Is DNA computing viable for 3-SAT problems?

AbstractAdleman reported how to solve a 7-vertex instance of the Hamiltonian path problem by means of DNA manipulations. After that a major goal of subsequent research is how to use DNA manipulations to solve NP-hard problems, especially 3-SAT problems. Lipton proposed DNA experiments on test tubes to solve 3-SAT problems. Liu et al. reported how to solve a simple case of 3-SAT using DNA computing on surfaces. Lipton's model of DNA computing is simple and intuitive for 3-SAT problems. The separate (or extract) operation, which is a key manipulation of DNA computing, only extracts some of the required DNA strands and Lipton thinks that a typical percentage might be 90. But it is unknown what would happen due to imperfect extract operation. Let p be the rate, where 0<p<1. Assume that for each distinct string s in a test tube, there are 10l (l=13 proposed by Adleman) copies of s and that extracting each of the required DNA strands is equally likely. Here, the present paper will report, no matter how large l is and no matter how close to 1 p is, there always exists a class of 3-SAT problems such that DNA computing error must occur. Therefore, DNA computing is not viable for 3-SAT

Whiplash PCR for O(1) Computing

This paper reviews the experimental technique of whiplash PCR, as introduced in Hagiya et al. (in press), and proposes a model of computation based on this technique in combination with assembly PCR (Stemmer et al. 1995). In this model, based on GOTO graphs, a number of NP-complete problems can be solved in O(1) biosteps, including branching program satisfiability, the independent set problem, and the Hamiltonian path problem. In addition, we propose a simple extension of the experimental technique that allows single DNA strands to simulate the execution of a feed-forward circuit, giving rise to a solution to the circuit satisfiability problem in O(1) biosteps

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

DNA Computation of Solutions to Edge-Matching Puzzles

The resilient, ancient, and fine-tuned DNA (deoxyribonucleic acid) has inspired many researchers to harness its power for material purposes. In this work, we use synthesized DNA strands to compute the solution to an instance of edge-matching puzzles (EMP), where the challenge is to pack a collection of edge-coloured square tiles on a square board such that all adjacent edges match in colour. We encode tiles with DNA strands and make use of structural, chemical and enzymatic properties of DNA to effectively carry out a brute-force search of the solution to the puzzle. The solution ultimately results as a 2-dimensional DNA lattice encoding the position and orientation of each tile on the solution board. Our approach has been to represent a tile as the union of two half-tiles. This conceptual representation allows for the use of a supremely powerful heuristic: polymerase chain reaction (PCR), which can be inserted at any step of the protocol to selectively amplify certain strands to exponential quantities. Our abstract formalization of half-tiles and the DNA protocol we use to manipulate them have relevance in three ways. First, by solving an instance of the (NP-Complete) EMP problem we make precise characterizations of the processing power of DNA Computing. Second, the 2- dimensional self-assembly of half-tiles is Turing-complete. Thirdly, the 2-dimensional self- assembly of half-tiles can serve as a PCR-powered model for massive nano-scale fabrication of 2- dimensional DNA nano-shapes