Marta Kasprzak

DNA sequencing with positive and negative errors.

The problem addressed in this paper is concerned with DNA sequencing by hybridization. An algorithm is proposed that solves a computational phase of this approach in the presence of both positive and negative errors resulting from the hybridization experiment. No a priori knowledge of the nature and source of these errors is required. An extensive set of computational experiments showed that the algorithm behaves surprisingly well if only positive errors appear. The general case, where positive and negative errors occur, can be also solved satisfactorily for an error rate up to 10%.

Complexity of DNA sequencing by hybridization

In the paper, the question of the complexity of the combinatorial part of the DNA sequencing by hybridization, is analyzed. Subproblems of the general problem, depending on the type of error (positive, negative), are distinguished. Since decision versions of the subproblems assuming only one type of error are trivial, complexities of the search counterparts are studied. Both search subproblems are proved to be strongly NP-hard, as well as their uniquely promised versions.

Tabu search for DNA sequencing with false negatives and false positives

Abstract The paper deals with the problem of DNA (deoxyribonucleic acid) sequencing by hybridization. A computational phase of this approach, i.e. a construction of a DNA sequence from oligonucleotides, is NP-hard in the strong sense in case of errors. Thus, since the last problem does not admit a polynomial time solution, a need arises to construct efficient heuristics solving the problem. In the paper, such a heuristic algorithm based on tabu search is proposed. Computational tests have proved its low complexity and high accuracy for both types of errors: false negatives and false positives.

Hybrid Genetic Algorithm for DNA Sequencing with Errors

In the paper, a new hybrid genetic algorithm solving the DNA sequencing problem with negative and positive errors is presented. The algorithm has as its input a set of oligonucleotides coming from a hybridization experiment. The aim is to reconstruct an original DNA sequence of a known length on the basis of this set. No additional information about the oligonucleotides nor about the errors is assumed. Despite that, the algorithm returns for computationally hard instances surprisingly good results, of a very high similarity to original sequences.

Construction of DNA restriction maps based on a simplified experiment

MOTIVATION A formulation of a new problem of the restriction map construction based on a simplified digestion experiment and a development of an algorithm for solving both ideal and noisy data cases of the introduced problem. RESULTS A simplified partial digest problem and a branch and cut algorithm for finding the solution of the problem.

Selected combinatorial problems of computational biology

Recently we observe a great breakthrough in biology connected with the studies on genomes. These achievements would be impossible without an input from other sciences, combinatorial optimization being one of them. This study is devoted to a presentation of the most important (to our opinion) area of the computational biology, mostly connected with DNA studies, where combinatorial optimization impact was clearly visible. They include: sequencing DNA chains, assembling them, genome mapping and sequence comparison.

DNA Sequencing--Tabu and Scatter Search Combined

In this paper, a tabu-search algorithm enhanced by scatter search is presented. The algorithm solves the DNA sequencing problem with negative and positive errors, yielding outcomes of high quality. We compare the new method with two other metaheuristic approaches: a previous tabu-search method and a hybrid genetic algorithm, and also with an old branch-and-bound approach.

On the recognition of de Bruijn graphs and their induced subgraphs

The directed de Bruijn graphs appear often as models in computer science, because of the useful properties these graphs have. Similarly, the induced subgraphs of these graphs have applications related to the sequencing of DNA chains. In this paper, we show that the directed de Bruijn graphs can be recognized in polynomial time. We also show that it is possible to recognize in polynomial time whether a given directed graph is an induced subgraph of some directed de Bruijn graph with given size of the labels. This result answers a question raised in a previous paper studying the properties of these induced subgraphs.

Sequencing by hybridization with isothermic oligonucleotide libraries

The problem addressed in this paper is concerned with DNA sequencing by hybridization. A new type of oligonucleotide libraries is proposed for hybridization experiments. The libraries consist of oligonucleotides of different length dependent on an oligonucleotide A(T) and C(G) content in such a way that an increment of C(G) is twice of that of A(T) and the sum of increments for each oligonucleotide is constant for a library. The latter is called an isothermic oligonucleotide library and the way of its construction will be presented. It will be shown that two such libraries that differ in their sums of increments by an A(T) increment are sufficient for DNA sequencing by hybridization. The hybridization experiment using isothermic oligonucleotide libraries should supply data with a lower number of errors due to the expected similarity of melting temperatures of oligonucleotide duplexes, thus, offering more stable conditions of the hybridization experiment. The combinatorial part of the general problem of DNA sequencing (allowing all kinds of errors) with isothermic libraries will be then formulated, and the ways of solving it will be shown. The general problem will be proved to be strongly NP-hard, but heuristic algorithms solving this problem are reported to have better computational features than those for standard libraries.

Tabu search algorithm for DNA sequencing by hybridization with isothermic libraries

In this paper, a problem of isothermic DNA sequencing by hybridization (SBH) is considered. In isothermic SBH a new type of oligonucleotide libraries is used. The library consists of oligonucleotides of different lengths depending on an oligonucleotide content. It is assumed that every oligonucleotide in such a library has an equal melting temperature. Each nucleotide adds its increment to the oligonucleotide temperature and it is assumed that A and T add 2 degrees C and C and G add 4 degrees C. The hybridization experiment using isothermic libraries should provide data with a lower number of errors due to an expected similarity of melting temperatures. From the computational point of view the problem of isothermic DNA sequencing with errors is hard, similarly like its classical counterpart. Hence, there is a need for developing heuristic algorithms that construct good suboptimal solutions. The aim of the paper is to propose a heuristic algorithm based on tabu search approach. The algorithm solves the problem with both positive and negative errors. Results of an extensive computational experiment are presented, which prove the high quality of the proposed method.