45N-Colorability of Graphs Natasha JonoskaPhiset Sa-Ardyen
46A 3-Colorable Graph and its Prototype for Computation This is slide #3A graph is 3-colorable if it is possible to assign one color to each vertex such that no two adjacent vertices are colored with the same color. In this example, one 2-armed branched molecule, four 3-armed branched molecules and one 4-armed branched molecule are needed.(b) The same graph was chosen for the construction. Since the vertex V5 in (a) has degree 2, for the experiment a double helical DNA is used to represent the vertex V5 and the edges connecting V5 with V1 and V4. The target graph to be made consists of 5 vertices and 8 edges. (c) The target graph in DNA representation.
47ResultsAn irregular DNA graph whose edges correspond to DNA helix axes has been constructed and isolated based on its closed cyclic character.The molecule may contain multiple topoisomers, although this has no impact on the characterization of the product.The graph assembles with the correct edges between vertices, as demonstrated by restriction analysis
66Paranemic Cohesion with the PX Motif Left: Ubiquitous Reciprocal Exchange Creates a PX Molecule.Center Right: The Strand Connectivity of a PX Molecule.Far Right: The Blue and Red Dumbbell Molecules are Paranemic.
70One-Dimensional Arrays of Edge-Sharing Triangles (Short Direction)Yan, H. & Seeman, N.C. (2002) J. Supramol. Chem.,in press.
71One-Dimensional Arrays of Edge-Sharing Triangles (Long Direction)Yan, H. & Seeman, N.C. (2002) J. Supramol. Chem.,in press.
72One-Dimensional Arrays of Double Edge-Sharing Triangles Yan, H. & Seeman, N.C. (2002) J. Supramol. Chem.,in press.
73A Cassette for the Insertion of a PX-JX2 Device into a 2D TX Array Baoquan Ding
74TX Array With Rotated Components LaBean, T.H., Yan, H., Kopatsch, J., Liu, F., Winfree, E., Reif, J.H.& Seeman, N.C (2000), J. Am. Chem. Soc. 122,
75Cassette to Insert the PX-JX2 Device ~Perpendicularly Into a TX Lattice PX ConformationJX2 Conformation
76Molecular Models of the 2 states of the Sequence-Driven DNA Devices
77Application of the PX-JX2 Device in a 1D Molecular Pegboard
78Alessandra Carbone (IHES) Towards 2D CircuitsAlessandra Carbone (IHES)
79Circuits and triangular patterns We need to show that the shapes is one/unique and that we such a general hape we can implement any arbitrary function. I shall show it to youon this simpleexample. The generalisation goes the same way.How to programme molecules to do what we want them to do? As a toy model, we consider boolean circuits and we show that we can induce molecules to compute aboolean function, i.e. a function that computes on 0/1 values. This is clearly just an example. You can make molecules to do similar operations and drive them to follow specific pathways in the assembly.What we have shown is that one can generalise these ideas of molecular programming to compute any arbitrary boolean function and also to guide the construction of arbitrary 3D structures. A boolean circuit is always representable with a triangle of logical gates. The computation is realised afterwards by an assembly of other tiles over this plateform. In the first row, we have the input and the result is obtained on the tip of the triangle.The representation of the circuit on a plane resolves the ambiguities in the assembly.
81Tiles TX Molecule inputs operation outputs We need 13 different tiles to realise all boolean functions.The molecule has 4 strands that form 3 helices each.On the bottom we see the schematisation of a tile and its realisation with DNA. The codes….The size of a tile is 15-20nm x 7nmoperationTX Moleculeoutputs
82Molecular Programming: programmed board 4 different statesL’idee mathematique derriere mon travail en colaboration avec Seeman est de s’apercevoir qu’on peut concevoir des reseaux programmables bidimensionnelles pour en suite construire des objets tridimensionnels.Dans la pratiques, ces reseaux 2D sont similaires aux reseaux ABCD precedent mais les molecules intercales C et D sont des plots moleculaires programmables a 4 etats differents, construit avec une paire de molecules programmables vues precedemment.On peut faire un reseau aussi grand qu’on veut ou bien lui donner une forme triangulaire par exemple.
89An Algorithmic Arrangement Based on Mix & Split Synthesis
90Summary of Results (1)Reciprocal exchange generates new DNA motifs, and sequence-symmetry minimization provides an effective way to generate sequences for them.Sticky ends, PX cohesion and edge-sharing are can hold DNA motifs together in a sequence-specific fashion.
91Summary of Results (2)2D lattices with tunable features have been built from DX, TX and DNA parallelogram motifs. Preliminary evidence for 3D assembly has been obtained.DNA nanomechanical devices have been produced using both the B-Z transition and PX-JX2 conversion through sequence control.
92Summary of Results (3)An algorithmic 4-bit cumulative XOR calculation has been performed.An irregular graph has been synthesized in solution, establishing the principle of using this type of assembly for calculations.New motifs include a 6-helix bundle and a cassette for inserting a PX-JX2 device into a TX array.