From the Publisher:
Although it originated as a method to study general dynamical systems, symbolic dynamics is useful in coding for data storage and transmission as well as in linear algebra. Requiring only a undergraduate knowledge of linear algebra, this first general textbook includes over 500 exercises.

An Introduction to Symbolic Dynamics and Coding

Artificial biochemical circuits are likely to play as large a role in biological engineering as electrical circuits have played in the engineering of electromechanical devices. Toward that end, nucleic acids provide a designable substrate for the regulation of biochemical reactions. However, it has been difficult to incorporate signal amplification components. We introduce a design strategy that allows a specified input oligonucleotide to catalyze the release of a specified output oligonucleotide, which in turn can serve as a catalyst for other reactions. This reaction, which is driven forward by the configurational entropy of the released molecule, provides an amplifying circuit element that is simple, fast, modular, composable, and robust. We have constructed and characterized several circuits that amplify nucleic acid signals, including a feedforward cascade with quadratic kinetics and a positive feedback circuit with exponential growth kinetics.

http://science.sciencemag.org/content/sci/318/5853/1121.full.pdf

Engineering entropy-driven reactions and networks catalyzed by DNA.

Nanotechnology: convergence with modern biology and medicine.

A device, system and method for molecular computing which not only includes a suitable, renewable power source, but actually is able to receive power through the performance of the computations themselves. The molecular computing machine of the present invention actually employs the free-energy difference between its input and output to accomplish a computation, preferably by using its input DNA molecule as a partial source of energy, or alternatively by using the input DNA molecule as the sole source of energy. This molecular finite automaton preferably transforms an input DNA molecule into an output DNA molecule by digesting the input as it computes.

Programmable and autonomous computing machine made of biomolecules

Summary form only given. Nucleic acids have proven to be remarkably versatile as an engineering material for chemical tasks including the storage of information, catalyzing reactions creating and breaking bonds, mechanical manipulation using molecular motors, and constructing supramolecular structures. This talk will focus particularly on molecular self-assembly, giving examples of engineered DNA "tiles" that crystallize into two-dimensional sheets, one-dimensional tubes and ribbons, and information-guided patterns such as a Sierpinski triangle and a binary counter. A theme is how cooperative binding can be used to control nucleation and direct selective tile attachment. Such "algorithmic" self-assembly may provide a bottom-up fabrication method for creating complex, well-defined supramolecular structures that can be used as scaffolds or templates for applications such as arranging molecular electronic components into active circuits

/pdf/algorithmic-self-assembly-of-dna-2wgck1v5s8.pdf

Algorithmic Self-Assembly of DNA

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.

Three dimensional DNA structures in computing.

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.-

Nanotechnology : science and computation

RNA-guided DNA assembly.

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.

Aspects of Molecular Computing

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.

Nataša Jonoska

Papers

Three dimensional DNA structures in computing.

Nanotechnology : science and computation

RNA-guided DNA assembly.

Aspects of Molecular Computing

Languages of DNA Based Code Words