On the Computational Power of DNA Annealing and Ligation

In [20] it was shown that the DNA primitives of Separate, Merge, and Amplify were not sufficiently powerful to invert functions defined by circuits in linear time. Dan Boneh et al [4] show that the addition of a ligation primitive, Append, provides the missing power. The question becomes, "How powerful is ligation? Are Separate, Merge, and Amplify necessary at all?" This paper proposes to informally explore the power of annealing and ligation for DNA computation. We conclude, in fact, that annealing and ligation alone are theoretically capable of universal computation

Protein-DNA computation by stochastic assembly cascade

The assembly of RecA on single-stranded DNA is measured and interpreted as a stochastic finite-state machine that is able to discriminate fine differences between sequences, a basic computational operation. RecA filaments efficiently scan DNA sequence through a cascade of random nucleation and disassembly events that is mechanistically similar to the dynamic instability of microtubules. This iterative cascade is a multistage kinetic proofreading process that amplifies minute differences, even a single base change. Our measurements suggest that this stochastic Turing-like machine can compute certain integral transforms.Comment: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC129313/ http://www.pnas.org/content/99/18/11589.abstrac

Experimental Progress in Computation by Self-Assembly of DNA Tilings

Approaches to DNA-based computing by self-assembly require the use of D. T A nanostructures, called tiles, that have efficient chemistries, expressive computational power: and convenient input and output (I/O) mechanisms. We have designed two new classes of DNA tiles: TAO and TAE, both of which contain three double-helices linked by strand exchange. Structural analysis of a TAO molecule has shown that the molecule assembles efficiently from its four component strands. Here we demonstrate a novel method for I/O whereby multiple tiles assemble around a single-stranded (input) scaffold strand. Computation by tiling theoretically results in the formation of structures that contain single-stranded (output) reported strands, which can then be isolated for subsequent steps of computation if necessary. We illustrate the advantages of TAO and TAE designs by detailing two examples of massively parallel arithmetic: construction of complete XOR and addition tables by linear assemblies of DNA tiles. The three helix structures provide flexibility for topological routing of strands in the computation: allowing the implementation of string tile models

Algorithmic Self-Assembly of DNA: Theoretical Motivations and 2D Assembly Experiments

Biology makes things far smaller and more complex than anything produced by human engineering. The biotechnology revolution has for the first time given us the tools necessary to consider engineering on the molecular level. Research in DNA computation, launched by Len Adleman, has opened the door for experimental study of programmable biochemical reactions. Here we focus on a single biochemical mechanism, the self-assembly of DNA structures, that is theoretically sufficient for Turing-universal computation. The theory combines Hao Wang?s purely mathematical Tiling Problem with the branched DNA constructions of Ned Seeman. In the context of mathematical logic, Wang showed how jigsaw-shaped tiles can be designed to simulate the operation of any Turing Machine. For a biochemical implementation, we will need molecular Wang tiles. DNA molecular structures and intermolecular interactions are particularly amenable to design and are sufficient for the creation of complex molecular objects. The structure of individual molecules can be designed by maximizing desired and minimizing undesired Watson-Crick complementarity. Intermolecular interactions are programmed by the design of sticky ends that determine which molecules associate, and how. The theory has been demonstrated experimentally using a system of synthetic DNA double-crossover molecules that self-assemble into two-dimensional crystals that have been visualized by atomic force microscopy. This experimental system provides an excellent platform for exploring the relationship between computation and molecular self-assembly, and thus represents a first step toward the ability to program molecular reactions and molecular structures

A Mathematical Formulation of DNA Computation

DNA computation is to use DNA molecules for information storing and processing. The task is accomplished by encoding and interpreting DNA molecules in suspended solutions before and after the complementary binding reactions. DNA computation is attractive, due to its fast parallel information processing, remarkable energy efficiency, and high storing capacity. Challenges currently faced by DNA computation are (1) lack of theoretical computational models for applications, and (2) high error rate for implementation. This paper attempts to address these problems from mathematical modeling and genetic coding aspects. The first part of this paper presents a mathematical formulation of DNA computation. The model may serve as a theoretical framework for DNA computation. In the second part, a genetic code based DNA computation approach is presented to reduce error rate for implementation, which has been a major concern for DNA computation. The method provides a promising alternative to reduce error rate for DNA computation

DNA Computation Based Approach for Enhanced Computing Power

DNA computing is a discipline that aims at harnessing individual molecules at the nano-scopic level for computational purposes. Computation with DNA molecules possesses an inherent interest for researchers in computers and biology. Given its vast parallelism and high-density storage, DNA computing approaches are employed to solve many problems. DNA has also been explored as an excellent material and a fundamental building block for building large-scale nanostructures, constructing individual nano-mechanical devices, and performing computations. Molecular-scale autonomous programmable computers are demonstrated allowing both input and output information to be in molecular form. This paper presents a review of recent advancements in DNA computing and presents major achievements and challenges for researchers in the coming future

A Pseudo DNA Cryptography Method

The DNA cryptography is a new and very promising direction in cryptography research. DNA can be used in cryptography for storing and transmitting the information, as well as for computation. Although in its primitive stage, DNA cryptography is shown to be very effective. Currently, several DNA computing algorithms are proposed for quite some cryptography, cryptanalysis and steganography problems, and they are very powerful in these areas. However, the use of the DNA as a means of cryptography has high tech lab requirements and computational limitations, as well as the labor intensive extrapolation means so far. These make the efficient use of DNA cryptography difficult in the security world now. Therefore, more theoretical analysis should be performed before its real applications. In this project, We do not intended to utilize real DNA to perform the cryptography process; rather, We will introduce a new cryptography method based on central dogma of molecular biology. Since this method simulates some critical processes in central dogma, it is a pseudo DNA cryptography method. The theoretical analysis and experiments show this method to be efficient in computation, storage and transmission; and it is very powerful against certain attacks. Thus, this method can be of many uses in cryptography, such as an enhancement insecurity and speed to the other cryptography methods. There are also extensions and variations to this method, which have enhanced security, effectiveness and applicability.Comment: A small work that quite some people asked abou

DNA computation

This is the first ever doctoral thesis in the field of DNA computation. The field has its roots in the late 1950s, when the Nobel laureate Richard Feynman first introduced the concept of computing at a molecular level. Feynman's visionary idea was only realised in 1994, when Leonard Adleman performed the first ever truly molecular-level computation using DNA combined with the tools and techniques of molecular biology. Since Adleman reported the results of his seminal experiment, there has been a flurry of interest in the idea of using DNA to perform computations. The potential benefits of using this particular molecule are enormous: by harnessing the massive inherent parallelism of performing concurrent operations on trillions of strands, we may one day be able to compress the power of today's supercomputer into a single test tube. However, if we compare the development of DNA-based computers to that of their silicon counterparts, it is clear that molecular computers are still in their infancy. Current work in this area is concerned mainly with abstract models of computation and simple proof-of-principle experiments. The goal of this thesis is to present our contribution to the field, placing it in the context of the existing body of work. Our new results concern a general model of DNA computation, an error-resistant implementation of the model, experimental investigation of the implementation and an assessment of the complexity and viability of DNA computations. We begin by recounting the historical background to the search for the structure of DNA. By providing a detailed description of this molecule and the operations we may perform on it, we lay down the foundations for subsequent chapters. We then describe the basic models of DNA computation that have been proposed to date. In particular, we describe our parallel filtering model, which is the first to provide a general framework for the elegant expression of algorithms for NP-complete problems. The implementation of such abstract models is crucial to their success. Previous experiments that have been carried out suffer from their reliance on various error-prone laboratory techniques. We show for the first time how one particular operation, hybridisation extraction, may be replaced by an error-resistant enzymatic separation technique. We also describe a novel solution read-out procedure that utilizes cloning, and is sufficiently general to allow it to be used in any experimental implementation. The results of preliminary tests of these techniques are then reported. Several important conclusions are to be drawn from these investigations, and we report these in the hope that they will provide useful experimental guidance in the future. The final contribution of this thesis is a rigorous consideration of the complexity and viability of DNA computations. We argue that existing analyses of models of DNA computation are flawed and unrealistic. In order to obtain more realistic measures of the time and space complexity of DNA computations we describe a new strong model, and reassess previously described algorithms within it. We review the search for "killer applications": applications of DNA computing that will establish the superiority of this paradigm within a certain domain. We conclude the thesis with a description of several open problems in the field of DNA computation