses physical modeling to predict DNA/RNA origami structural properties and shape, integrated with any one of a number of optimization algorithms that can be used with objective functions based on mechanics and other considerations such as financial cost of oligos in order to rationally design DNA/RNA-based structures.