The DNA sequence in every human being is a text of three billion characters from a four letter alphabet; determining this sequence is a major project in molecular biology. The fundamental task biologists face is to reconstruct a long sequence given short fragments from unknown locations. These fragments contain errors, and may represent the sequence on one strand of the double-helix, or the reverse complement sequence on the other strand. The Sequence Reconstruction Problem is, given a collection F of fragment sequences and an error rate 0 ≤ ε < 1, find a shortest sequence S such that every fragment F ∈ F, or its reverse complement, matches a substring of S with at most ε|F| errors. Sequence Reconstruction is NP-complete. We decompose the problem into (1) constructing a graph of approximate overlaps between pairs of fragments, (2) selecting a set of overlaps of maximum total weight that induce a consistent layout of the fragments, (3) merging the overlaps into a multiple sequence alignment and voting on a consensus. A solution to (1) through (3) yields a reconstructed sequence feasible at error rate 2ε/(1-ε) and at most a factor 1/1-ε longer than the shortest reconstruction, given some assumptions on fragment error. We define a measure of the overlap in a reconstruction, show that maximizing the overlap minimizes the length, and that approximating (2) within a factor of α approximates Sequence Reconstruction within a factor of (1- ε)α under the overlap measure. We construct the overlap graph for (1) in O(εN²) time given fragments of total length N at error rate ε. We develop two exact and two approximation algorithms for (2). Our best exact algorithm computes an optimal layout for a graph of E overlaps and V fragments in O(K(E + V log V)) time, where K ≤ 2ᴱ is the size of the branch-and-bound search tree. Our best approximation algorithm computes a layout with overlap at least 1/2 the maximum in O(V(E + V log V)log V) time. This is the first treatment of Sequence Reconstruction with inexact data and unknown complementarity.

published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

The rapid developments in the field of DNA computing reflects two substantial questions: 1. Which models for DNA based computation are really universal? 2. Which model fulfills the requirements to a universal lab-practicable programmable DNA computer that is based on one of these models? This paper introduces the functional model DNA-HASKELL focussing its lab-practicability. This aim could be reached by specifying the DNA based operations in accordiance to an analysis of molecular biological processes. The specification is determined by an abstraction level that includes nucleotides and strand end labels like 5'-phosphate. Our model is able to describe DNA algorithms for any NP-complete problem - here exemplified by the knapsacik problem - as well as it is able to simulate some established mathematical models for computation. We point out the splicing operation as an example. The computational completeness of DNA-HASKELL can be supposed. This paper is based on discussions about the potenzial and limits of DNA computing, in particular the practicability of a universal DNA computer.

The rapid developments in the field of DNA computing reflects two substantial questions: 1. Which models for DNA based computation are really universal? 2. Which model fulfills the requirements to a universal lab-practicable programmable DNA computer that is based on one of these models? This paper introduces the functional model DNA-HASKELL focussing its lab-practicability. This aim could be reached by specifying the DNA based operations in accordiance to an analysis of molecular biological processes. The specification is determined by an abstraction level that includes nucleotides and strand end labels like 5'-phosphate. Our model is able to describe DNA algorithms for any NP-complete problem - here exemplified by the knapsacik problem - as well as it is able to simulate some established mathematical models for computation. We point out the splicing operation as an example. The computational completeness of DNA-HASKELL can be supposed. This paper is based on discussions about the potenzial and limits of DNA computing, in particular the practicability of a universal DNA computer.