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Computation 2015, 3(2), 285-298; doi:10.3390/computation3020285

Computational Recognition of RNA Splice Sites by Exact Algorithms for the Quadratic Traveling Salesman Problem

1
Department of Mathematics, TU Dortmund, D-44227 Dortmund, Germany
2
Institute of Mathematics, University of Kassel, D-34132 Kassel, Germany
3
Department of Mathematics and Mathematical Statistics, University of Umeå, S-90187 Umeå, Sweden
4
Institute for Biosafety in Plant Biotechnology, Julius Kühn-Institut, D-06484 Quedlinburg, Germany
5
Institute of Computer Science and Universitätszentrum Informatik, Martin Luther University Halle-Wittenberg, D-06120 Halle, Germany
6
German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, D-04103 Leipzig, Germany
*
Author to whom correspondence should be addressed.
Academic Editors: Marnix Medema and Rainer Breitling
Received: 3 December 2014 / Revised: 16 April 2015 / Accepted: 12 May 2015 / Published: 3 June 2015
(This article belongs to the Special Issue Genomes and Evolution: Computational Approaches)
View Full-Text   |   Download PDF [249 KB, uploaded 5 June 2015]   |  

Abstract

One fundamental problem of bioinformatics is the computational recognition of DNA and RNA binding sites. Given a set of short DNA or RNA sequences of equal length such as transcription factor binding sites or RNA splice sites, the task is to learn a pattern from this set that allows the recognition of similar sites in another set of DNA or RNA sequences. Permuted Markov (PM) models and permuted variable length Markov (PVLM) models are two powerful models for this task, but the problem of finding an optimal PM model or PVLM model is NP-hard. While the problem of finding an optimal PM model or PVLM model of order one is equivalent to the traveling salesman problem (TSP), the problem of finding an optimal PM model or PVLM model of order two is equivalent to the quadratic TSP (QTSP). Several exact algorithms exist for solving the QTSP, but it is unclear if these algorithms are capable of solving QTSP instances resulting from RNA splice sites of at least 150 base pairs in a reasonable time frame. Here, we investigate the performance of three exact algorithms for solving the QTSP for ten datasets of splice acceptor sites and splice donor sites of five different species and find that one of these algorithms is capable of solving QTSP instances of up to 200 base pairs with a running time of less than two days. View Full-Text
Keywords: splice site; permuted Markov model; permuted variable length Markov model; quadratic traveling salesman problem; combinatorial optimization; dynamic programming; branch and bound; branch and cut; integer linear programming splice site; permuted Markov model; permuted variable length Markov model; quadratic traveling salesman problem; combinatorial optimization; dynamic programming; branch and bound; branch and cut; integer linear programming
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Fischer, A.; Fischer, F.; Jäger, G.; Keilwagen, J.; Molitor, P.; Grosse, I. Computational Recognition of RNA Splice Sites by Exact Algorithms for the Quadratic Traveling Salesman Problem. Computation 2015, 3, 285-298.

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