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

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the Chaos Game Representation (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene-coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent sub-periods in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration.;This work examines the model\u27s behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system information dynamics correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed

The Complexity and Viability of DNA Computations

In this paper we examine complexity issues in DNA computation. We believe that these issues are paramount in the search for so-called "killer applications", that is, applications of DNA computation that would establish the superiority of this paradigm over others in particular domains. An assured future for DNA computation can only be established through the discovery of such applications. We demonstrate that current measures of complexity fall short of reality. Consequently, we define a more realistic model, a so-called strong model of computation which provides better estimates of the resources required by DNA algorithms. We also compare the complexities of published algorithms within this new model and the weaker, extant model which is commonly (often implicitly) assumed. 1 Introduction Following the inital promise and enthusiastic response to Adleman's seminal work [1] in DNA computation, progress towards the realisation of worthwhile computations in the laboratory has become st..