Nataša Jonoska

Three dimensional DNA structures in computing.

We show that 3-dimensional graph structures can be used for solving computational problems with DNA molecules. Vertex building blocks consisting of k-armed (k = 3 or 4) branched junction molecules are used to form graphs. We present procedures for the 3-SAT and 3-vertex-colorability problems. Construction of one graph structure (in many copies) is sufficient to determine the solution to the problem. In our proposed procedure for 3-SAT, the number of steps required is equal to the number of variables in the formula. For the 3-vertex-colorability problem, the procedure requires a constant number of steps regardless of the size of the graph.

Nanotechnology : science and computation

- Part 1 DNA Nanotechnology - Algorithmic Self-assembly: Scaffolded DNA Origami: From Generalized Multi-crossovers to Polygonal Networks.- A Fresh Look at DNA Nanotechnology.- DNA Nanotechnology: An Evolving Field.- Self-healing Tile Sets.- Compact Error Resilient Computational DNA Tilings.- Forbidding-Enforcing Conditions in DNA Self-assembly of Graphs.- Part 2: Codes for DNA Nanotechnology: Finding MFE Structures Formed by Nucleic Acid Strands in a Combinatorial Set.- Selection of Large Independent Sets of DNA Oligonucleotides.- Involution Solid Codes.- Part III: DNA Nanodevices: DNA-Based Motor Work at Bell Laboratories.- Nanoscale Molecular Transport by Synthetic DNA Machines.- Part IV: Electronics, Nanowires and DNA: A Supramolecular Approach to Metal Array Programming Using Artificial DNA.- Multicomponent Assemblies Including Long DNA and Nanoparrticles - An Answer for the Integration Problem? Molecular Electronics - From Physics to Computing.- Part V: Other Bio-molecules in Self-assembly: Towards an Increase of the Hierarchy in the Construction of DNA-Based Nanostructures Through the Integration of Inorganic Materials.- Adding Functionality to DNA Arrays: The Developments of Semisynthetic DNA-Protein Conjugates.- Bacterial Surface Layer Proteins: A Simple but Versatile Biological Self-assembly System in Nature.- Part VI: Biomolecular Computational Models: Computing with Hairpins and Secondary Structures of DNA.- Bottom-up Approach to Complex Molecular Behaviors.- Aqueous Computing: Writing on Molecules Dissolved in Water.- Part VII: Computations Inspired by Cells: Turing Machines with Cells on the Tape.- Insights into a Biological Computer: Detangling Scrambled Genes of Ciliates.- Modeling Simple Operations for Gene Assembly.-

Aspects of Molecular Computing

P systems are parallel molecular computing models based on processing multisets of objects in cell-like membrane structures. In this paper we give membrane algorithms to solve the vertex cover problem and the clique problem in linear time with respect to the number of vertices and edges of the graph by recognizing P systems with active membranes using 2-division. Also, the linear time solution of the vertex cover problem is given using P systems with active membranes using 2-division and linear resources.

Languages of DNA Based Code Words

The set of all sequences that are generated by a biomolecular protocol forms a language over the four letter alphabet Δ={A,G,C,T}. This alphabet is associated with a natural involution mapping θ, A↦ T and G↦ C which is an antimorphism of Δ*. In order to avoid undesirable Watson-Crick bonds between the words (undesirable hybridization), the language has to satisfy certain coding properties. In this paper we build upon the study initiated in [11] and give necessary and sufficient conditions for a finite set of “good” code words to generate (through concatenation) an infinite set of “good” code words with the same properties. General methods for obtaining sets of “good” code words are described. Also we define properties of a splicing system such that the language generated by the system preserves the desired properties of code words.

Computation by Self-assembly of DNA Graphs

Using three dimensional graph structure and DNA self-assembly we show that theoretically 3-SAT and 3-colorability can be solved in a constant number of laboratory steps. In this assembly, junction molecules and duplex DNA molecules are the basic building blocks. The graphs involved are not necessarily regular, so experimental results of self-assembling non regular graphs using junction molecules as vertices and duplex DNA molecules as edge connections are presented.

Involution codes: with application to DNA coded languages

For an involution θ : Σ* → Σ* over a finite alphabet Σ we consider involution codes: θ-infix, θ-comma-free, θ-k -codes and θ-subword-k-codes. These codes arise from questions on DNA strand design. We investigate conditions under which both X and X+ are same type of involution codes. General methods for generating such involution codes are given. The information capacity of these codes show to be optimized in most cases. A specific set of these codes was chosen for experimental testing and the results of these experiments are presented.

Blueprints for dodecahedral DNA cages

Cage structures engineered from nucleic acids are of interest in nanotechnology, for example as a means of drug delivery (Destito et al 2007). Until now, most experimentally realized DNA cages have crystallographic symmetry, such as the shape of a cube (Chen and Seeman 1991 Nature 350 631?3), a tetrahedron (Goodman et al 2005 Science 310 1661?5), an octahedron (Shih et al 2004 Nature 427 618?21) or a truncated octahedron (Zhang and Seeman 1994 J. Am. Chem. Soc. 116 1661?9). Two examples of cages with non-crystallographic symmetry, a dodecahedron and a buckyball, have been realized recently (He et al 2008 Nature 452 198?201). A characteristic feature of these realizations is the fact that the cages are built from a number of identical building blocks called tiles: 20 for the case of the dodecahedron, and 60 for the case of the buckyball. We derive here a blueprint for the organization of nucleic acid in a dodecahedral cage such that the final product has a minimal number of strands. In particular, we show that a dodecahedral cage can be realized in terms of only two circular DNA molecules. We focus on the dodecahedral cage, because the volume to surface ratio of such a cage is larger than that of its crystallographic counterparts given the same fixed radial distance of the polyhedral vertices from the centre of the structure, whilst still requiring a smaller complexity than the truncated icosahedron (buckyball). We therefore expect that the dodecahedral DNA cages discussed here may be of interest in further applications in nanotechnology.

ACTIVE TILE SELF-ASSEMBLY, PART 1: UNIVERSALITY AT TEMPERATURE 1

We present an active tile assembly model which extends Winfrees abstract tile assembly model to tiles that are capable of transmitting and receiving binding site activation signals. We also prove that this model has universal computational power in 2D at temperature 1 by showing an active tile assembly construction that simulates one-dimensional cellular automata in 2D at temperature 1.

Boundary Components of Thickened Graphs

Using linear DNA segments and branched junction molecules many different three-dimensional DNA structures (graphs) could be self-assembled. We investigate maximum and minimum numbers of circular DNA that form these structures. For a given graph G, we consider compact orientable surfaces, called thickened graphs of G, that have G as a deformation retract. The number of boundary curves of a thickened graph G corresponds to the number of circular DNA strands that assemble into the graph G. We investigate how this number changes by recombinations or edge additions and relate to some results from topological graph theory.

A computational model for self-assembling flexible tiles

We present a theoretical model for self-assembling tiles with flexible branches motivated by DNA branched junction molecules. We encode an instance of a “problem” as a pot of such tiles, and a “solution” as an assembled complete complex without any free sticky ends (called ports), whose number of tiles is within predefined bounds. We develop an algebraic representation of this self-assembly process and use it to prove that this model of self-assembly precisely captures NP-computability when the number of tiles in the minimal complete complexes is bounded by a polynomial.