Stable nanoscale nucleic acid assemblies and methods thereof

Abstract

Methods for the top-down design of nucleic acid nanostructures of arbitrary geometry based on target shape of spherical or non-spherical topology are described. The methods facilitate 3D molecular programming of lipids, proteins, sugars, and RNAs based on a DNA scaffold of arbitrary 2D or 3D shape. Geometric objects are rendered as node-edge networks of parallel nucleic acid duplexes, and a nucleic acid scaffold routed throughout the network using a spanning tree formula. Nucleic acid nanostructures produced according to top-down design methods are also described. In some embodiments, the nanostructures include single-stranded nucleic acid scaffold, DX crossovers, and staple strands. In other embodiments, the nanostructures include single-stranded nucleic acid scaffold, PX crossovers and no staples. Modified nanostructures include chemically modified nucleotides and conjugated to other molecules are described.

1 - 3 . (canceled) 
     
     
         4 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein each edge of the nanostructure comprises four or more parallel or anti-parallel helices arranged in square cross-sectional morphology, or six or more parallel or anti-parallel helices arranged in honeycomb lattice morphology. 
     
     
         5 . The polyhedral nucleic acid nanostructure of  claim 4 , wherein each vertex of the nanostructure has two or more edges that come together in an aligned angle to create a bevel at the vertex. 
     
     
         6 . The method of  claim 27 , wherein the geometric shape does not have spherical topology. 
     
     
         7 .- 9 . (canceled) 
     
     
         10 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the crossovers are anti-parallel crossovers,
 wherein the target nucleic acid nanostructure comprises B-form nucleic acid helices along the edges,   wherein the length of each edge is expressed as a multiple of 10.5 base pairs rounded up or down to the nearest whole number, and   wherein the length of each edge is between 21 base pairs and 1,000 base pairs, inclusive.   
     
     
         11 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the crossovers are anti-parallel crossovers,
 wherein the target nucleic acid nanostructure comprises A-form nucleic acid helices along the edge,   wherein the length of each edge is expressed as a multiple of 11 base pairs, and   wherein the length of each edge is between 22 base pairs and 1,100 base pairs, inclusive.   
     
     
         12 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the crossovers are parallel crossovers, and
 wherein the target nucleic acid nanostructure comprises A-form or B-form nucleic acid helices along the edges, and   wherein the length of each edge is between 20 base pairs and 1,100 base pairs, inclusive.   
     
     
         13 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the target nucleic acid nanostructure comprises A-form or B-form nucleic acid helices along the edge, and
 wherein the length of each edge is 21 base pairs, 31 base pairs, 42 base pairs, 52 base pairs, 63 base pairs, or 73 base pairs.   
     
     
         14 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the nucleic acid scaffold is RNA, the staple strands are RNA or the scaffold and staple strands are RNA, and
 wherein the length of each edge is 44 base pairs, 55 base pairs, 66 base pairs, or 77 base pairs.   
     
     
         15 . (canceled) 
     
     
         16 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein identifying a route for a single-stranded nucleic acid scaffold that traces throughout the geometric shape in step (b) further comprises:
 classifying each edge of the network based on its membership in the spanning tree,   wherein edges that are members of the spanning tree do not have a scaffold double crossover, and edges that are not members of the spanning tree have a scaffold double crossover;   splitting each edge that is not a member of the spanning tree into two edges, each containing a pseudo-node at the point of the scaffold crossover;   splitting each node at each of the vertices into two pseudo-nodes; and   wherein the Euler cycle represents the route of a single-stranded nucleic acid scaffold that traces once along each edge in both directions throughout the entire geometric shape.   
     
     
         17 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein identifying a route for a single-stranded nucleic acid scaffold that traces throughout the geometric shape in step (b) further comprises:
 classifying each edge of the network as one of four types based on its membership in the spanning tree and on whether it employs anti-parallel or parallel crossovers; edges that are members of the spanning tree have each scaffold portion start and end at different vertices, and edges that are not members of the spanning tree have each scaffold portion start and end at the same vertex   splitting each edge that is not a member of the spanning tree into two edges, each containing a pseudo-node at the point of the scaffold crossover;   splitting each node at each of the vertices into two pseudo-nodes; and   
       wherein the Euler cycle represents the route of a single-stranded nucleic acid scaffold by superimposing and connecting units of partial scaffold routing within an edge based on its classification and length. 
     
     
         18 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein identifying a route for a single-stranded nucleic acid scaffold that traces throughout the geometric shape in step (b) further comprises:
 rendering each helix in the network as a line, based on the target cross-section of each edge;   calculating a loop-crossover structure, wherein two or more adjacent lines are connected to form loops and all possible double-crossover locations between two loops are calculated;   calculating a dual graph of the loop-crossover structure, wherein the loops and double-crossover locations of the network are converted to nodes and edges of the dual graph, respectively,   wherein the spanning tree is of the dual graph network;   calculating which of the locations of double-strand crossovers will be used, wherein a single double-strand crossover is placed at each edge that is the part of the spanning tree of the dual graph; and   calculating the Euler cycle of the network, wherein the Euler cycle represents the route of a single-stranded nucleic acid scaffold that traces once through each duplex throughout the entire geometric shape.   
     
     
         19 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the spanning tree of the network is determined using a breadth-first search or depth-first search. 
     
     
         20 . The polyhedral nucleic acid nanostructure of  claim 19 , wherein the spanning tree is calculated using Prim's formula or Kruskal's formula. 
     
     
         21 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the Euler cycle is the A-trail Euler cycle. 
     
     
         22 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the geometric shape is a 3D polyhedral. 
     
     
         23 .- 26 . (canceled) 
     
     
         27 . A polyhedral nucleic acid nanostructure designed according to a method of comprising:
 (a) providing or determining the geometric parameters of an input, wherein the input comprises a 3D polyhedral or 2D polygonal geometric shape of a target nucleic acid nanostructure;   (b) identifying a route for a single-stranded nucleic acid scaffold that traces throughout the geometric shape comprising:
 rendering a wireframe mesh of the geometric shape as a node-edge network; 
 using a spanning tree of the node-edge network to define the placement of scaffold crossovers; and 
 determining a Euler cycle, wherein the single-stranded nucleic acid scaffold traces the Euler cycle throughout the node-edge network; 
   (c) assembling the target nucleic acid nanostructure having the 3D polyhedral or 2D polygonal geometric shape comprising hybridizing the single-stranded nucleic acid scaffold to itself and/or staple strands to form the target nucleic acid nanostructure designed according to steps (a) and (b).   
     
     
         28 . A three-dimensional polyhedral nucleic acid nanostructure comprising two nucleic acid anti-parallel helices spanning each edge of the nanostructure,
 wherein the three-dimensional structure is formed from single-stranded nucleic acid staple strands hybridized to a single-stranded nucleic acid scaffold,   wherein the scaffold is routed through the Euler cycle of the network defined by vertices and lines of a node-edge network of the polyhedral nanostructure,   wherein the nucleic acid nanostructure comprises at least one edge including a double-strand crossover,   wherein the location of the double-strand crossover is determined by the spanning tree of the node-edge network of the polyhedral nanostructure, and   wherein the staple strands are hybridized to the vertices, edges and double strand crossovers of the scaffold to define the shape of the nanostructure.   
     
     
         29 . A three-dimensional polyhedral nucleic acid nanostructure comprising two nucleic acid parallel helices spanning each edge of the nanostructure,
 wherein the three-dimensional structure is formed from a single-stranded nucleic acid scaffold hybridized to itself and may also hybridize to single-stranded nucleic acid staple strands,   wherein the scaffold is routed through the Euler cycle of the network defined by vertices and lines of a node-edge network of the polyhedral nanostructure,   wherein the scaffold hybridizes to itself in at least one edge using parallel crossovers,   and   wherein the staple strands, if any, are hybridized to the edges and double strand crossovers of the scaffold to define the shape of the nanostructure.   
     
     
         30 . A three-dimensional polyhedral or polygonal nucleic acid nanostructure comprising four or more nucleic acid anti-parallel helices spanning each edge of the nanostructure,
 wherein the three-dimensional structure is formed from the single-stranded nucleic acid staple sequences hybridized to a single-stranded nucleic acid scaffold sequence,   wherein the scaffold is routed through the Euler cycle of the network defined by vertices and lines of a node-edge network of the polyhedral nanostructure,   wherein the nucleic acid nanostructure comprises at least one edge including a double strand crossover,   wherein the location of the double strand crossover is determined by a spanning tree of the dual graph of the network of the polyhedral or polygonal nanostructure,   wherein the helices comprising an edge are arranged as a square lattice of four or more helices, or honeycomb lattice of six or more helices,   wherein the helices meeting at a vertex are beveled or non-beveled, and   wherein the staple strands are hybridized to the vertices, edges and double strand crossovers of the scaffold to define the shape of the nanostructure.   
     
     
         31 . The polyhedral nucleic acid nanostructure of  claim 27 , further comprising a molecule selected from the group consisting of PNA, protein, lipid, carbohydrate, a small-molecule, a dye, and RNA,
 wherein the molecule is covalently or non-covalently bound to the nanostructure.   
     
     
         32 . The polyhedral nucleic acid nanostructure of  claim 27 , further comprising a therapeutic, diagnostic or prophylactic agent. 
     
     
         33 . A method of using the polyhedral nucleic acid nanostructure of  claim 32  for the delivery of the therapeutic, diagnostic or prophylactic agent to a subject, the method comprising the step of administering the nanostructure to the subject. 
     
     
         34 .- 38 . (canceled) 
     
     
         39 . The polyhedral nucleic acid nanostructure of  claim 27 , wherein the scaffold comprises deoxyribonucleic acid selected from the group consisting of naturally-occurring dNTP, dUTP, fluorescent dNTP, alpha-phosphate dNTP, radioactive dNTP, and polyethylene glycol-modified dNTP, or combinations thereof. 
     
     
         40 .- 41 . (canceled) 
     
     
         42 . The nucleic acid nanostructure of  claim 28 , wherein single-stranded or double-stranded nucleic acid overhang sequences extend from nick positions from the oligonucleotide staple strands. 
     
     
         43 . The nucleic acid nanostructure of  claim 42 , wherein the nucleic acid overhang sequences that extend from nick positions from the oligonucleotide staple strands form duplex reinforcements along one or more edges of the structure, or span between two vertices of the structure. 
     
     
         44 . The nucleic acid nanostructure of  claim 42 , wherein the single-stranded or double-stranded nucleic acid overhangs comprise one or more sequences of nucleic acids that is complementary to a target RNA or DNA sequence. 
     
     
         45 . The nucleic acid nanostructure of  claim 42 , wherein the single-stranded or double-stranded nucleic acid overhangs comprise one or more sequences of nucleic acids that interact with DNA binding proteins or RNA-binding proteins. 
     
     
         46 . The nucleic acid nanostructure of  claim 42 , wherein the edge length and nanoparticle geometry is greater than the size of the target molecule that is to be captured, to allow for 1, 2, 3, or more than 3 molecules to be bound independently of any other. 
     
     
         47 . The nanostructure of  claim 27 , wherein the nanostructure has a molecular weight of between 200 Daltons and 100 mega Dalton, inclusive. 
     
     
         48 . The nanostructure of  claim 27 , wherein the nanostructure comprises a single-stranded scaffold sequence including one or more nucleic acid sequences complementary to a nucleic acid sequence corresponding to one or more of an mRNA, DNA, or an epitope recognized by a DNA binding protein.